Artykuły w czasopismach: „Cell-Centered Finite-Volume Methods”

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Zhang, Wenjuan, i Mohammed Al Kobaisi. "Cell-Centered Nonlinear Finite-Volume Methods With Improved Robustness". SPE Journal 25, nr 01 (2.07.2019): 288–309. http://dx.doi.org/10.2118/195694-pa.

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Summary We present a nonlinear finite-volume method (NFVM) that is either positivity-preserving or extremum-preserving with improved robustness. The key ingredient of the method is the construction of one-sided fluxes, which involves decomposition of conormal vectors by introducing harmonic-averaging points as auxiliary points. The original NFVM using harmonic-averaging points is not robust in the sense that decomposition of conormal vectors with nonnegative coefficients can easily run into difficulties for heterogeneous and anisotropic permeability tensors on general nonorthogonal meshes. To improve NFVM robustness, we first present an alternative derivation of harmonic-averaging points and give a different formula that shows more clearly a point's location. On the basis of the derivation of the new formula, a correction algorithm is proposed to make modifications to those problematic harmonic-averaging points so that all the conormal vectors can be decomposed with nonnegative coefficients successfully. As a result, the resulting NFVM can be applied to more-challenging problems when conormal decomposition with nonnegative coefficients is not possible without correction. The correction algorithm is a compromise between robustness and accuracy. While it improves the robustness of the resulting NFVM, results of numerical convergence tests show that the effect of our correction algorithm on accuracy is problem-dependent. Optimal order of convergence is still maintained for some problems, and the convergence rate is reduced for others. Monotonicity and extremum-preserving properties are verified by numerical experiments. Finally, a field test case is used to demonstrate that the NFVM combined with our correction algorithm can be applied to simulate real-life reservoirs of industry-standard complexity.

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Nicaise, Serge. "A posteriori error estimations of some cell-centered finite volume methods". SIAM Journal on Numerical Analysis 43, nr 4 (styczeń 2005): 1481–503. http://dx.doi.org/10.1137/s0036142903437787.

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Bidégaray, B., i J. M. Ghidaglia. "Multidimensional corrections to cell-centered finite volume methods for Maxwell equations". Applied Numerical Mathematics 44, nr 3 (luty 2003): 281–98. http://dx.doi.org/10.1016/s0168-9274(02)00171-x.

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Chen, Long, i Ming Wang. "Cell Conservative Flux Recovery and A Posteriori Error Estimate of Vertex-Centered Finite Volume Methods". Advances in Applied Mathematics and Mechanics 5, nr 05 (październik 2013): 705–27. http://dx.doi.org/10.4208/aamm.12-m1279.

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AbstractA cell conservative flux recovery technique is developed here for vertex-centered finite volume methods of second order elliptic equations. It is based on solving a local Neumann problem on each control volume using mixed finite element methods. The recovered flux is used to construct a constant freea posteriorierror estimator which is proven to be reliable and efficient. Some numerical tests are presented to confirm the theoretical results. Our method works for general order finite volume methods and the recovery-based and residual-baseda posteriorierror estimators is the first result ona posteriorierror estimators for high order finite volume methods.

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Terekhov, Kirill M., Bradley T. Mallison i Hamdi A. Tchelepi. "Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem". Journal of Computational Physics 330 (luty 2017): 245–67. http://dx.doi.org/10.1016/j.jcp.2016.11.010.

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Jahandari, Hormoz, i Colin G. Farquharson. "Forward modeling of gravity data using finite-volume and finite-element methods on unstructured grids". GEOPHYSICS 78, nr 3 (1.05.2013): G69—G80. http://dx.doi.org/10.1190/geo2012-0246.1.

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Minimum-structure inversion is one of the most effective tools for the inversion of gravity data. However, the standard Gauss-Newton algorithms that are commonly used for the minimization procedure and that employ forward solvers based on analytic formulas require large memory storage for the formation and inversion of the involved matrices. An alternative to the analytical solvers are numerical ones that result in sparse matrices. This sparsity suits gradient-based minimization methods that avoid the explicit formation of the inversion matrices and that solve the system of equations using memory-efficient iterative techniques. We have developed several numerical schemes for the forward modeling of gravity data using the finite-element and finite-volume methods on unstructured grids. In the finite-volume method, a Delaunay tetrahedral grid and its dual Voronoï grid are used to find the primary solution (i.e., gravitational potential) at the centers and vertices of the tetrahedra, respectively (cell-centered and vertex-centered schemes). In the finite-element method, Delaunay tetrahedral grids are used to develop linear and quadratic finite-element schemes. Different techniques are used to recover the vertical component of gravitational acceleration from the gravitational potential. In the finite-volume scheme, a differencing method is used; in the finite-element method, basis functions are used. The capabilities of the finite-volume and finite-element schemes were tested on simple and realistic synthetic examples. The results showed that the quadratic finite-element scheme is the most accurate but also the most computationally demanding scheme. The best trade-offs between accuracy and computational resource requirement were achieved by the linear finite-element and vertex-centered finite-volume schemes.

