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Journal articles on the topic "ENO (Essentially Non-Oscillatory) and WENO method.]"
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Janett, Gioele, Oskar Steiner, Ernest Alsina Ballester, Luca Belluzzi, and Siddhartha Mishra. "A novel fourth-order WENO interpolation technique." Astronomy & Astrophysics 624 (April 2019): A104. http://dx.doi.org/10.1051/0004-6361/201834761.
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Context. Several numerical problems require the interpolation of discrete data that present at the same time (i) complex smooth structures and (ii) various types of discontinuities. The radiative transfer in solar and stellar atmospheres is a typical example of such a problem. This calls for high-order well-behaved techniques that are able to interpolate both smooth and discontinuous data. Aims. This article expands on different nonlinear interpolation techniques capable of guaranteeing high-order accuracy and handling discontinuities in an accurate and non-oscillatory fashion. The final aim is to propose new techniques which could be suitable for applications in the context of numerical radiative transfer. Methods. We have proposed and tested two different techniques. Essentially non-oscillatory (ENO) techniques generate several candidate interpolations based on different substencils. The smoothest candidate interpolation is determined from a measure for the local smoothness, thereby enabling the essentially non-oscillatory property. Weighted ENO (WENO) techniques use a convex combination of all candidate substencils to obtain high-order accuracy in smooth regions while keeping the essentially non-oscillatory property. In particular, we have outlined and tested a novel well-performing fourth-order WENO interpolation technique for both uniform and nonuniform grids. Results. Numerical tests prove that the fourth-order WENO interpolation guarantees fourth-order accuracy in smooth regions of the interpolated functions. In the presence of discontinuities, the fourth-order WENO interpolation enables the non-oscillatory property, avoiding oscillations. Unlike Bézier and monotonic high-order Hermite interpolations, it does not degenerate to a linear interpolation near smooth extrema of the interpolated function. Conclusion. The novel fourth-order WENO interpolation guarantees high accuracy in smooth regions, while effectively handling discontinuities. This interpolation technique might be particularly suitable for several problems, including a number of radiative transfer applications such as multidimensional problems, multigrid methods, and formal solutions.
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Shu, Chi-Wang. "Essentially non-oscillatory and weighted essentially non-oscillatory schemes." Acta Numerica 29 (May 2020): 701–62. http://dx.doi.org/10.1017/s0962492920000057.
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Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popular in applications, most noticeably in computational fluid dynamics but also in other areas of computational physics and engineering. Since the main idea of the ENO and WENO schemes is an approximation procedure not directly related to partial differential equations (PDEs), ENO and WENO schemes also have non-PDE applications. In this paper we will survey the basic ideas behind ENO and WENO schemes, discuss their properties, and present examples of their applications to different types of PDEs as well as to non-PDE problems.
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Schmidt, Alex A., Alice de Jesus Kozakevicius, and Stefan Jakobsson. "A parallel wavelet adaptive WENO scheme for 2D conservation laws." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 7 (July 3, 2017): 1467–86. http://dx.doi.org/10.1108/hff-08-2016-0295.
