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1
Mani Aouadi, S., W. Mbarki und N. Zemzemi. „Stability Analysis of Decoupled Time-stepping Schemes for the Specialized Conduction System/myocardium Coupled Problem in Cardiology“. Mathematical Modelling of Natural Phenomena 12, Nr. 5 (2017): 208–39. http://dx.doi.org/10.1051/mmnp/201712513.
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The Purkinje network is the rapid conduction system in the heart. It ensures the physiological spread of the electrical wave in the ventricles. In this work, we consider a problem that models the coupling between the Purkinje network and the myocardium. We first prove the stability of the space semi-discretized problem. Then we present four different strategies for solving the Purkinje/ myocardium coupling. The strategies are based on different time discretization of the coupling terms. The first scheme is fully coupled, where the coupling terms are considered implicit. The second and the third schemes are based on Gauss-Seidel time-splitting schemes where one coupling term is considered explicit and the other is implicit. The last is a Jacobi-like time-splitting scheme where both coupling terms are considered explicit. Our main result is the proof of the stability of the three considered schemes under the same restriction on the time step. Moreover, we show that the energy of the problem is slightly affected by the time-splitting schemes. We illustrate the theoretical result by different numerical simulations in 2D. We also conduct 3D simulations using physiologically detailed ionic models.
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Miller, Scott T., Gregory Bunting und Nicholas A. Reynolds. „Numerical investigation of coupling schemes for structural acoustics“. Journal of the Acoustical Society of America 143, Nr. 3 (März 2018): 1717. http://dx.doi.org/10.1121/1.5035592.
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Best, M. J., A. Beljaars, J. Polcher und P. Viterbo. „A Proposed Structure for Coupling Tiled Surfaces with the Planetary Boundary Layer“. Journal of Hydrometeorology 5, Nr. 6 (01.12.2004): 1271–78. http://dx.doi.org/10.1175/jhm-382.1.
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Abstract A generalized coupling is proposed between atmospheric models and surface schemes (land and ocean). A set of input and output variables is defined for this purpose in such a way that it can be used by many current and future models, including mosaic or tile schemes. The basic concept is to pass atmospheric variables from the lowest model level and their relation to corresponding fluxes to the surface scheme. The surface scheme returns the fluxes. In this framework, there is no need for the atmospheric model to have detailed information about the surface. Only the result of the surface computations is needed; namely, the fluxes, which are applied as a boundary condition. The equations for fully implicit coupling are derived, and the relevance for numerical stability is demonstrated. It is also shown that fully implicit coupling in a tile scheme leads to more robust results than partially implicit coupling.
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Tang, Jinyun, und William J. Riley. „Predicted Land Carbon Dynamics Are Strongly Dependent on the Numerical Coupling of Nitrogen Mobilizing and Immobilizing Processes: A Demonstration with the E3SM Land Model“. Earth Interactions 22, Nr. 11 (01.05.2018): 1–18. http://dx.doi.org/10.1175/ei-d-17-0023.1.
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AbstractWhile coupling carbon and nitrogen processes is critical for Earth system models to accurately predict future climate and land biogeochemistry feedbacks, it has not yet been analyzed how numerical methods that land biogeochemical models apply to couple soil mineral nitrogen mobilizing and immobilizing processes affect predicted ecosystem carbon and nitrogen cycling. These effects were investigated here by using the E3SM land model and an evaluation of three plausible and widely used numerical couplings: 1) the mineral nitrogen–based limitation scheme, 2) the net uptake–based limitation scheme, and 3) the proportional nitrogen flux–based limitation scheme. It was found that these three schemes resulted in large differences (with a range of 316 PgC) in predicted cumulative land–atmosphere carbon exchanges under the RCP4.5 atmospheric CO2 simulations. This large uncertainty is without accounting for the different representations of the many land biogeochemical processes, but is about 73% of the range (434 PgC) reported for CMIP5 RCP4.5 simulations. These results help explain the large uncertainty found in various model intercomparison experiments and suggest that more robust numerical implementations are needed to improve carbon–nutrient cycle coupling in terrestrial ecosystem models.
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Regazzoni, Francesco. „Stabilization of loosely coupled schemes for 0D–3D fluid–structure interaction problems with application to cardiovascular modelling“. Numerische Mathematik 157, Nr. 1 (25.01.2025): 249–306. https://doi.org/10.1007/s00211-025-01452-z.
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Abstract In this paper we analyze the numerical oscillations affecting loosely coupled schemes for hybrid-dimensional 0D–3D fluid–structure interaction (FSI) problems, which arise e.g. in the field of cardiovascular modeling, and we propose a novel stabilized scheme that cures this issue. We study several loosely coupled schemes, including the Dirichlet–Neumann (DN) and Neumann–Dirichlet (ND) schemes. In the first one, the 0D fluid model prescribes the pressure to the 3D structural mechanics model and receives the flow. In the second one, on the contrary, the fluid model receives the pressure and prescribes the flow. The terms DN and ND, employed in the FSI literature, are borrowed from domain decomposition methods, although here a single iteration is performed before moving on to the next time step (that is, the coupling is treated explicitly). Should the fluid be enclosed in a cavity, the DN scheme is affected by non-physical oscillations whose origin lies in the balloon dilemma, for which we provide an algebraic interpretation. Moreover, we show that also the ND scheme can be unstable for a range of parameter choices. Surprisingly, increasing either the viscous dissipation or the inertia of the structure favours the onset of oscillations and, for certain parameter choices, the ND is unconditionally unstable. In the presence of inertial terms, by reducing the time step size below a certain threshold, the amplitude of the numerical oscillations is even amplified. We provide an explanation for these facts and establish sharp stability bounds on the time step size. Our analysis extends to Robin–Robin schemes, based on linear combinations of the conditions of pressure continuity and either volume or flux continuity. While appropriate choices of Robin coefficients can achieve numerical stability, tuning these coefficients can be challenging in practice. To address these issues, we propose a numerically consistent stabilization term for the Neumann–Dirichlet scheme, inspired by physical insight on the onset of oscillations. We prove that our proposed stabilized scheme is absolutely stable for any choice of time step size. Notably, the proposed scheme does not require parameter tuning. These results are verified by several numerical tests. Finally, we apply the proposed stabilized scheme to an important problem in cardiac electromechanics, namely the coupling between a 3D cardiac model and a closed-loop lumped-parameter model of blood circulation. In this setting, our proposed scheme successfully removes the non-physical oscillations that would otherwise affect the numerical solution.
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Banda, Mapundi K., Axel-Stefan Häck und Michael Herty. „Numerical Discretization of Coupling Conditions by High-Order Schemes“. Journal of Scientific Computing 69, Nr. 1 (18.04.2016): 122–45. http://dx.doi.org/10.1007/s10915-016-0185-x.
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QI, GUANXIAO, HONGBIN HUANG und HAIJUN WANG. „SIZE INSTABILITIES IN THE RING AND LINEAR ARRAYS OF CHAOTIC SYSTEMS“. Advances in Complex Systems 10, Nr. 03 (September 2007): 301–13. http://dx.doi.org/10.1142/s0219525907001185.