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Berzins, M., i J. M. Ware. "Positive cell-centered finite volume discretization methods for hyperbolic equations on irregular meshes". Applied Numerical Mathematics 16, nr 4 (luty 1995): 417–38. http://dx.doi.org/10.1016/0168-9274(95)00007-h.

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Zou, Dongyang, Chunguang Xu, Haibo Dong i Jun Liu. "A shock-fitting technique for cell-centered finite volume methods on unstructured dynamic meshes". Journal of Computational Physics 345 (wrzesień 2017): 866–82. http://dx.doi.org/10.1016/j.jcp.2017.05.047.

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Vakilipour, Shidvash, Masoud Mohammadi, Vahid Badrkhani i Scott Ormiston. "Developing a physical influence upwind scheme for pressure‐based cell‐centered finite volume methods". International Journal for Numerical Methods in Fluids 89, nr 1-2 (październik 2018): 43–70. http://dx.doi.org/10.1002/fld.4682.

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Asmouh, Ilham, Mofdi El-Amrani, Mohammed Seaid i Naji Yebari. "A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations". Computational and Mathematical Methods 2022 (13.02.2022): 1–18. http://dx.doi.org/10.1155/2022/8192192.

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A cell-centered finite volume semi-Lagrangian method is presented for the numerical solution of two-dimensional coupled Burgers’ problems on unstructured triangular meshes. The method combines a modified method of characteristics for the time integration and a cell-centered finite volume for the space discretization. The new method belongs to fractional-step algorithms for which the convection and the viscous parts in the coupled Burgers’ problems are treated separately. The crucial step of interpolation in the convection step is performed using two local procedures accounting for the element where the departure point is located. The resulting semidiscretized system is then solved using a third-order explicit Runge-Kutta scheme. In contrast to the Eulerian-based methods, we apply the new method for each time step along the characteristic curves instead of the time direction. The performance of the current method is verified using different examples for coupled Burgers’ problems with known analytical solutions. We also apply the method for simulation of an example of coupled Burgers’ flows in a complex geometry. In these test problems, the new cell-centered finite volume semi-Lagrangian method demonstrates its ability to accurately resolve the two-dimensional coupled Burgers’ problems.

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Chang, Lina, i Guangwei Yuan. "Cell-centered finite volume methods with flexible stencils for diffusion equations on general nonconforming meshes". Computer Methods in Applied Mechanics and Engineering 198, nr 17-20 (kwiecień 2009): 1638–46. http://dx.doi.org/10.1016/j.cma.2009.01.023.

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Nicaise, Serge. "A Posteriori Error Estimations of Some Cell Centered Finite Volume Methods for Diffusion-Convection-Reaction Problems". SIAM Journal on Numerical Analysis 44, nr 3 (styczeń 2006): 949–78. http://dx.doi.org/10.1137/040611483.

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Langguth, J., N. Wu, J. Chai i X. Cai. "Parallel performance modeling of irregular applications in cell-centered finite volume methods over unstructured tetrahedral meshes". Journal of Parallel and Distributed Computing 76 (luty 2015): 120–31. http://dx.doi.org/10.1016/j.jpdc.2014.10.005.

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Mangani, Luca, Mhamad Mahdi Alloush, Raphael Lindegger, Lucian Hanimann i Marwan Darwish. "A Pressure-Based Fully-Coupled Flow Algorithm for the Control Volume Finite Element Method". Applied Sciences 12, nr 9 (5.05.2022): 4633. http://dx.doi.org/10.3390/app12094633.

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A pressure-based fully-coupled flow algorithm is developed for the control volume finite element method (CVFEM), which covers speeds up to the transonic regime. The CVFEM is used because it presents a number of advantages as compared to the popular cell-centered finite volume method (CCFVM), while retaining the properties of the finite volume method (FVM) in terms of flux conservation and numerical integration simplicity. The implementation presents a novel weak formulation of Dirichlet boundary conditions to resolve the disadvantages emerging from the strong formulation, by mimicking the methods followed in the CCFVM. Derivation and implementation details are presented, and a number of test cases are used to evaluate the accuracy and performance of this approach.