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Purpose The current work aims to present a parallel code using the open multi-processing (OpenMP) programming model for an adaptive multi-resolution high-order finite difference scheme for solving 2D conservation laws, comparing efficiencies obtained with a previous message passing interface formulation for the same serial scheme and considering the same type of 2D formulations laws. Design/methodology/approach The serial version of the code is naturally suitable for parallelization because the spatial operator formulation is based on a splitting scheme per direction for which the flux components are numerically computed by a Lax–Friedrichs factorization independently for each row or column. High-order approximations for numerical fluxes are computed by the third-order essentially non-oscillatory (ENO) and fifth-order weighted essentially non-oscillatory (WENO) interpolation schemes, assuming sparse grids in each direction. The grid adaptivity is obtained by a cubic interpolating wavelet transform applied in each space dimension, associated to a threshold operator. Time is evolved by a third order TVD Runge–Kutta method. Findings The parallel formulation is implemented automatically at compiling time by the OpenMP library routines, being virtually transparent to the programmer. This over simplifies any concerns about managing and/or updating the adaptive grid when compared to what is necessary to be done when other parallel approaches are considered. Numerical simulations results and the large speedups obtained for the Euler equations in gas dynamics highlight the efficiency of the OpenMP approach. Research limitations/implications The resulting speedups reflect the effectiveness of the OpenMP approach but are, to a large extension, limited by the hardware used (2 E5-2620 Intel Xeon processors, 6 cores, 2 threads/core, hyper-threading enabled). As the demand for OpenMP threads increases, the code starts to make explicit use of the second logical thread available in each E5-2620 processor core and efficiency drops. The speedup peak is reached near the possible maximum (24) at about 22, 23 threads. This peak reflects the hardware configuration and the true software limit should be located way beyond this value. Practical implications So far no attempts have been made to parallelize other possible code segments (for instance, the ENO|-WENO-TVD code lines that process the different data components which could potentially push the speed up limit to higher values even further. The fact that the speedup peak is located close to the present hardware limit reflects the scalability properties of the OpenMP programming and of the splitting scheme as well. Consequently, it is likely that the speedup peak with the OpenMP approach for this kind of problem formulation will be close to the physical (and/or logical) limit of the hardware used. Social implications This work is the result of a successful collaboration among researchers from two different institutions, one internationally well-known and with a long-term experience in applied mathematics for industrial applications and the other in a starting process of international academic insertion. In this way, this scientific partnership has the potential of promoting further knowledge exchange, involving students and other collaborators. Originality/value The proposed methodology (use of OpenMP programming model for the wavelet adaptive splitting scheme) is original and contributes to a very active research area in the past years, namely, adaptive methods for conservation laws and their parallel formulations, which is of great interest for the entire scientific community.
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Kuo, F. A., and J. S. Wu. "Implementation of a parallel high-order WENO-type Euler equation solver using a CUDA PTX paradigm." Journal of Mechanics 37 (2021): 496–512. http://dx.doi.org/10.1093/jom/ufab016.
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ABSTRACT This study proposes the optimization of a low-level assembly code to reconstruct the flux for a splitting flux Harten–Lax–van Leer (SHLL) scheme on high-end graphic processing units. The proposed solver is implemented using the weighted essentially non-oscillatory reconstruction method to simulate compressible gas flows that are derived using an unsteady Euler equation. Instructions in the low-level assembly code, i.e. parallel thread execution and instruction set architecture in compute unified device architecture (CUDA), are used to optimize the CUDA kernel for the flux reconstruction method. The flux reconstruction method is a fifth-order one that is used to process the high-resolution intercell flux for achieving a highly localized scheme, such as the high-order implementation of SHLL scheme. Many benchmarking test cases including shock-tube and four-shock problems are demonstrated and compared. The results show that the reconstruction method is computationally very intensive and can achieve excellent performance up to 5183 GFLOP/s, ∼66% of peak performance of NVIDIA V100, using the low-level CUDA assembly code. The computational efficiency is twice the value as compared with the previous studies. The CUDA assembly code reduces 26.7% calculation and increases 37.5% bandwidth. The results show that the optimal kernel reaches up to 990 GB/s for the bandwidth. The overall efficiency of bandwidth and computation performance achieves 127% of the predicted performance based on the HBM2-memory roofline model estimated by Empirical Roofline Tool.
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Wolf, W. R., and J. L. F. Azevedo. "IMPLEMENTATION OF ENO AND WENO SCHEMES FOR FINITE VOLUME UNSTRUCTURED GRID SOLUTIONS OF COMPRESSIBLE AERODYNAMIC FLOWS." Revista de Engenharia Térmica 6, no. 1 (June 30, 2007): 48. http://dx.doi.org/10.5380/reterm.v6i1.61817.