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We investigate the dynamical stabilities of ring and linear arrays of chaotic oscillators with asymmetric nearest-neighbor and long-range couplings. It is shown that the instabilities of complete chaotic synchronization occur as the numbers of oscillators are increased beyond critical values which depend on the coupling schemes and coupling parameters of the systems. Based on the master stability function and eigenvalue analysis methods, we give the semi-analytical relations between the critical values and the coupling parameters. Results are demonstrated with numerical simulations in a set of coupled Lorenz oscillators.
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An, Xingwei, Tonghui Deng, Lei Chen, Saiyun Ye und Zhirong Zhong. „Generation of Schrödinger Cat States in a Hybrid Cavity Optomechanical System“. Entropy 24, Nr. 11 (29.10.2022): 1554. http://dx.doi.org/10.3390/e24111554.
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We present an alternative scheme to achieve Schrödinger cat states in a strong coupling hybrid cavity optomechanical system. Under the single-photon strong-coupling regime, the interaction between the atom–cavity–oscillator system can induce the mesoscopic mechanical oscillator to Schrödinger cat states. Comparing to previous schemes, the proposed proposal consider the second order approximation on the Lamb–Dicke parameter, which is more universal in the experiment. Numerical simulations confirm the validity of our derivation.
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Ketata, Ahmed, Zied Driss und Mohamed Salah Abid. „1D gas dynamic code for performance prediction of one turbocharger radial turbine with different finite difference schemes“. Mechanics & Industry 20, Nr. 6 (2019): 627. http://dx.doi.org/10.1051/meca/2019073.
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The turbine, a key component of a turbocharger, is usually characterized by steady flow solutions. This method seems to be physically unrealistic as the fluid flow within a turbine is strongly unsteady due to the pulsating nature of the flow in the exhaust manifold of a reciprocating engine. This paper presents a new 1D gas dynamic code, written in the FORTRAN language, to characterize a radial turbine of one turbocharger embedded to a small gasoline engine. This code presents the novelty of meanline-1D coupling and the feature of numerical schemes choice. In this study, the turbocharger turbine is simulated with six different finite difference schemes. The computed distribution of the downstream mass flow rate, from the different cases, is compared to test data in order to choose the most suitable scheme. Test data are gathered from a developed test facility. Based on the computed results, unsteady performance of the turbine has been computed and discussed for the different schemes at two engine frequencies of 50 and 83.33 Hz. The results showed a significant impact of the numerical scheme on the 1D prediction of the turbine performance. Results indicated that the MR2LW finite-difference scheme has led to the minimum deviation of the numerical results to test data compared to the other considered schemes.
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Bishop, Michael P., Brennan W. Young und Jeffrey D. Colby. „Numerical Modeling and Parameter Sensitivity Analysis for Understanding Scale-Dependent Topographic Effects Governing Anisotropic Reflectance Correction of Satellite Imagery“. Remote Sensing 14, Nr. 21 (25.10.2022): 5339. http://dx.doi.org/10.3390/rs14215339.
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Anisotropic reflectance correction (ARC) of satellite imagery is required to remove multi-scale topographic effects in imagery. Commonly utilized ARC approaches have not effectively accounted for atmosphere-topographic coupling. Furthermore, it is not clear which topographic effects need to be formally accounted for. Consequently, we simulate the direct and diffuse-skylight irradiance components and formally account for multi-scale topographic effects. A sensitivity analysis was used to determine if characterization schemes can account for a collective treatment of effects, using our parameterization scheme as a basis for comparison. We found that commonly used assumptions could not account for topographic modulation in our simulations. We also found that the use of isotropic diffuse irradiance and a topographic shielding parameter also failed to characterize topographic modulation. Our results reveal that topographic effects govern irradiance variations in a synergistic way, and that issues of ARC need to be formally addressed given atmosphere-topography coupling. Collectively, our results suggest that empirical ARC methods cannot be used to effectively address topographic effects, given inadequate parameterization schemes. Characterizing and removing spectral variation from multispectral imagery will most likely require numerical modeling efforts. More research is warranted to develop/evaluate parameterization schemes that better characterize the anisotropic nature of atmosphere-topography coupling.
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Gnanadesikan, Anand. „Numerical issues for coupling biological models with isopycnal mixing schemes“. Ocean Modelling 1, Nr. 1 (Januar 1999): 1–15. http://dx.doi.org/10.1016/s1463-5003(99)00002-5.
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Luskin, Mitchell, und Christoph Ortner. „Atomistic-to-continuum coupling“. Acta Numerica 22 (02.04.2013): 397–508. http://dx.doi.org/10.1017/s0962492913000068.
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Atomistic-to-continuum (a/c) coupling methods are a class of computational multiscale schemes that combine the accuracy of atomistic models with the efficiency of continuum elasticity. They are increasingly being utilized in materials science to study the fundamental mechanisms of material failure such as crack propagation and plasticity, which are governed by the interaction between crystal defects and long-range elastic fields.In the construction of a/c coupling methods, various approximation errors are committed. A rigorous numerical analysis approach that classifies and quantifies these errors can give confidence in the simulation results, as well as enable optimization of the numerical methods for accuracy and computational cost. In this article, we present such a numerical analysis framework, which is inspired by recent research activity.
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LI, CHANGPIN, und WEIHUA DENG. „CHAOS SYNCHRONIZATION OF FRACTIONAL-ORDER DIFFERENTIAL SYSTEMS“. International Journal of Modern Physics B 20, Nr. 07 (20.03.2006): 791–803. http://dx.doi.org/10.1142/s0217979206033620.
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Chaos synchronization of the Duffing, Lorenz and Rössler systems with fractional orders are studied theoretically and numerically. Three methods are applied in this paper: combination of active-passive decomposition (APD) and one-way coupling methods, Pecora–Carroll method, bidirectional coupling method. The sufficient conditions of achieving synchronization between two identical fractional systems are derived by using the Laplace transform theory. Numerical simulations demonstrate the effectiveness of the proposed synchronization schemes for these fractional systems.
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Liu, Shan, Deng Ke Tong und Shu Heng Tang. „Research on Optimization of Perforated Horizontal Wells with Separated Production Scheme Based on Genetic Algorithm“. Advanced Materials Research 1044-1045 (Oktober 2014): 495–502. http://dx.doi.org/10.4028/www.scientific.net/amr.1044-1045.495.
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Based on the separated production scheme of perforated horizontal well, the production is closely related to the number, length and location of horizontal intervals. New reservoir / wellbore coupling models were modeled which included two boundaries: closed boundary and constant pressure boundary. For these coupling models, two new optimization models were modeled, which took the production as the objective function and took the length and location of horizontal intervals as the optimization variables. Then the numerical calculation models were proposed by using the Gauss-Laguerre quadrature formula. Applying the genetic algorithm and writing the numerical stimulation software, the optimized schemes with 2 segments, 3 segments and 4 segments for planning intervals of the perforated horizontal wells were presented. By comparing the optimized schemes, we can see that the horizontal well production was not infinite increasing with the length of horizontal intervals, but only in the suitable length of horizontal intervals to maintain high production. And it is not the more segments the higher production. For the perforated horizontal well in closed reservoir, the production was the highest based on the optimized schemes with 3 segments.