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Zangeneh, Reza, i Carl F. Ollivier-Gooch. "Stability analysis and improvement of the solution reconstruction for cell-centered finite volume methods on unstructured meshes". Journal of Computational Physics 393 (wrzesień 2019): 375–405. http://dx.doi.org/10.1016/j.jcp.2019.05.002.

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Erath, Christoph. "A nonconforming a posteriori estimator for the coupling of cell-centered finite volume and boundary element methods". Numerische Mathematik 131, nr 3 (9.12.2014): 425–51. http://dx.doi.org/10.1007/s00211-014-0694-1.

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Alakashi, Abobaker Mohammed, i Bambang Basuno. "Comparison between Cell-Centered Schemes Computer Code and Fluent Software for a Transonic Flow Pass through an Array of Turbine Stator Blades". Applied Mechanics and Materials 437 (październik 2013): 271–74. http://dx.doi.org/10.4028/www.scientific.net/amm.437.271.

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The Finite Volume Method (FVM) is a discretization method which is well suited for the numerical simulation of various types (elliptic, parabolic or hyperbolic, for instance) of conservation laws; it has been extensively used in several engineering fields. The Finite volume method uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations [. the developed computer code based Cell-centered scheme and Fluent software had been used to investigate the inviscid Transonic Flow Pass Through an array of Turbine Stator Blades. The governing equation of fluid motion of the flow problem in hand is assumed governed by the compressible Euler Equation. Basically this equation behave as a mixed type of partial differential equation elliptic and hyperbolic type of partial differential equation. If the local Mach number is less than one, the governing equation will behave as elliptic type of differential equation while if the Mach number is greater than one it will behave as hyperbolic type of differential equation. To eliminate the presence a mixed type behavior, the governing equation of fluid motion are treated as the governing equation of unsteady flow although the problem in hand is steady flow problems. Presenting the Euler equation in their unsteady form makes the equation becomes hyperbolic with respect to time. There are various Finite Volume Methods can used for solving hyperbolic type of equation, such as Cell-centered scheme [, Roe Upwind Scheme [ and TVD Scheme [. The present work use a cell centered scheme applied to the case of flow pass through an array of turbine stator blades. The comparison carried out with the result provided by Fluent Software for three different value of back pressure. The developed computer code shows the result close to the Fluent software although the Fluent software use a Time Averaged Navier stokes equation as its governing equation of fluid motion.

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Griffith, Boyce E. "On the Volume Conservation of the Immersed Boundary Method". Communications in Computational Physics 12, nr 2 (sierpień 2012): 401–32. http://dx.doi.org/10.4208/cicp.120111.300911s.

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AbstractThe immersed boundary (IB) method is an approach to problems of fluid-structure interaction in which an elastic structure is immersed in a viscous incompressible fluid. The IB formulation of such problems uses a Lagrangian description of the structure and an Eulerian description of the fluid. It is well known that some versions of the IB method can suffer from poor volume conservation. Methods have been introduced to improve the volume-conservation properties of the IB method, but they either have been fairly specialized, or have used complex, nonstandard Eulerian finite-difference discretizations. In this paper, we use quasi-static and dynamic benchmark problems to investigate the effect of the choice of Eulerian discretization on the volume-conservation properties of a formally second-order accurate IB method. We consider both collocated and staggered-grid discretization methods. For the tests considered herein, the staggered-grid IB scheme generally yields at least a modest improvement in volume conservation when compared to cell-centered methods, and in many cases considered in this work, the spurious volume changes exhibited by the staggered-grid IB method are more than an order of magnitude smaller than those of the collocated schemes. We also compare the performance of cell-centered schemes that use either exact or approximate projection methods. We find that the volume-conservation properties of approximate projection IB methods depend strongly on the formulation of the projection method. When used with the IB method, we find that pressure-free approximate projection methods can yield extremely poor volume conservation, whereas pressure-increment approximate projection methods yield volume conservation that is nearly identical to that of a cell-centered exact projection method.

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Kang, Myeongseok, i Donghyun You. "A Low Dissipative and Stable Cell-Centered Finite Volume Method with the Simultaneous Approximation Term for Compressible Turbulent Flows". Mathematics 9, nr 11 (26.05.2021): 1206. http://dx.doi.org/10.3390/math9111206.