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In this work the essentially non-oscillatory schemes (ENO) and the weighted essentially non-oscillatory schemes (WENO) are implemented in a cell centered finite volume context on unstructured meshes. The 2-D Euler equations will be considered to represent the flows of interest. The ENO and WENO schemes have been developed with the purpose of accurately capturing discontinuities appearing in problems governed by hyperbolic conservation laws. In the high Mach number aerodynamic studies of interest in the present paper, these discontinuities are mainly represented by shock waves and contact discontinuities. The entire reconstruction process of ENO and WENO schemes is described in detail for linear polynomials and, therefore, second-order of accuracy. An extension to higher orders of accuracy is presented in the paper in a straightforward manner and applications for compressible flows are shown. These applications compare the accuracy of the schemes with some related data that appear in the references cited in this paper or that come from analytical solutions.
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Kadioglu, Samet Y., and Veli Colak. "An Essentially Non-Oscillatory Spectral Deferred Correction Method for Conservation Laws." International Journal of Computational Methods 13, no. 05 (August 31, 2016): 1650027. http://dx.doi.org/10.1142/s0219876216500274.
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We present a computational method based on the Spectral Deferred Corrections (SDC) time integration technique and the Essentially Non-Oscillatory (ENO) finite volume method for the conservation laws (one-dimensional Euler equations). The SDC technique is used to advance the solutions in time with high-order of accuracy. The ENO method is used to define high-order cell edge quantities that are then used to evaluate numerical fluxes. The coupling of the SDC method with a high-order finite volume method (Piece-wise Parabolic Method (PPM)) for solving the conservation laws is first carried out by Layton et al. in [Layton, A. T. and Minion, M. L. [2004] “Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics,” J. Comput. Phys. 194(2), 697–714]. Issues about this approach have been addressed and some improvements have been added to it in [Kadioglu et al. [2012] “A gas dynamics method based on the spectral deferred corrections (SDC) time integration technique and the piecewise parabolic method (PPM),” Am. J. Comput. Math. 1–4, 303–317]. Here, we investigate the implications when the PPM method is replaced with the well-known ENO method. We note that the SDC-PPM method is fourth-order accurate in time and space. Therefore, we kept the order of accuracy of the ENO procedure as fourth-order in order to be able to make a consistent comparison between the two approaches (SDC-ENO versus SDC-PPM methods). We have tested the new SDC-ENO technique by solving several test problems involving moderate to strong shock waves and smooth/complex flow structures. Our numerical results show that we have numerically achieved the formally fourth-order convergence of the new method for smooth problems. Our numerical results also indicate that the newly proposed technique performs very well providing highly resolved shock discontinuities and fairly good contact solutions. More importantly, the discontinuities in the flow test problems are captured with essentially no-oscillations. We have numerically compared the fourth-order SDC-ENO scheme to the fourth-order SDC-PPM method for the same test problems. The results are similar for most of the test problems except in some cases the SDC-PPM method suffers from minor oscillations compared to SDC-ENO scheme being completely oscillation free.
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Zhu, Jun, and Jianxian Qiu. "Runge-Kutta Discontinuous Galerkin Method Using Weno-Type Limiters: Three-Dimensional Unstructured Meshes." Communications in Computational Physics 11, no. 3 (March 2012): 985–1005. http://dx.doi.org/10.4208/cicp.300810.240511a.
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AbstractThis paper further considers weighted essentially non-oscillatory (WENO) and Hermite weighted essentially non-oscillatory (HWENO) finite volume methods as limiters for Runge-Kutta discontinuous Galerkin (RKDG) methods to solve problems involving nonlinear hyperbolic conservation laws. The application discussed here is the solution of 3-D problems on unstructured meshes. Our numerical tests again demonstrate this is a robust and high order limiting procedure, which simultaneously achieves high order accuracy and sharp non-oscillatory shock transitions.