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Rahikainen, Jarkko, Francisco González, Miguel Ángel Naya, Jussi Sopanen und Aki Mikkola. „On the cosimulation of multibody systems and hydraulic dynamics“. Multibody System Dynamics 50, Nr. 2 (10.02.2020): 143–67. http://dx.doi.org/10.1007/s11044-020-09727-z.
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Abstract The simulation of mechanical devices using multibody system dynamics (MBS) algorithms frequently requires the consideration of their interaction with components of a different physical nature, such as electronics, hydraulics, or thermodynamics. An increasingly popular way to perform this task is through co-simulation, that is, assigning a tailored formulation and solver to each subsystem in the application under study and then coupling their integration processes via the discrete-time exchange of coupling variables during runtime. Co-simulation makes it possible to deal with complex engineering applications in a modular and effective way. On the other hand, subsystem coupling can be carried out in a wide variety of ways, which brings about the need to select appropriate coupling schemes and simulation options to ensure that the numerical integration remains stable and accurate. In this work, the co-simulation of hydraulically actuated mechanical systems via noniterative, Jacobi-scheme co-simulation is addressed. The effect of selecting different co-simulation configuration options and parameters on the accuracy and stability of the numerical integration was assessed by means of representative numerical examples.
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Wong, Kelvin K. L., Pongpat Thavornpattanapong, Sherman C. P. Cheung und Jiyuan Tu. „Numerical Stability of Partitioned Approach in Fluid-Structure Interaction for a Deformable Thin-Walled Vessel“. Computational and Mathematical Methods in Medicine 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/638519.
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Added-mass instability is known to be an important issue in the partitioned approach for fluid-structure interaction (FSI) solvers. Despite the implementation of the implicit approach, convergence of solution can be difficult to achieve. Relaxation may be applied to improve this implicitness of the partitioned algorithm, but this commonly leads to a significant increase in computational time. This is because the critical relaxation factor that allows stability of the coupling tends to be impractically small. In this study, a mathematical analysis for optimizing numerical performance based on different time integration schemes that pertain to both the fluid and solid accelerations is presented. The aim is to determine the most efficient configuration for the FSI architecture. Both theoretical and numerical results suggest that the choice of time integration schemes has a significant influence on the stability of FSI coupling. This concludes that, in addition to material and its geometric properties, the choice of time integration schemes is important in determining the stability of the numerical computation. A proper selection of the associated parameters can improve performance considerably by influencing the condition of coupling stability.
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LALLEMAND, PIERRE, und LI-SHI LUO. „HYBRID FINITE-DIFFERENCE THERMAL LATTICE BOLTZMANN EQUATION“. International Journal of Modern Physics B 17, Nr. 01n02 (20.01.2003): 41–47. http://dx.doi.org/10.1142/s0217979203017060.
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We analyze the acoustic and thermal properties of athermal and thermal lattice Boltzmann equation (LBE) in 2D and show that the numerical instability in the thermal lattice Boltzmann equation (TLBE) is related to the algebraic coupling among different modes of the linearized evolution operator. We propose a hybrid finite-difference (FD) thermal lattice Boltzmann equation (TLBE). The hybrid FD-TLBE scheme is far superior over the existing thermal LBE schemes in terms of numerical stability. We point out that the lattice BGK equation is incompatible with the multiple relaxation time model.
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Stavre, Ruxandra, und Alexandra Ciorogar. „Influence of a Given Field of Temperature on the Blood Pressure Variation: Variational Analysis, Numerical Algorithms and Simulations“. Axioms 14, Nr. 2 (25.01.2025): 88. https://doi.org/10.3390/axioms14020088.
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This article presents a fluid–elastic structure interaction (FSI) problem when the temperature variation of the two media is also taken into account. We introduced the mathematical description of this interaction in a recent article. Our model includes the coupling between the fluid and the elastic medium equations and, in addition, the coupling with the temperature equations. The novelty of this approach is that we succeed in analyzing a complicated double-coupled problem that allows us to describe more complex physical phenomena both from the theoretical and numerical points of view. Since the main goal of this article is to analyze the influence of an exterior field of temperature on fluid pressure variations, the theoretical results obtained in our previous article are completed with qualitative properties concerning the fluid pressure, such as existence, regularity and uniqueness. Our study continues with approximation schemes: in order to improve the unknowns regularity, we introduce the pressure approximation by a sequence of viscoelastic pressure functions and we prove the weak convergence of this sequence to the pressure; then, we present a numerical approximation scheme with stability and convergence results and Uzawa’s algorithm. The last part of the article is devoted to numerical simulations that rely on the numerical schemes introduced and studied before and highlight some physical phenomena related to the considered problem.
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KUMAR, RAJESH, JITENDRA KUMAR und GERALD WARNECKE. „MOMENT PRESERVING FINITE VOLUME SCHEMES FOR SOLVING POPULATION BALANCE EQUATIONS INCORPORATING AGGREGATION, BREAKAGE, GROWTH AND SOURCE TERMS“. Mathematical Models and Methods in Applied Sciences 23, Nr. 07 (02.04.2013): 1235–73. http://dx.doi.org/10.1142/s0218202513500085.
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In this work we present some moment preserving finite volume schemes (FVS) for solving population balance equations. We are considering unified numerical methods to simultaneous aggregation, breakage, growth and source terms, e.g. for nucleation. The criteria for the preservation of different moments are given. The property of conservation is a special case of preservation. First we present a FVS which shows the preservation with respect to one-moment depending upon the processes under consideration. In case of the aggregation and breakage it satisfies first-moment preservation whereas for the growth and nucleation we observe zeroth-moment preservation. This is due to the well-known property of conservativity of FVS. However, coupling of all the processes shows no preservation for any moments. To overcome this issue, we reformulate the cell average technique into a conservative formulation which is coupled together with a modified upwind scheme to give moment preservation with respect to the first two-moments for all four processes under consideration. This allows for easy coupling of these processes. The preservation is proven mathematically and verified numerically. The numerical results for the first two-moments are verified for various coupled processes where analytical solutions are available.
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Siewe, R. Thepi, U. Simo Domguia und P. Woafo. „Microcontroller Control/Synchronization of the Dynamics of Van der Pol Oscillators Submitted to Disturbances“. International Journal of Nonlinear Sciences and Numerical Simulation 19, Nr. 2 (25.04.2018): 153–63. http://dx.doi.org/10.1515/ijnsns-2017-0025.
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AbstractIn this article, we present a microcontroller implementation of the synchronization of two Van der Pol oscillators submitted to disturbances of the pulse-like type. Three coupling schemes are used: the classical linear proportional coupling, a power order coupling and an adaptive coupling. After obtaining the coupling coefficients for synchronization through numerical simulation, the microcontroller implementation is carried out using simulation based on Euler algorithm. Agreement is found between both simulation strategies.
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Schukmann, Alexander, Andreas Schneider, Viktor Haas und Martin Böhle. „Analysis of Hierarchical Grid Refinement Techniques for the Lattice Boltzmann Method by Numerical Experiments“. Fluids 8, Nr. 3 (21.03.2023): 103. http://dx.doi.org/10.3390/fluids8030103.