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A simultaneous-approximation term is a non-reflecting boundary condition that is usually accompanied by summation-by-parts schemes for provable time stability. While a high-order convective flux based on reconstruction is often employed in a finite-volume method for compressible turbulent flow, finite-volume methods with the summation-by-parts property involve either equally weighted averaging or the second-order central flux for convective fluxes. In the present study, a cell-centered finite-volume method for compressible Naiver–Stokes equations was developed by combining a simultaneous-approximation term based on extrapolation and a low-dissipative discretization method without the summation-by-parts property. Direct numerical simulations and a large eddy simulation show that the resultant combination leads to comparable non-reflecting performance to that of the summation-by-parts scheme combined with the simultaneous-approximation term reported in the literature. Furthermore, a characteristic boundary condition was implemented for the present method, and its performance was compared with that of the simultaneous-approximation term for a direct numerical simulation and a large eddy simulation to show that the simultaneous-approximation term better maintained the average target pressure at the compressible flow outlet, which is useful for turbomachinery and aerodynamic applications, while the characteristic boundary condition better preserved the flow field near the outlet.

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Zhang, Huajian, Xiao-Wei Guo, Chao Li, Qiao Liu, Hanwen Xu i Jie Liu. "Accelerating FVM-Based Parallel Fluid Simulations with Better Grid Renumbering Methods". Applied Sciences 12, nr 15 (28.07.2022): 7603. http://dx.doi.org/10.3390/app12157603.

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Grid renumbering techniques have been shown to be effective in improving the efficiency of computational fluid dynamics (CFD) numerical simulations based on the finite volume method (FVM). However, with the increasing complexity of real-world engineering scenarios, there is still a huge challenge to choose better sequencing techniques to improve parallel simulation performance. This paper designed an improved metric (MDMP) to evaluate the structure of sparse matrices. The metric takes the aggregation of non-zero elements inside the sparse matrix as an evaluation criterion. Meanwhile, combined with the features of the cell-centered finite volume method supporting unstructured grids, we proposed the cell quotient (CQ) renumbering algorithm to further reduce the maximum bandwidth and contours of large sparse matrices with finite volume discretization. Finally, with real-world engineering cases, we quantitatively analyzed the evaluation effect of MDMP and the optimization effect of different renumbering algorithms. The results showed that the classical greedy algorithm reduces the maximum bandwidth of the sparse matrix by at most 60.34% and the profile by 95.38%. Correspondingly, the CQ algorithm reduced them by at most 92.94% and 98.70%. However, in terms of MDMP, the CQ algorithm was 83.43% less optimized than the Greedy algorithm. In terms of overall computational speed, the Greedy algorithm was optimized by a maximum of 38.19%, and the CQ algorithm was optimized by a maximum of 27.31%. The above is in accordance with the evaluation results of the MDMP metric. Thus, our new metric can more accurately evaluate the renumbering method for numerical fluid simulations, which is of great value in selecting a better mesh renumbering method in engineering applications of CFD.

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Selzer, Philipp, i Olaf A. Cirpka. "Postprocessing of standard finite element velocity fields for accurate particle tracking applied to groundwater flow". Computational Geosciences 24, nr 4 (24.06.2020): 1605–24. http://dx.doi.org/10.1007/s10596-020-09969-y.

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Abstract Particle tracking is a computationally advantageous and fast scheme to determine travel times and trajectories in subsurface hydrology. Accurate particle tracking requires element-wise mass-conservative, conforming velocity fields. This condition is not fulfilled by the standard linear Galerkin finite element method (FEM). We present a projection, which maps a non-conforming, element-wise given velocity field, computed on triangles and tetrahedra, onto a conforming velocity field in lowest-order Raviart-Thomas-Nédélec ($\mathcal {RTN}_{0}$ R T N 0 ) space, which meets the requirements of accurate particle tracking. The projection is based on minimizing the difference in the hydraulic gradients at the element centroids between the standard FEM solution and the hydraulic gradients consistent with the $\mathcal {RTN}_{0}$ R T N 0 velocity field imposing element-wise mass conservation. Using the conforming velocity field in $\mathcal {RTN}_{0}$ R T N 0 space on triangles and tetrahedra, we present semi-analytical particle tracking methods for divergent and non-divergent flow. We compare the results with those obtained by a cell-centered finite volume method defined for the same elements, and a test case considering hydraulic anisotropy to an analytical solution. The velocity fields and associated particle trajectories based on the projection of the standard FEM solution are comparable to those resulting from the finite volume method, but the projected fields are smoother within zones of piecewise uniform hydraulic conductivity. While the $\mathcal {RTN}_{0}$ R T N 0 -projected standard FEM solution is thus more accurate, the computational costs of the cell-centered finite volume approach are considerably smaller.