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Wang, Zhenming, Jun Zhu, Chunwu Wang, and Ning Zhao. "Finite difference alternative unequal-sized weighted essentially non-oscillatory schemes for hyperbolic conservation laws." Physics of Fluids 34, no. 11 (November 2022): 116108. http://dx.doi.org/10.1063/5.0123597.
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In this paper, two unequal-sized weighted essentially non-oscillatory (US-WENO) schemes are proposed for solving hyperbolic conservation laws. First, an alternative US-WENO (AUS-WENO) scheme based directly on the values of conserved variables at the grid points is designed. This scheme can inherit all the advantages of the original US-WENO scheme [J. Zhu and J. Qiu, “A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws,” J. Comput. Phys. 318, 110–121 (2016).], such as the arbitrariness of the linear weights. Moreover, this presented AUS-WENO scheme enables any monotone fluxes applicable to this framework, whereas the original US-WENO scheme is only suitable for the more dissipative smooth flux splitting. Therefore, the method in this paper has a smaller L1 and [Formula: see text] numerical errors than the original scheme under the same conditions. Second, in order to further improve the computational efficiency of the above AUS-WENO scheme, a hybrid AUS-WENO scheme is proposed by combining a hybrid strategy. This strategy identifies the discontinuous regions directly based on the extreme points of the reconstruction polynomial corresponding to the five-point stencil, which brings the important advantage that it does not depend on the specific problem and does not contain any artificial adjustable parameters. Finally, the performance of the above two AUS-WENO schemes in terms of low dissipation, shock capture capability, discontinuity detection capability, and computational efficiency is verified by some benchmark one- and two-dimensional numerical examples.
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Zhu, Jun, Xinghui Zhong, Chi-Wang Shu, and Jianxian Qiu. "Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter." Communications in Computational Physics 19, no. 4 (April 2016): 944–69. http://dx.doi.org/10.4208/cicp.070215.200715a.
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AbstractIn this paper, we propose a new type of weighted essentially non-oscillatory (WENO) limiter, which belongs to the class of Hermite WENO (HWENO) limiters, for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving hyperbolic conservation laws. This new HWENO limiter is a modification of the simple WENO limiter proposed recently by Zhong and Shu [29]. Both limiters use information of the DG solutions only from the target cell and its immediate neighboring cells, thus maintaining the original compactness of the DG scheme. The goal of both limiters is to obtain high order accuracy and non-oscillatory properties simultaneously. The main novelty of the new HWENO limiter in this paper is to reconstruct the polynomial on the target cell in a least square fashion [8] while the simple WENO limiter [29] is to use the entire polynomial of the original DG solutions in the neighboring cells with an addition of a constant for conservation. The modification in this paper improves the robustness in the computation of problems with strong shocks or contact discontinuities, without changing the compact stencil of the DG scheme. Numerical results for both one and two dimensional equations including Euler equations of compressible gas dynamics are provided to illustrate the viability of this modified limiter.
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Antona, Rubén, Renato Vacondio, Diego Avesani, Maurizio Righetti, and Massimiliano Renzi. "Towards a High Order Convergent ALE-SPH Scheme with Efficient WENO Spatial Reconstruction." Water 13, no. 17 (September 4, 2021): 2432. http://dx.doi.org/10.3390/w13172432.
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This paper studies the convergence properties of an arbitrary Lagrangian–Eulerian (ALE) Riemann-based SPH algorithm in conjunction with a Weighted Essentially Non-Oscillatory (WENO) high-order spatial reconstruction, in the framework of the DualSPHysics open-source code. A convergence analysis is carried out for Lagrangian and Eulerian simulations and the numerical results demonstrate that, in absence of particle disorder, the overall convergence of the scheme is close to the one guaranteed by the WENO spatial reconstruction. Moreover, an alternative method for the WENO spatial reconstruction is introduced which guarantees a speed-up of 3.5, in comparison with the classical Moving Least-Squares (MLS) approach.