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Over the last few decades, several grid coupling techniques for hierarchically refined Cartesian grids have been developed to provide the possibility of varying mesh resolution in lattice Boltzmann methods. The proposed schemes can be roughly categorized based on the individual grid transition interface layout they are adapted to, namely cell-vertex or cell-centered approaches, as well as a combination of both. It stands to reason that the specific properties of each of these grid-coupling algorithms influence the stability and accuracy of the numerical scheme. Consequently, this naturally leads to a curiosity regarding the extent to which this is the case. The present study compares three established grid-coupling techniques regarding their stability ranges by conducting a series of numerical experiments for a square duct flow, including various collision models. Furthermore the hybrid-recursive regularized collision model, originally introduced for cell-vertex algorithms with co-located coarse and fine grid nodes, has been adapted to cell-centered and combined methods.
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Borsche, R., J. Kall, A. Klar und T. N. H. Pham. „Kinetic and related macroscopic models for chemotaxis on networks“. Mathematical Models and Methods in Applied Sciences 26, Nr. 06 (12.04.2016): 1219–42. http://dx.doi.org/10.1142/s0218202516500299.
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In this paper we consider kinetic and associated macroscopic models for chemotaxis on a network. Coupling conditions at the nodes of the network for the kinetic problem are presented and used to derive coupling conditions for the macroscopic approximations. The results of the different models are compared and relations to a Keller–Segel model on networks are discussed. For a numerical approximation of the governing equations asymptotic preserving relaxation schemes are extended to directed graphs. Kinetic and macroscopic equations are investigated numerically and their solutions are compared for tripod and more general networks.
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Ramegowda, Prakasha Chigahalli, Daisuke Ishihara, Tomoya Niho und Tomoyoshi Horie. „Performance Evaluation of Numerical Finite Element Coupled Algorithms for Structure–Electric Interaction Analysis of MEMS Piezoelectric Actuator“. International Journal of Computational Methods 16, Nr. 07 (26.07.2019): 1850106. http://dx.doi.org/10.1142/s0219876218501062.
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This work presents multiphysics numerical analysis of piezoelectric actuators realized using the finite element method (FEM) and their performances to analyze the structure-electric interaction in three-dimensional (3D) piezoelectric continua. Here, we choose the piezoelectric bimorph actuator without the metal shim and with the metal shim as low-frequency problems and a surface acoustic wave device as a high-frequency problem. More attention is given to low-frequency problems because in our application micro air vehicle’s wings are actuated by piezoelectric bimorph actuators at low frequency. We employed the Newmark’s time integration and the central difference time integration to study the dynamic response of piezoelectric actuators. Monolithic coupling, noniterative partitioned coupling and partitioned iterative coupling schemes are presented. In partitioned iterative coupling schemes, the block Jacobi and the block Gauss–Seidel methods are employed. Resonance characteristics are very important in micro-electro-mechanical system (MEMS) applications. Therefore, using our proposed coupled algorithms, the resonance characteristics of bimorph actuator is analyzed. Comparison of the accuracy and computational efficiency of the proposed numerical finite element coupled algorithms have been carried out for 3D structure–electric interaction problems of a piezoelectric actuator. The numerical results obtained by the proposed algorithms are in good agreement with the theoretical solutions.
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Liogky, Alexey A., Alexey Yu Chernyshenko, Alexander A. Danilov und Fyodor A. Syomin. „CarNum: parallel numerical framework for computational cardiac electromechanics“. Russian Journal of Numerical Analysis and Mathematical Modelling 38, Nr. 3 (01.06.2023): 127–44. http://dx.doi.org/10.1515/rnam-2023-0011.
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Abstract A new parallel numerical framework CarNum is presented for efficient coupling of mathematical models in multiphysics problems such as computational cardiac electromechanics. This framework is based on open source projects, which provide the core functionality of the platform. Computational cardiac electromechanics requires a complex pipeline of solving different types of ordinary and partial differential equations. Our framework allows one to implement different numerical schemes and provides more control in multiphysics coupling. This paper outlines a concept of the new platform and details of numerical modelling of cardiac electromechanics. First experiments with well-known cardiac electromechanics benchmarks show good agreement with other groups and decent parallel scalability.
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Hodyss, Daniel, Kevin C. Viner, Alex Reinecke und James A. Hansen. „The Impact of Noisy Physics on the Stability and Accuracy of Physics–Dynamics Coupling“. Monthly Weather Review 141, Nr. 12 (25.11.2013): 4470–86. http://dx.doi.org/10.1175/mwr-d-13-00035.1.
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Abstract The coupling of the dynamical core of a numerical weather prediction model to the physical parameterizations is an important component of model design. This coupling between the physics and the dynamics is explored here from the perspective of stochastic differential equations (SDEs). It will be shown that the basic properties of the impact of noisy physics on the stability and accuracy of common numerical methods may be obtained through the application of the basic principles of SDEs. A conceptual model setting is used that allows the study of the impact of noise whose character may be tuned to be either very red (smooth) or white (noisy). The change in the stability and accuracy of common numerical methods as the character of the noise changes is then studied. Distinct differences are found between the ability of multistage (Runge–Kutta) schemes as compared with multistep (Adams–Bashforth/leapfrog) schemes to handle noise of various characters. These differences will be shown to be attributable to the basic philosophy used to design the scheme. Additional experiments using the decentering of the noisy physics will also be shown to lead to strong sensitivity to the quality of the noise. As an example, the authors find the novel result that noise of a diffusive character may lead to instability when the scheme is decentered toward greater implicitness. These results are confirmed in a nonlinear shear layer simulation using a subgrid-scale mixing parameterization. This subgrid-scale mixing parameterization is modified stochastically and shown to reproduce the basic principles found here, including the notion that decentering toward implicitness may lead to instability.
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Kim, J., H. A. A. Tchelepi und R. Juanes. „Stability, Accuracy, and Efficiency of Sequential Methods for Coupled Flow and Geomechanics“. SPE Journal 16, Nr. 02 (17.01.2011): 249–62. http://dx.doi.org/10.2118/119084-pa.
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Summary We perform detailed stability and convergence analyses of sequential-implicit solution methods for coupled fluid flow and reservoir geomechanics. We analyze four different sequential-implicit solution strategies, where each subproblem (flow and mechanics) is solved implicitly: two schemes in which the mechanical problem is solved first—namely, the drained and undrained splits—and two schemes in which the flow problem is solved first—namely, the fixed-strain and fixed-stress splits. The von Neumann method is used to obtain the linear-stability criteria of the four sequential schemes, and numerical simulations are used to test the validity and sharpness of these criteria for representative problems. The analysis indicates that the drained and fixed-strain splits, which are commonly used, are conditionally stable and that the stability limits depend only on the strength of coupling between flow and mechanics and are independent of the timestep size. Therefore, the drained and fixed-strain schemes cannot be used when the coupling between flow and mechanics is strong. Moreover, numerical solutions obtained using the drained and fixed-strain sequential schemes suffer from oscillations, even when the stability limit is honored. For problems where the deformation may be plastic (nonlinear) in nature, the drained and fixed-strain sequential schemes become unstable when the system enters the plastic regime. On the other hand, the undrained and fixed-stress sequential schemes are unconditionally stable regardless of the coupling strength, and they do not suffer from oscillations. While both the undrained and fixed-stress schemes are unconditionally stable, for the cases investigated we found that the fixed-stress split converges more rapidly than the undrained split. On the basis of these findings, we strongly recommend the fixed-stress sequential-implicit method for modeling coupled flow and geomechanics in reservoirs.