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Alakashi, Abobaker Mohammed, Hamidon Bin Salleh i Bambang Basuno. "The Implementation of Cell-Centred Finite Volume Method over Five Nozzle Models". Applied Mechanics and Materials 393 (wrzesień 2013): 305–10. http://dx.doi.org/10.4028/www.scientific.net/amm.393.305.

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The continued research and development of high-order methods in Computational Fluid Dynamics (CFD) is primarily motivated by their potential to significantly reduce the computational cost and memory usage required to obtain a solution to a desired level of accuracy. The present work presents the developed computer code based on Finite Volume Methods (FVM) Cell-centred Finite Volume Method applied for the case of Quasi One dimensional Inviscid Compressible flow, namely the flow pass through a convergent divergent nozzle. In absence of the viscosity, the governing equation of fluid motion is well known as Euler equation. This equation can behave as Elliptic or as Hyperbolic partial differential equation depended on the local value of its flow Mach number. As result, along the flow domain, governed by two types of partial differential equation, in the region in which the local mach number is less than one, the governing equation is elliptic while the other part is hyperbolic due to the local Mach number is a higher than one. Such a mixed type of equation is difficult to be solved since the boundary between those two flow domains is not clear. However by treating as time dependent flow problems, in respect to time, the Euler equation becomes a hyperbolic partial differential equation over the whole flow domain. There are various Finite Volume Methods can be used for solving hyperbolic type of equation, such as Cell-centered scheme, Cusp Scheme Roe Upwind Scheme and TVD Scheme. The present work will concentrate on the case of one dimensional flow problem through five nozzle models. The results of implementation of Cell Centred Finite Volume method to these five flow nozzle problems are very encouraging. This approach able to capture the presence of shock wave with very good results.

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WANG, Y. J., N. ZHAO, C. W. WANG i D. H. WANG. "A SECOND-ORDER ADAPTIVE ARBITRARY LAGRANGIAN–EULERIAN METHOD FOR THE COMPRESSIBLE EULER EQUATIONS". Modern Physics Letters B 23, nr 04 (10.02.2009): 583–601. http://dx.doi.org/10.1142/s0217984909017923.

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Most of finite volume schemes in the Arbitrary Lagrangian–Eulerian (ALE) method are constructed on the staggered mesh, where the momentum is defined at the nodes and the other variables (density, pressure and specific internal energy) are cell-centered. However, this kind of schemes must use a cell-centered remapping algorithm twice which is very inefficient. Furthermore, there is inconsistent treatment of the kinetic and internal energies.1 Recently, a new class of cell-centered Lagrangian scheme for two-dimensional compressible flow problems has been proposed in Ref. 2. The main new feature of the algorithm is the introduction of four pressures on each edge, two for each node on each side of the edge. This scheme is only first-order accurate. In this paper, a second-order cell-centered conservative ENO Lagrangian scheme is constructed by using an ENO-type approach to extend the spatial second-order accuracy. Time discretization is based on a second-order Runge–Kutta scheme. Combining a conservative interpolation (remapping) method3,4 with the second-order Lagrangian scheme, a kind of cell-centered second-order ALE methods can be obtained. Some numerical experiments are made with this method. All results show that our method is effective and have second-order accuracy. At last, in order to further increase the resolution of shock regions, we use an adaptive mesh generation based on the variational principle5 as a rezoned strategy for developing a class of adaptive ALE methods. Numerical experiments are also presented to valid the performance of the proposed method.

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Charest, Marc R. J., Clinton P. T. Groth i Pierre Q. Gauthier. "A High-Order Central ENO Finite-Volume Scheme for Three-Dimensional Low-Speed Viscous Flows on Unstructured Mesh". Communications in Computational Physics 17, nr 3 (marzec 2015): 615–56. http://dx.doi.org/10.4208/cicp.091013.281114a.

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AbstractHigh-order discretization techniques offer the potential to significantly reduce the computational costs necessary to obtain accurate predictions when compared to lower-order methods. However, efficient and universally-applicable high-order discretizations remain somewhat illusive, especially for more arbitrary unstructured meshes and for incompressible/low-speed flows. A novel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is proposed for the solution of the conservation equations of viscous, incompressible flows on three-dimensional unstructured meshes. Similar to finite element methods, coordinate transformations are used to maintain the scheme’s order of accuracy even when dealing with arbitrarily-shaped cells having non-planar faces. The proposed scheme is applied to the pseudo-compressibility formulation of the steady and unsteady Navier-Stokes equations and the resulting discretized equations are solved with a parallel implicit Newton-Krylov algorithm. For unsteady flows, a dual-time stepping approach is adopted and the resulting temporal derivatives are discretized using the family of high-order backward difference formulas (BDF). The proposed finite-volume scheme for fully unstructured mesh is demonstrated to provide both fast and accurate solutions for steady and unsteady viscous flows.