Dissertations / Theses on the topic "ENO (Essentially Non-Oscillatory) and WENO method.]"
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Ivan, Lucian. "Development of High-order CENO Finite-volume Schemes with Block-based Adaptive Mesh Refinement (AMR)." Thesis, 2011. http://hdl.handle.net/1807/29759.
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A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares
reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction
procedure is used for cells in which the solution is fully resolved. Switching in the
hybrid procedure is determined by a solution smoothness indicator. The hybrid approach
avoids the complexity associated with other ENO schemes that require reconstruction on
multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional
compressible gaseous flows as well as for advection-diffusion problems characterized
by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent
solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.
Books on the topic "ENO (Essentially Non-Oscillatory) and WENO method.]"
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Chang-Qing, Hu, Shu Chi-Wang, and Institute for Computer Applications in Science and Engineering., eds. A technique of treating negative weights in WENO schemes. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2000.
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Jay, Casper, Old Dominion University. Research Foundation., and Langley Research Center, eds. Finite-volume application of high order eno schemes to two-dimensional boundary-value problems. Norfolk, Va: Old Dominion University Research Foundation, 1990.
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Jay, Casper, Old Dominion University. Research Foundation., and Langley Research Center, eds. Finite-volume application of high order eno schemes to two-dimensional boundary-value problems. Norfolk, Va: Old Dominion University Research Foundation, 1990.
Find full textBook chapters on the topic "ENO (Essentially Non-Oscillatory) and WENO method.]"
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Epstein, B., and S. Peigin. "Application of WENO (weighted essentially non-oscillatory) method to computational aerodynamics." In Computational Fluid and Solid Mechanics 2003, 893–97. Elsevier, 2003. http://dx.doi.org/10.1016/b978-008044046-0.50219-0.
Full textConference papers on the topic "ENO (Essentially Non-Oscillatory) and WENO method.]"
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Ibrahim, Osama M., Prasanna Welahettige, Knut Vågsæther, and Bernt Lie. "Modeling of the two-phase flow during depressurization of liquified CO2 in a pipe." In 63rd International Conference of Scandinavian Simulation Society, SIMS 2022, Trondheim, Norway, September 20-21, 2022. Linköping University Electronic Press, 2022. http://dx.doi.org/10.3384/ecp192032.
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Modeling transient CO2 two-phase flow in a pipe is essential in studying depressurization mechanisms resulting from liquified CO2 accidental release. Generated data from such models predict the released flow characteristics and possible propagating fractures. Accordingly, they provide valuable input for risk prevention in designing and safely operating CO2 transport pipelines. CO2 depressurization simulation involves fluid-mechanical and thermodynamic models, primarily expressed by hyperbolic partial differential equations and an equation of state (EOS). Besides, these models are solved with appropriate numerical methods. This paper deals with a drift flux - homogeneous equilibrium model (HEM) construction utilizing central-upwind-weighted essentially non-oscillatory (WENO) numerical schemes to describe two-phase flow during CO2 decompression in a pipe. Rapid transition in mass, momentum, and energy at the interface between liquid and vapor phases is assumed in the flow HEM. Thus, the two-phase flow is in a thermal, mechanical, and chemical equilibrium. The thermodynamic properties are calculated by applying Span-Wagner EOS. The high-resolution second-order central, central-upwind, and third-order weighted essentially non-oscillatory (WENO) schemes have been executed with the HEM, and they effectively captured rapid phase transition. The central-upwind and essentially non-oscillatory (ENO) schemes' stencils can be appropriate for constructing a higher-order accuracy central-upwind-WENO scheme. This structured scheme uses a smoothness indicator as an alternative to the limiter function. Besides, the variables in the cell interface are determined by WENO reconstruction, while central-upwind is used to compute the flux properties.
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Rajput, Uttam Singh, and Krishna Mohan Singh. "An Improved Hybrid Alternative WENO Scheme for High Mach Number Flows." In ASME 2021 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/fedsm2021-65717.