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Jacobson, M. Z. „Numerical Solution to Drop Coalescence/Breakup with a Volume-Conserving, Positive-Definite, and Unconditionally Stable Scheme“. Journal of the Atmospheric Sciences 68, Nr. 2 (01.02.2011): 334–46. http://dx.doi.org/10.1175/2010jas3605.1.
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Abstract This paper discusses a new volume- and volume concentration–conserving, positive-definite, unconditionally stable iterative numerical scheme for solving temporary cloud/raindrop coalescence followed by breakup and the coupling of the scheme with an existing noniterative, volume- and volume concentration–conserving collision/coalescence (coagulation) scheme. The breakup scheme alone compares nearly exactly with a constant-kernel analytical solution at a 300-s time step. The combined coagulation/breakup schemes are stable and conservative, regardless of the time step and number of size bins, and convergent with higher temporal and size resolution. The schemes were designed with these characteristics in mind for use in long-term global or regional simulations. The use of 30 geometrically spaced size bins and a time step of 60 s provides a good compromise between obtaining sufficient accuracy (relative to a much higher-resolution result) and speed, although solutions with a 600-s time step and 30 bins are stable and conservative and take one-eighth the computer time. The combined coagulation/breakup schemes were implemented into the nested Gas, Aerosol, Transport, Radiation, General Circulation, Mesoscale, and Ocean Model (GATOR-GCMOM), a global–urban climate–weather–air pollution model. Coagulation was solved over liquid, ice, and graupel distributions and breakup simultaneously over the liquid distribution. Each distribution included 30 size bins and 16 chemical components per bin. Timing tests demonstrate the feasibility of the scheme in long-term global simulations.
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Dgheim, J., A. Chahine, M. Ghazeleh und M. Abdallah. „Numerical computation of thermoelectric effiency of graphite sheet optimal dimension“. Lebanese Science Journal 20, Nr. 1 (27.04.2019): 122–33. http://dx.doi.org/10.22453/lsj-020.1.122-133.
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Thermoelectric Graphite sheet has been studied numerically due to their ability to convert directly heat to electricity. Electro-thermal heat transfer equations coupling to initial and boundary conditions, are solved using finite difference and finite element schemes. The obtained results of both numerical techniques show good qualitative and quantitative agreements. In addition, the results of our numerical models present good conformity with the experimental result of Luo et al.. The voltage difference, the temperature variation, the Seebeck coefficient, the figure of merit and the maximum efficiency of graphite sheet are determined numerically. The ZT of the graphite sheet is calculated to be 1.27 at a temperature of 850 K for a graphite sheet surface of 0.26×0.25 cm2.
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Konarski, Stephanie G., und Caleb F. Sieck. „Extraction of dynamic effective material properties for 2D acoustic Willis media“. Journal of the Acoustical Society of America 151, Nr. 4 (April 2022): A95. http://dx.doi.org/10.1121/10.0010769.
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Acoustic Willis media is characterized by coupling between the kinetic and potential energy through the pressure-strain and momentum density-velocityrelationships. The introduction of additional constitutive properties allows more appropriate characterization of complex unit cells, including effects related to physical asymmetry, finite phase and multiple scattering, and nonreciprocal biases. Similar to traditional composites or other metamaterials, homogenization is a valuable modeling tool that simplifies numerical study of Willis media. However, homogenization schemes must be altered to account for even and/or odd Willis coupling parameters. In this work, we extend a 2D homogenization approach to account for the Willis coupling using the modified dynamic equations. With this homogenization scheme, finite layers of N unit cells and N + 1 unit cells are utilized with different propagation angles and incident directions to isolate the response across a single unit cell. Numerical simulations with the finite element method will then be presented to validate the homogenization model and demonstrate the effective material properties obtained for an asymmetric unit cell. [This work was supported by the Office of Naval Research.]
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Islam, Mohammad, Nicolas Huerta und Robert Dilmore. „Effect of Computational Schemes on Coupled Flow and Geo-Mechanical Modeling of CO2 Leakage through a Compromised Well“. Computation 8, Nr. 4 (13.11.2020): 98. http://dx.doi.org/10.3390/computation8040098.
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Carbon capture, utilization, and storage (CCUS) describes a set of technically viable processes to separate carbon dioxide (CO2) from industrial byproduct streams and inject it into deep geologic formations for long-term storage. Legacy wells located within the spatial domain of new injection and production activities represent potential pathways for fluids (i.e., CO2 and aqueous phase) to leak through compromised components (e.g., through fractures or micro-annulus pathways). The finite element (FE) method is a well-established numerical approach to simulate the coupling between multi-phase fluid flow and solid phase deformation interactions that occur in a compromised well system. We assumed the spatial domain consists of a three-phases system: a solid, liquid, and gas phase. For flow in the two fluids phases, we considered two sets of primary variables: the first considering capillary pressure and gas pressure (PP) scheme, and the second considering liquid pressure and gas saturation (PS) scheme. Fluid phases were coupled with the solid phase using the full coupling (i.e., monolithic coupling) and iterative coupling (i.e., sequential coupling) approaches. The challenge of achieving numerical stability in the coupled formulation in heterogeneous media was addressed using the mass lumping and the upwinding techniques. Numerical results were compared with three benchmark problems to assess the performance of coupled FE solutions: 1D Terzaghi’s consolidation, Liakopoulos experiments, and the Kueper and Frind experiments. We found good agreement between our results and the three benchmark problems. For the Kueper and Frind test, the PP scheme successfully captured the observed experimental response of the non-aqueous phase infiltration, in contrast to the PS scheme. These exercises demonstrate the importance of fluid phase primary variable selection for heterogeneous porous media. We then applied the developed model to the hypothetical case of leakage along a compromised well representing a heterogeneous media. Considering the mass lumping and the upwinding techniques, both the monotonic and the sequential coupling provided identical results, but mass lumping was needed to avoid numerical instabilities in the sequential coupling. Additionally, in the monolithic coupling, the magnitude of primary variables in the coupled solution without mass lumping and the upwinding is higher, which is essential for the risk-based analyses.
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LU, HONGTAO, und GUANRONG CHEN. „GLOBAL SYNCHRONIZATION IN AN ARRAY OF LINEARLY COUPLED DELAYED NEURAL NETWORKS WITH AN ARBITRARY COUPLING MATRIX“. International Journal of Bifurcation and Chaos 16, Nr. 11 (November 2006): 3357–68. http://dx.doi.org/10.1142/s0218127406016847.
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In this paper, we investigate global synchronization in an array of linearly coupled identical delayed neural networks. We consider the array with an arbitrary coupling matrix without assuming it to be symmetric, irreducible and diffusive. Moreover, we consider the array being connected through two different coupling schemes, state-coupling and output-coupling, respectively. For state-coupling, we derive a more general sufficient condition ensuring global synchronization, which is an extension of some existing results in the literature. For output-coupling, we derive a new sufficient condition for global synchronization. Numerical simulations are given to illustrate the theoretical results.