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Vadakkepatt, Ajay, Sanjay R. Mathur i Jayathi Y. Murthy. "Efficient automatic discrete adjoint sensitivity computation for topology optimization – heat conduction applications". International Journal of Numerical Methods for Heat & Fluid Flow 28, nr 2 (5.02.2018): 439–71. http://dx.doi.org/10.1108/hff-01-2017-0011.

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Purpose Topology optimization is a method used for developing optimized geometric designs by distributing material pixels in a given design space that maximizes a chosen quantity of interest (QoI) subject to constraints. The purpose of this study is to develop a problem-agnostic automatic differentiation (AD) framework to compute sensitivities of the QoI required for density distribution-based topology optimization in an unstructured co-located cell-centered finite volume framework. Using this AD framework, the authors develop and demonstrate the topology optimization procedure for multi-dimensional steady-state heat conduction problems. Design/methodology/approach Topology optimization is performed using the well-established solid isotropic material with penalization approach. The method of moving asymptotes, a gradient-based optimization algorithm, is used to perform the optimization. The sensitivities of the QoI with respect to design variables, required for optimization algorithm, are computed using a discrete adjoint method with a novel AD library named residual automatic partial differentiator (Rapid). Findings Topologies that maximize or minimize relevant quantities of interest in heat conduction applications are presented. The efficacy of the technique is demonstrated using a variety of realistic heat transfer applications in both two and three dimensions, in conjugate heat transfer problems with finite conductivity ratios and in non-rectangular/non-cuboidal domains. Originality/value In contrast to most published work which has either used finite element methods or Cartesian finite volume methods for transport applications, the topology optimization procedure is developed in a general unstructured finite volume framework. This permits topology optimization for flow and heat transfer applications in complex design domains such as those encountered in industry. In addition, the Rapid library is designed to provide a problem-agnostic pathway to automatically compute all required derivatives to machine accuracy. This obviates the necessity to write new code for finding sensitivities when new physics are added or new cost functions are considered and permits general-purpose implementations of topology optimization for complex industrial applications.

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Denicolai, Emilie, Stéphane Honoré, Florence Hubert i Rémi Tesson. "Microtubules (MT) a key target in oncology: mathematical modeling of anti-MT agents on cell migration". Mathematical Modelling of Natural Phenomena 15 (2020): 63. http://dx.doi.org/10.1051/mmnp/2020004.

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Microtubules (MTs) are protein filaments found in all eukaryotic cells which are crucial for many cellular processes including cell movement, cell differentiation, and cell division, making them a key target for anti-cancer treatment. In particular, it has been shown that at low dose, MT targeted agents (MTAs) may induce an anti-migratory effect on cancer and endothelial cells, leading to new prospects in cancer therapy. In that context, we propose to better understand the role of MT dynamics and thus of MTAs on cell migration using a mathematical cell centered model of cell migration taking into account the action of microtubules in the process. The model use a fluid based approach that describes, through level-set techniques, the deformation of the membrane during cell migration. The fluid part of the model is mainly composed of Stokes equations and the biochemical state of the cell is described using Reaction-Diffusion equations. Microtubules act on the biochemical state by activating or inactivating proteins of the Rho-GTPases family. The numerical simulation of the model is performed using Discrete Duality Finite Volume techniques. We describe the different schemes used for the simulation, focusing on the adaptation of preexisting methods to our particular case. Numerical simulation are performed, showing a realistic behavior of the simulated cells in term of shape, speed and microtubules dynamics. Different strategies for a depolymerizing MTA (Vincristin) mechanisms are investigated and show the robutness of our model.

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Tseng, K. C., Y. Y. Lian, Y. S. Chen, T. C. Kuo, B. R. Gu i J. S. Wu. "Simulations of the FORMOSAT-5 Cold Gas Propulsion System by Using the Hybrid Continuum-Particle Method". Applied Mechanics and Materials 110-116 (październik 2011): 707–14. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.707.