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Abstract This study presents the development of a fifth-order hybrid alternative mapped weighted essentially non-oscillatory scheme (HAW-M) for high-speed compressible flows. A new, improved smoothness indicator has been developed to design the HAW-M scheme. The performance of the present scheme has been evaluated through different one and two-dimensional test cases. The developed scheme shows higher accuracy and low dissipation. Further, it captures the fine-scale structures smoothly than the existing high-resolution method.
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Niu, Yang-Yao. "Numerical Simulation of Low-Speed Two Phase Flows Based on Preconditioning." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-04005.
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This paper first applies flux vector type splitting method based on numerical speed of sound for computing incompressible single and multi-fluid flows. Here, a preconditioning matrix based on Chorin’s artificial compressibility concept is used to modify the incompressible multi-fluid Navier-Stokes Equations to be hyperbolic and density or volume fraction independent. The current approach can reduce eigenvalues disparity induced from density or volume fraction ratio and enhance numerical stability. Also, a simple convection-pressure flux-splitting method with high-order essentially non-oscillatory (ENO) type primitive variable extrapolations coupling with an ENO-MUSCL type volume fraction recompressed reconstruction within a mesh cell is used to maintain the preservation of sharp interface evolutions in multi-fluid flow simulation. Benchmark tests including a solid rotation test of a notched 2D cylinder, the evolution of spiral and rotational shapes of deformable circles, a dam breaking problem, the Rayleigh-Taylor instability and the cavitated flow problems are chosen to validate the current incompressible multi-fluid methodology.
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Zhang, Juntao, and Raj M. Manglik. "Numerical Investigation of Single Bubble Dynamics During Nucleate Boiling in Aqueous Surfactant Solutions." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47047.
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The dynamics of a single growing and departing bubble during nucleate boiling from a horizontal heated surface in an aqueous surfactant solution has been numerically simulated. The full Navier-Stokes equations together with the bulk transport and adsorption-desorption-controlled surfactant interfacial transport equations are solved. A PDE-based fast local level-set method is used to computationally capture the vapor-liquid interface, and the dynamic surface tension is modeled as a body force on the interface. A second-order projection method along with a third-order ENO (essentially non-oscillatory) scheme for differencing the convection terms are applied for solving the momentum equation. The time discretization is dealt with a high order Runge-Kutta method. The multigrid preconditioned conjugate method (MPCG) is employed to solve the projection, which has strongly discontinuous coefficients caused by the physical properties jump across the vapor-liquid interface. The results illustrate the altered bubble dynamics in aqueous surfactant solutions, and their role in enhancing heat transfer.
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Wu, Benxin, Sha Tao, Yibo Gao, Yun Zhou, and Gary Cheng. "The Effect of External Magnetic Field on the Plasma Induced by Laser Ablation in Vacuum." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63259.
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During short-pulsed laser ablation (machining) process at sufficiently high intensities, a plasma plume may be generated above the target surface. In this paper, the effect of external magnetic fields on laser-induced plasma has been studied using a physics-based model. In the model, hydrodynamic equations coupled with wide-range equations of state are solved numerically using a finite-difference essentially non-oscillatory (ENO) method. The magnetic field affects the plasma evolution by inducing electric currents, and the associated electromagnetic force and Joule heating effect in the plasma. The study shows that the external magnetic field may decrease the plasma front expanding speed, and increase the plasma temperature. The study provides useful information for the fundamental study of laser-induced plasma, and for the practical applications of short-pulsed lasers in laser ablation (machining), laser-induced breakdown spectroscopy (LIBS), and other areas, where laser-induced plasma may play a very important role.
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Yang, Xiaofan, Zhongquan Charlie Zheng, and Ying Xu. "A Study on Flow Through a Periodic Array of Porous Medium Cylinders by Immersed-Boundary Methods." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30535.