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de Rooij, Rob. „New insights into the differences between the dual node approach and the common node approach for coupling surface–subsurface flow“. Hydrology and Earth System Sciences 21, Nr. 11 (17.11.2017): 5709–24. http://dx.doi.org/10.5194/hess-21-5709-2017.
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Abstract. The common node approach and the dual node approach are two widely applied approaches to coupling surface–subsurface flow. In this study both approaches are analyzed for cell-centered as well as vertex-centered finite difference schemes. It is shown that the dual node approach should be conceptualized and implemented as a one-sided first-order finite difference to approximate the vertical subsurface hydraulic gradient at the land surface. This results in a consistent dual node approach in which the coupling length is related to grid topology. In this coupling approach the coupling length is not to be interpreted as a nonphysical model parameter. Although this particular coupling approach is technically not new, the differences between this consistent dual node approach and the common node approach have not been studied in detail. In fact, this coupling scheme is often believed to be similar to the common node approach. In this study it is illustrated that in comparison to the common node approach, the head continuity at the surface–subsurface interface is formulated more correctly in the consistent dual node approach. Numerical experiments indicate that the consistent dual node approach is less sensitive to the vertical discretization when simulating excess infiltration. It is also found that the consistent dual node approach can be advantageous in terms of numerical efficiency.
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Mönkölä, Sanna. „On the Accuracy and Efficiency of Transient Spectral Element Models for Seismic Wave Problems“. Advances in Mathematical Physics 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/9431583.
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This study concentrates on transient multiphysical wave problems for simulating seismic waves. The presented models cover the coupling between elastic wave equations in solid structures and acoustic wave equations in fluids. We focus especially on the accuracy and efficiency of the numerical solution based on higher-order discretizations. The spatial discretization is performed by the spectral element method. For time discretization we compare three different schemes. The efficiency of the higher-order time discretization schemes depends on several factors which we discuss by presenting numerical experiments with the fourth-order Runge-Kutta and the fourth-order Adams-Bashforth time-stepping. We generate a synthetic seismogram and demonstrate its function by a numerical simulation.
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Wen, Mengke, Weidong Li und Zhangyan Zhao. „A hybrid scheme coupling lattice Boltzmann method and finite-volume lattice Boltzmann method for steady incompressible flows“. Physics of Fluids 34, Nr. 3 (März 2022): 037114. http://dx.doi.org/10.1063/5.0085370.
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We present a new hybrid method coupling the adaptive mesh refinement lattice Boltzmann method (AMRLBM) and the finite-volume lattice Boltzmann method (FVLBM) to improve both the simulation efficiency and adaptivity for steady incompressible flows with complex geometries. The present method makes use of the domain decomposition, in which the FVLBM sub-domain is applied to the region adjacent to the walls, and is coupled to the lattice Boltzmann method (LBM) sub-domain in the rest of the flow field to enhance the ability of the LBM to deal with irregular geometries without sacrificing the high efficiency and accuracy property of the LBM. In the LBM sub-domain, a cell-centered lattice structure-based AMRLBM is used and, in the FVLBM sub-domain, the gas-kinetic Bhatnagar–Gross–Krook (BGK) scheme-based FVLBM is adopted to reduce the numerical dissipation and enhance the efficiency of FVLBM. Moreover, not like the conventional LBM and Navier–Stokes equation solver-based hybrid schemes, the present hybrid scheme combines two kinds of lattice Boltzmann equation solvers, that is, AMRLBM and FVLBM, which makes the present scheme much simpler and better consistency than the conventional hybrid schemes. To assess the accuracy and efficacy of the proposed method, various benchmark studies, including the Kovasznay flow, the lid-driven cavity flow with Reynolds number [Formula: see text], 400, and 1000, and the steady flow past a cylinder with [Formula: see text] and 40, are also conducted. The numerical results show that the present scheme can be an efficient and reliable method for steady incompressible flows.
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Gien, T. T. „Feshbach resonances in positron–hydrogen collisions“. Canadian Journal of Physics 74, Nr. 7-8 (01.07.1996): 343–52. http://dx.doi.org/10.1139/p96-050.
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Sequences of Feshbach resonances, predicted by theory to exist below the n = 2 H threshold in positron–hydrogen scattering, that have long evaded all previous numerical searches, were finally located in our close-coupling calculation employing various coupling schemes. The energy ratios and width ratios of the successive resonances of these sequences were, furthermore, found to agree very well with the values predicted by theory.
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Ma, Lina, Rui Chen, Xiaofeng Yang und Hui Zhang. „Numerical Approximations for Allen-Cahn Type Phase Field Model of Two-Phase Incompressible Fluids with Moving Contact Lines“. Communications in Computational Physics 21, Nr. 3 (07.02.2017): 867–89. http://dx.doi.org/10.4208/cicp.oa-2016-0008.
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AbstractIn this paper, we present some efficient numerical schemes to solve a two-phase hydrodynamics coupled phase field model with moving contact line boundary conditions. The model is a nonlinear coupling system, which consists the Navier-Stokes equations with the general Navier Boundary conditions or degenerated Navier Boundary conditions, and the Allen-Cahn type phase field equations with dynamical contact line boundary condition or static contact line boundary condition. The proposed schemes are linear and unconditionally energy stable, where the energy stabilities are proved rigorously. Various numerical tests are performed to show the accuracy and efficiency thereafter.
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Advani, S. H., T. S. Lee und J. K. Lee. „Three-Dimensional Modeling of Hydraulic Fractures in Layered Media: Part I—Finite Element Formulations“. Journal of Energy Resources Technology 112, Nr. 1 (01.03.1990): 1–9. http://dx.doi.org/10.1115/1.2905706.
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A comprehensive model represented by a set of equations governing the mechanics of planar hydraulic fracture propagation in a multi-layered reservoir is presented. A general-purpose integral formulation for the formation elasticity is developed along with a numerical scheme for mode I fracture response evaluation of an arbitrarily shaped planar pressurized crack in a layered medium. Non-Newtonian fluid flow in the hydraulically induced fracture is governed by a two-dimensional nonlinear partial differential equation. Finite element formulations for the governing equations as well as calibrative examples illustrating the computational features of the model are presented. Numerical schemes for determining the moving fracture front and coupling of the fluid flow and structural/fracture responses are also developed.
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Tang, Tao, Weidong Zhao und Tao Zhou. „Deferred Correction Methods for Forward Backward Stochastic Differential Equations“. Numerical Mathematics: Theory, Methods and Applications 10, Nr. 2 (Mai 2017): 222–42. http://dx.doi.org/10.4208/nmtma.2017.s02.
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AbstractThe deferred correction (DC) method is a classical method for solving ordinary differential equations; one of its key features is to iteratively use lower order numerical methods so that high-order numerical scheme can be obtained. The main advantage of the DC approach is its simplicity and robustness. In this paper, the DC idea will be adopted to solve forward backward stochastic differential equations (FBSDEs) which have practical importance in many applications. Noted that it is difficult to design high-order and relatively “clean” numerical schemes for FBSDEs due to the involvement of randomness and the coupling of the FSDEs and BSDEs. This paper will describe how to use the simplest Euler method in each DC step–leading to simple computational complexity–to achieve high order rate of convergence.