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Reaction control subsystem (RCS) is an onboard satellite propulsion system used to provide required thrusting for orbit raising, orbit maintenance, and attitude control etc.. High pressure flow with high temperature could be generated in a chamber by chemical reactions or other power resources then expelled through a convergent-divergent nozzle to obtain thrust. In order to optimize the thrusting performance, numerical simulation is an efficient method to study the physics and parameters in design phase. In the current study, a hybrid method coupled continuum and particle methods is proposed to simulate flows involving continuum and rarefied regions. The Navier-Stokes (NS) solver named UNIC is developed by Chen and his coworkers. It employs the cell-centered finite-volume method with a hybrid 2D/3D unstructured-grid topology. The proposed particle code named Parallel DSMC Code (PDSC) is a parallelized solver based on the well-known Direct Simulation of Monte Carlo (DSMC) method, which was proposed by Bird in 1976. The physical domain is decomposed into several regimes and each sub-domain executes the serial DSMC code at different processor for speeding up the computing. A practical cold gas thruster with different chamber pressures is simulated by using this hybrid code to study the potential malfunction of the pressure regulator. Then the curve-fitting thrusting equation can be referred to satellite control operations.

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Zhang, Wenjuan, i Mohammed Al Kobaisi. "A Globally Coupled Pressure Method for the Discretization of the Tensor-Pressure Equation on Non-K-orthogonal Grids". SPE Journal 22, nr 02 (27.10.2016): 679–98. http://dx.doi.org/10.2118/184405-pa.

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Summary Complex permeability tensors together with general nonorthogonal and unstructured grids pose great challenges to reservoir simulation. The widely used two-point flux approximation (TPFA) is inadequate for a rigorous discretization of the flow equations on such challenging grids. Multipoint flux approximation (MPFA) methods have been proposed to meet the challenges and are currently being deployed in next-generation simulators. In this work, we propose an alternative flux-continuous cell-centered finite-volume method called the globally coupled pressure (GCP) method to discretize the pressure equation on general grids with full permeability tensors. To accurately construct fluxes through control-volume interfaces, pressure at the centroid of all interfaces is introduced as auxiliary unknowns. Flux continuity across each interface gives one equation. Assembling all the flux-continuity equations together gives a system of linear equations that can be solved simultaneously for all the auxiliary unknowns. Flux across control-volume interfaces can then be approximated with the pressure values at control-volume centers only. The fundamental difference between the GCP method and MPFA methods is that, in the latter, auxiliary unknowns are locally coupled within an interaction region and then eliminated in a local stencil by imposing flux-continuity conditions, whereas in the former, all the auxiliary unknowns are globally coupled and can only be eliminated in a global stencil. Consequently, control volumes in our GCP method are directly associated with the edges of the original grid and not by means of a dual grid overlaid and allied with the centers of the grid. Two variants of the GCP method are presented here, and extensive numerical experiments are conducted to test the performance of the GCP methods. The results show that both variants of our GCP method are in good agreement with the classical MPFA-O method on non-K-orthogonal grids for less-challenging problems. Convergence studies reveal that the first variant of our GCP method has slower convergence rates than the MPFA-O method for some problems. However, the second variant of GCP has comparable, and in some cases, better convergence properties compared with the MPFA-O method. With numerical experiments, we further investigate monotonicity properties of our GCP method on highly anisotropic media. For Dirichlet boundary conditions, our GCP methods also suffer from nonphysical oscillations, with some degrees of improvement over the MFPA-O method. When no-flow boundary conditions are used, our GCP method is much more robust and does not produce spurious boundary extrema as MPFA methods do. Finally, we extend our GCP method to fully unstructured grids, and the results show that it is also more robust than the MPFA-O method on unstructured grids.

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Zhang, Wenjuan, i Mohammed Al Kobaisi. "A New Nonlinear Two-Point Flux Approximation Method for Solving the Anisotropic Diffusion Equation with Reduced Violations of the Discrete Maximum/Minimum Principle". SPE Journal 27, nr 01 (26.10.2021): 613–31. http://dx.doi.org/10.2118/206749-pa.

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Summary A class of monotone cell-centered nonlinear finite-volume methods has been proposed in the past decade to solve the anisotropic diffusion equation. The nonlinear two-point flux approximation (TPFA) (NTPFA) method preserves the nonnegativity of the solution values but can violate the discrete maximum/minimum principle (DMP). To enforce DMP, the nonlinear multipoint flux approximation (NMPFA) method ought to be used. In this work, we propose a novel NTPFA method that can reduce the severity of DMP violations significantly compared with the standard NTPFA method. The new formulation uses conormal decomposition for the construction of the one-sided fluxes. To define the unique flux through a connection between two cells, we choose a convex combination of the two one-sided fluxes such that the absolute differences of the magnitudes of the two transmissibility terms associated with the two neighboring cells are minimized, thus bringing the discrete coefficient matrix closer to having the zero row-sum property. Numerical experiments are conducted to test the performance of the new NTPFA method. The results demonstrate that the new scheme has comparable convergence order for both the solution and the flux compared with the standard NTPFA method or the classical multi-point flux approximation (MPFA-O) method. Moreover, the new NTPFA formulation shows marked improvements over the standard NTPFA in terms of reducing DMP violations. However, depending on the specific problem configuration, our new NTPFA formulation can lead to a system of nonlinear equations that is more difficult to solve.