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Numerical simulations with an immersed-boundary method are presented for the incompressible flow past a periodic array of porous-medium cylinders. Fluid/porous-medium interactions are greatly influenced by the accuracy on the interface between the surface of the porous cylinder and the flow around it, because of the sudden change in the governing equations for the fluid and for the porous material. In order to retain the smoothness on the interface, momentum fluxes near the interface are discretized using several schemes, including the 2nd- and 3rd-order upwind schemes and the 5th-order Weighted Essentially Non-Oscillatory (WENO) scheme. These schemes are combined with a direct-forcing immersed-boundary method to remove the discontinuity between the fluid and the porous material, and thus accuracy near the interface can be improved. Low and moderate Reynolds number flows, both outside and inside the porous cylinders, are computed simultaneously by solving a combined governing equation set for incompressible flow. The simulation is first validated using flow over an array of impermeable cylinders. The advantage of high-order schemes is then investigated by looking at the flow parameters near the interfaces between the porous cylinders and the outside flow. Species transport in flow with the porous-cylinder-array configuration is also studied.
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Farzin, Amir, Zahir Barahmand, and Bernt Lie. "Experimental PDE solver in Julia – comparison of flux limiting schemes." In 63rd International Conference of Scandinavian Simulation Society, SIMS 2022, Trondheim, Norway, September 20-21, 2022. Linköping University Electronic Press, 2022. http://dx.doi.org/10.3384/ecp192007.
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Finite Volume Methods (FVM) are high quality methods for solving conservative/hyperbolic partial differential equations (PDEs). A popular class of high-resolution methods utilize a nonlinear combination of low order methods and high order methods via flux limiting functions. Another class of high-resolution methods is the class of weighted essentially non-oscillatory (WENO) schemes. Here, the focus is on flux limiting schemes. An experimental finite volume (FV) semi-discrete solver for systems of hyperbolic PDEs has been implemented in Julia, utilizing Julia’s DifferentialEquations.jl package for handling the time marching. A first order upwind formulation is used for the low order method, and a central second order formulation is used for the high order method. The PDE can be provided either in flux form, or in quasi-linear form. In the former case, automatic differentiation (AD) package ForwardDiff.jl is used to compute the Jacobians of the flux vector. Package LinearAlgebra.jl is used to compute the eigenspace of the Jacobians. The implementation allows for up to 3 internal/external coordinates. More than a dozen flux limiting functions are given, with the possibility of the users to write their own flux limiters. The implementation allows for user provided spatial discretization points, and source terms in the PDE. In this paper, we will compare various flux limiting schemes for PDEs with analytic solutions, and will also compare flux limiting schemes for a simple granulation model (layering). Possible extensions of the experimental implementation include: (i) higher order methods, (ii) more extensive support for boundary conditions, (iii) improved support for source terms.
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Chella, Mayilvahanan Alagan, Hans Bihs, Arun Kamath, and Michael Muskulus. "Numerical Modeling of Breaking Waves Over a Reef With a Level-Set Based Numerical Wave Tank." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10363.
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Wave breaking is a highly unsteady, non-linear and extremely turbulent phenomenon. During the wave breaking process, the energy of the wave system is focused close to the crest of the wave and a spatial spread of wave energy occurs. Thus, the description of such a physical phenomenon is highly complex and it requires a deep insight into the breaking wave process. The accurate assessment of breaking wave kinematics is essential for an accurate prediction of hydrodynamic loads on structures. Besides, the understanding of the transformation of waves propagating over an artificial or natural reef is important concerning the coastal processes. The numerical model used in this study is a two-phase model, which solves the flow problem for air and water simultaneously. The Navier-Stokes equations are solved on uniform Cartesian grids in two dimensions. The complex free surface is captured by the level set method. A staggered grid is used for the computation with the velocities defined at the cell edges and the pressure at the cell centres. This avoids unphysical pressure oscillations that can occur due to the coupling of pressure and velocity in the incompressible Navier-Stokes equations. The Ghost Cell Immersed Boundary Method is employed to handle the boundary conditions for complex boundaries. Turbulence modelling is carried out using the k-ω model. Discretization of the convective terms is performed using the 5th order Weighted Essentially Non-Oscillatory (WENO) scheme. In this study, a two-dimensional numerical wave tank is used to simulate waves propagating over steep slopes and wave dissipation. The main objective of the present study is to investigate the wave breaking process over a submerged reef. This is accomplished by examining the wave profile during wave breaking and the breaker indices. Also, the numerical results are compared to data from physical experiments and the numerical results exhibit reasonable agreement with experimental data.