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Lei, Xin-Qing, Jia-He Zhu, Da-Wei Wang und Wen-Sheng Zhao. „Design for Ultrahigh-Density Vertical Phase Change Memory: Proposal and Numerical Investigation“. Electronics 11, Nr. 12 (08.06.2022): 1822. http://dx.doi.org/10.3390/electronics11121822.
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The integration level is a significant index that can be used to characterize the performance of non-volatile memory devices. This paper proposes innovative design schemes for high-density integrated phase change memory (PCM). In these schemes, diploid and four-fold memory units, which are composed of nano-strip film GST-based memory cells, are employed to replace the memory unit of a conventional vertical PCM array. As the phase transformation process of the phase change material involves the coupling of electrical and thermal processes, an in-house electrothermal coupling simulator is developed to analyze the performance of the proposed memory cells and arrays. In the simulator, a proven mathematical model is used to describe the phase change mechanism, with a finite element approach implemented for numerical calculations. The characteristics of the GST-strip-based memory cell are simulated first and compared with a conventional vertical cell, with a decrease of 32% in the reset current amplitude achieved. Next, the influences of geometric parameters on the characteristics of memory cell are investigated systematically. After this, the electrothermal characteristics of the proposed vertical PCM arrays are simulated and the results indicate that they possess both excellent performance and scalability. At last, the integration densities of the proposed design schemes are compared with the reference array, with a maximum time of 5.94 achieved.
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MAR-OR, ASSAF, und DAN GIVOLI. „A FINITE ELEMENT STRUCTURAL-ACOUSTIC MODEL OF COUPLED MEMBRANES“. Journal of Computational Acoustics 12, Nr. 04 (Dezember 2004): 605–18. http://dx.doi.org/10.1142/s0218396x04002407.
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A simple model displaying structural-acoustic behavior is considered. The model comprises of two parallel infinitely-long flat membranes lying on elastic foundations and the acoustic medium separating them. The structural-acoustic coupling manifests itself in that a vibrational excitation of one of the membranes triggers vibrations in the other. The governing equations are stated, and the associated finite element formulation is constructed. The model is then analyzed numerically and its vibrational properties are investigated. The proposed model is especially simple, being two-dimensional and involving a small number of parameters, but at the same time it brings to light some important features associated with structural-acoustic coupling. Therefore it may serve as a benchmark for evaluating structural-acoustic numerical schemes and as an educational tool for studying structural-acoustic coupling in a simple context.
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Appadu, A. R., und A. A. I. Peer. „Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws“. Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/428681.
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We describe briefly how a third-order Weighted Essentially Nonoscillatory (WENO) scheme is derived by coupling a WENO spatial discretization scheme with a temporal integration scheme. The scheme is termed WENO3. We perform a spectral analysis of its dispersive and dissipative properties when used to approximate the 1D linear advection equation and use a technique of optimisation to find the optimal cfl number of the scheme. We carry out some numerical experiments dealing with wave propagation based on the 1D linear advection and 1D Burger’s equation at some different cfl numbers and show that the optimal cfl does indeed cause less dispersion, less dissipation, and lowerL1errors. Lastly, we test numerically the order of convergence of the WENO3 scheme.
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Yu, Quan Gang, Lin Hua Piao und Xing Wang. „New Ways of Improving the Property of the Piezoelectric Fluidic Angular Rate Sensor“. Advanced Materials Research 462 (Februar 2012): 587–91. http://dx.doi.org/10.4028/www.scientific.net/amr.462.587.
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New ways of improving the property of the piezoelectric fluidic angular rate sensor are described in the paper. According to the improved schemes of the structure and the process, the repeatability of null voltage, the cross-coupling and stability of the sensor are improved. The numerical results have shown that the repeatability of null voltage increases from 0.2°/S to 0.1°/S and the cross-coupling decreases from 2% to 1%.
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Lac, Christine, Jean-Pierre Chaboureau, Valéry Masson, Jean-Pierre Pinty, Pierre Tulet, Juan Escobar, Maud Leriche et al. „Overview of the Meso-NH model version 5.4 and its applications“. Geoscientific Model Development 11, Nr. 5 (29.05.2018): 1929–69. http://dx.doi.org/10.5194/gmd-11-1929-2018.
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Abstract. This paper presents the Meso-NH model version 5.4. Meso-NH is an atmospheric non hydrostatic research model that is applied to a broad range of resolutions, from synoptic to turbulent scales, and is designed for studies of physics and chemistry. It is a limited-area model employing advanced numerical techniques, including monotonic advection schemes for scalar transport and fourth-order centered or odd-order WENO advection schemes for momentum. The model includes state-of-the-art physics parameterization schemes that are important to represent convective-scale phenomena and turbulent eddies, as well as flows at larger scales. In addition, Meso-NH has been expanded to provide capabilities for a range of Earth system prediction applications such as chemistry and aerosols, electricity and lightning, hydrology, wildland fires, volcanic eruptions, and cyclones with ocean coupling. Here, we present the main innovations to the dynamics and physics of the code since the pioneer paper of Lafore et al. (1998) and provide an overview of recent applications and couplings.
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MOUS, ILHEM, und ABDELHAMID LAOUAR. „A Numerical Solution of a Coupling System of Conformable Time-Derivative Two-Dimensional Burgers’ Equations“. Kragujevac Journal of Mathematics 48, Nr. 1 (2024): 7–23. http://dx.doi.org/10.46793/kgjmat2401.007m.
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In this paper, we deal with a numerical solution of a coupling system of fractional conformable time-derivative two-dimensional (2D) Burgers’ equations. The presence of both the fractional time derivative and the nonlinear terms in this system of equations makes solving it more difficult. Firstly, we use the Cole-Hopf transformation in order to reduce the coupling system of equations to a conformable time-derivative 2D heat equation for which the numerical solution is calculated by the explicit and implicit schemes. Secondly, we calculate the numerical solution of the proposed system by using both the obtained solution of the conformable time-derivative heat equation and the inverse Cole-Hopf transformation. This approach shows its efficiency to deal with this class of fractional nonlinear problems. Some numerical experiments are displayed to consolidate our approach
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Min, Byung-Ju, Yeon-Ji Kim und You-Shin No. „On-Demand Waveguide-Integrated Microlaser-on-Silicon“. Applied Sciences 13, Nr. 16 (17.08.2023): 9329. http://dx.doi.org/10.3390/app13169329.
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The integration of high-quality III–V light sources on the Si platform has encountered a challenge that demands a highly precise on-demand addressability of single devices in a significantly reduced integration area. However, simple schemes to address the issue without causing major optical losses remain elusive. Here, we propose a waveguide-integrated microlaser-on-silicon in which the III–V/Si integration requires only a small micron-sized post structure with a diameter of <2 µm and enables efficient light coupling with an estimated coupling efficiency of 44.52%. Top-down fabricated high-quality microdisk cavities with an active gain medium were precisely micro-transferred on a small Si-post structure that was rationally designed in the vicinity of a strip-type Si waveguide (WG). Spectroscopic measurements exhibit successful lasing emission with a threshold of 378.0 µW, bi-directional light coupling, and a propagation of >50 µm through the photonic Si WG. Numerical study provides an in-depth understanding of light coupling and verifies the observations in the experiment. We believe that the proposed microlaser-on-Si is a simple and efficient scheme requiring a minimum integration volume smaller than the size of the light source, which is hard to achieve in conventional integration schemes and is readily applicable to various on-demand integrated device applications.