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Kong, Lingfa, i Yidao Dong and Wei Liu. "Corrected Linear-Galerkin Schemes to Preserve Second-Order Accuracy for Cell-Centered Unstructured Finite Volume Methods". Advances in Applied Mathematics and Mechanics, czerwiec 2024, 0. http://dx.doi.org/10.4208/aamm.oa-2023-0113.

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Coatléven, Julien. "Unconditionally stable small stencil enriched multiple point flux approximations of heterogeneous diffusion problems on general meshes". IMA Journal of Numerical Analysis, 24.11.2023. http://dx.doi.org/10.1093/imanum/drad087.

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Abstract We derive new multiple point flux approximations (MPFA) for the finite volume approximation of heterogeneous and anisotropic diffusion problems on general meshes, in dimensions 2 and 3. The resulting methods are unconditionally stable while preserving the small stencil typical of MPFA finite volumes. The key idea is to solve local variational problems with a well-designed stabilization term from which we deduce conservative flux instead of directly prescribing a flux formula and solving the usual flux continuity equations. The boundary conditions of our local variational problems are handled through additional cell-centered unknowns, leading to an overall scheme with the same number of unknowns than first-order discontinuous Galerkin methods. Convergence results follow from well-established frameworks, while numerical experiments illustrate the good behavior of the method.

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Stefanin Volpiani, Pedro, Jean-Baptiste Chapelier, Axel Schwöppe, Jens Jägersküpper i Steeve Champagneux. "Aircraft Simulations Using the New CFD Software from ONERA, DLR, and Airbus". Journal of Aircraft, 23.02.2024, 1–13. http://dx.doi.org/10.2514/1.c037506.

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This paper presents a thorough comparison between RANS simulations performed with the computational fluid dynamics by ONERA, DLR, and Airbus (CODA) new-generation flow solver and reference legacy codes TAU (DLR) and elsA (ONERA) for high-speed cruising NASA Common Research Model (CRM) configurations that were considered in the context of the 5th, 6th, and 7th Drag Prediction Workshops. The solver’s accuracy is assessed with several meshing strategies, including block-structured, hybrid-structured/unstructured, and fully unstructured tetrahedral meshes. This solver features both a cell-centered finite-volume (FV) scheme suited to arbitrary meshes as well as a modern high-order discontinuous Galerkin (DG) scheme. We show that for all cases considered, the FV component recovers an equivalent accuracy compared to elsA (cell-centered FV) on block-structured meshes and TAU (node-centered FV) on hybrid and unstructured meshes. The high-order DG scheme (third-order accurate) is found to significantly enhance the drag prediction on coarse meshes compared to legacy FV methods, both for structured and unstructured meshes.

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Katsuno, Eduardo Tadashi, Andreas Peters i Ould el Moctar. "Numerical Seakeeping Analysis for a Floating Helicopter after Ditching in Waters". Journal of Offshore Mechanics and Arctic Engineering, 10.06.2024, 1–45. http://dx.doi.org/10.1115/1.4065709.

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Abstract This paper investigates the seakeeping behavior of helicopters after an emergency landing in water, focusing on a Northern North Sea wave climate and considering a realistic helicopter geometry. Computational Fluid Dynamics (CFD) techniques, including the cell-centered Finite Volume Method and Boundary Element Methods (BEM), were utilized to analyze motion responses and load distribution. The study ensures numerical result reliability through best simulation practices. Results indicate that the inviscid model produces similar outcomes to the viscous model in decay tests with roll, pitch, and heave motions. Natural periods for roll, pitch, and heave motions were obtained. Linearity between incident wave amplitude and pitch/heave response was noted for regular waves, while roll linearity was limited for small angles. In irregular wave conditions, helicopters tended to align perpendicular to waves over time, resulting in increased peak roll angles with higher significant wave heights. Exceedance rates of maximum roll peaks, useful for the assessment of capsizing probability, were quantified for different significant wave heights.

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