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Simson, Anna, Henning Löwe und Julia Kowalski. „Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes“. Cryosphere 15, Nr. 12 (07.12.2021): 5423–45. http://dx.doi.org/10.5194/tc-15-5423-2021.
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Abstract. A coupled treatment of transport processes, phase changes and mechanical settling is the core of any detailed snowpack model. A key concept underlying the majority of these models is the notion of layers as deforming material elements that carry the information on their physical state. Thereby an explicit numerical solution of the ice mass continuity equation can be circumvented, although with the downside of virtual no flexibility in implementing different coupling schemes for densification, phase changes and transport. As a remedy we consistently recast the numerical core of a snowpack model into an extendable Eulerian–Lagrangian framework for solving the coupled non-linear processes. In the proposed scheme, we explicitly solve the most general form of the ice mass balance using the method of characteristics, a Lagrangian method. The underlying coordinate transformation is employed to state a finite-difference formulation for the superimposed (vapor and heat) transport equations which are treated in their Eulerian form on a moving, spatially non-uniform grid that includes the snow surface as a free upper boundary. This formulation allows us to unify the different existing viewpoints of densification in snow or firn models in a flexible way and yields a stable coupling of the advection-dominated mechanical settling with the remaining equations. The flexibility of the scheme is demonstrated within several numerical experiments using a modular solver strategy. We focus on emerging heterogeneities in (two-layer) snowpacks, the coupling of (solid–vapor) phase changes with settling at layer interfaces and the impact of switching to a non-linear mechanical constitutive law. Lastly, we discuss the potential of the scheme for extensions like a dynamical equation for the surface mass balance or the coupling to liquid water flow.
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Balcázar-Arciniega, N., J. Rigola und A. Oliva. „Unstructured Conservative Level-Set (UCLS) method for reactive mass transfer in bubble swarms at high density ratio“. Journal of Physics: Conference Series 2766, Nr. 1 (01.05.2024): 012062. http://dx.doi.org/10.1088/1742-6596/2766/1/012062.
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Abstract This research presents a parallel Unstructured Conservative Level-Set (UCLS) method for reactive mass transfer in bubbles with a high-density ratio. This method uses the multiple-marker UCLS approach to circumvent the numerical coalescence of bubbles, combined with the finite-volume method to discretize transport equations on 3D collocated unstructured meshes. The fractional-step projection method solves the pressure-velocity coupling. The central difference scheme discretizes the diffusive term, whereas convective term within the momentum transport equation, level-set advection equations, and mass transfer equation are discretized by unstructured flux-limiters schemes. Such a combination of numerical techniques preserves the numerical stability in bubbly flows with a high Reynolds number and high-density ratio. Numerical and physical findings on the effect of physical properties ratios on the reactive mass transfer are reported, including their effect on the Reynolds number, interfacial area and Sherwood number.
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Liu, Chin Chia. „Dynamic Analysis of Micro Devices with Squeeze-Film Damping Effect Using Hybrid Numerical Scheme“. Advanced Materials Research 811 (September 2013): 474–77. http://dx.doi.org/10.4028/www.scientific.net/amr.811.474.
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Using traditional methods such as perturbation theory or Galerkin approach method to analyze the dynamic response of electrostatic devices is not easy due to the complexity of the interactions between the electrostatic coupling effect, the fringing field effect, the residual stress, the nonlinear electrostatic force and squeeze-film damping effect. Accordingly, the present study proposes a new approach for analyzing the dynamic response of such devices using a hybrid numerical scheme comprising the differential transformation method and the finite difference method by pure DC or combined DC / AC loading. The validity of the proposed scheme is confirmed by comparing the results obtained for the pull-in voltage of the micro-beam with those presented in the literature derived using a variety of schemes. Overall, the results show that the hybrid numerical scheme provides a suitable means of analyzing the nonlinear dynamic behavior of a wide variety of common electrostatically-actuated microstructures.
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Tudor, Martina, und Piet Termonia. „Alternative Formulations for Incorporating Lateral Boundary Data into Limited-Area Models“. Monthly Weather Review 138, Nr. 7 (01.07.2010): 2867–82. http://dx.doi.org/10.1175/2010mwr3179.1.
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Abstract Limited-area models (LAMs) use higher resolutions and more advanced parameterizations of physical processes than global numerical weather prediction models, but suffer from one additional source of error—the lateral boundary condition (LBC). The large-scale model passes the information on its fields to the LAM only over the narrow coupling zone at discrete times separated by a coupling interval of several hours. The LBC temporal resolution can be lower than the time necessary for a particular meteorological feature to cross the boundary. A LAM user who depends on LBC data acquired from an independent prior analysis or parent model run can find that usual schemes for temporal interpolation of large-scale data provide LBC data of inadequate quality. The problem of a quickly moving depression that is not recognized by the operationally used gridpoint coupling scheme is examined using a simple one-dimensional model. A spectral method for nesting a LAM in a larger-scale model is implemented and tested. Results for a traditional flow-relaxation scheme combined with temporal interpolation in spectral space are also presented.
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Vogl, Christopher J., Hui Wan, Carol S. Woodward und Quan M. Bui. „Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 2: A semi-discrete error analysis framework for assessing coupling schemes“. Geoscientific Model Development 17, Nr. 3 (16.02.2024): 1409–28. http://dx.doi.org/10.5194/gmd-17-1409-2024.
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Abstract. Part 1 (Wan et al., 2024) of this study discusses the motivation and empirical evaluation of a revision to the aerosol-related numerical process coupling in the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) to address the previously reported issue of strong sensitivity of the simulated dust aerosol lifetime and dry removal rate to the model's vertical resolution. This paper complements that empirical justification of the revised scheme with a mathematical justification leveraging a semi-discrete analysis framework for assessing the splitting error of process coupling methods. The framework distinguishes the error due to numerical splitting from the error due to the time integration method(s) used for each individual process. Such a distinction results in a framework that provides an intuitive understanding of the causes of the splitting error. The application of this framework to the dust life cycle in EAMv1 confirms (i) that the original EAMv1 scheme artificially strengthens the effect of dry removal processes and (ii) that the revised splitting reduces that artificial strengthening. While the error analysis framework is presented in the context of the dust life cycle in EAMv1, the framework can be broadly leveraged to evaluate process coupling schemes, both in other physical problems and for any number of processes. This framework will be particularly powerful when the various process implementations support a variety of time integration approaches. Whereas traditional local truncation error approaches require separate consideration of each combination of time integration methods, this framework enables evaluation of coupling schemes independent of particular time integration approaches for each process while still allowing for the incorporation of these specific time integration errors if so desired. The framework also explains how the splitting error terms result from (i) the integration of individual processes in isolation from other processes and (ii) the choices of input state and time step size for the isolated integration of processes. Such a perspective has the potential for the rapid development of alternative coupling approaches that utilize knowledge both about the desired accuracy and about the computational costs of individual processes.