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Bihs, Hans, Arun Kamath, Mayilvahanan Alagan Chella, and Øivind A. Arntsen. "Extreme Wave Generation, Breaking and Impact Simulations With REEF3D." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61524.
Full textAbstract:
An accurate description of extreme waves is necessary in order to estimate maximum wave forces on offshore structures. On several occasions freak waves have been observed in the past, some causing severe damage. In order to model such extreme wave conditions with a computational fluid dynamics (CFD) model, emphasize needs to be put on the wave generation. One possibility is to use focused waves of first or second order based on irregular sea state wave spectra. For focused waves, the wave phase is chosen, so that the waves focus in a predetermined location at a specified time. Numerical tests have shown, that generating extreme waves based on this method is somewhat limited. The individual wave components are steep enough, that they start to break before the focus location. In the current paper, transient wave packets are used for extreme wave generation. This way, extreme waves can be generated that are higher, but only break at the concentration point. The transient wave packets method is implemented in the open-source CFD software REEF3D. This model uses the level set method for interface capturing. For the hydrodynamics, the Navier-Stokes equations are solved in three dimensions. The code employs a staggered Cartesian mesh, ensuring tight pressure-velocity coupling. Complex geometries are handled with a ghost cell immersed boundary method. High-performance computing is enabled through domain decomposition based parallelization. Convection discretization of the different flow variables is performed with the fifth-order WENO (weighted essentially non-oscillatory) scheme. For the explicit time treatment a third-order Runge-Kutta scheme is selected. In order to validate the extreme wave generation, numerical tests in an empty wave tank are performed and compared with experimental data. Then, the extreme wave breaking on a vertical circular cylinder is investigated.
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Bihs, Hans, Mayilvahanan Alagan Chella, Arun Kamath, and Øivind A. Arnsten. "Wave-Structure Interaction of Focussed Waves With REEF3D." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54917.
Full textAbstract:
For the stability of offshore structures, such as offshore wind foundations, extreme wave conditions need to be taken into account. Waves from extreme events can become critical from design perspective. In a numerical wave tank, extreme waves can be generated through focussed waves. Here, linear waves are generated from a wave spectrum. The wave crests of the generated waves coincide at a pre-selected location and time. In order to test the generated waves, the time series of the free surface elevation are compared with experimental benchmark cases. The numerically simulated free surface shows good agreement with the measurements from experiments. In further computations, the wave impact of the focussed waves on a vertical circular cylinder is investigated. The focussed wave generation is implemented in the numerical wave tank module of REEF3D, which has been extensively and successfully tested for various wave hydrodynamics and wave-structure interaction problems in particular and for free surface flows in general. The open-source CFD code REEF3D solves the three-dimensional Navier-Stokes equations on a staggered Cartesian grid. Solid boundaries are taken into account with the ghost cell immersed boundary method. For the discretization of the convection terms of the momentum equations, the conservative finite difference version of the fifth-order WENO (weighted essentially non-oscillatory) scheme is used. For temporal treatment, the third-order TVD (total variation diminishing) Runge-Kutta scheme is employed. For the pressure, the projection method is used. The free surface flow is solved as two-phase fluid system. For the interface capturing, the level set method is selected. The level set function can be discretized with high-order differencing schemes. This makes it the appropriate solution for wave propagation problems based on Navier-Stokes solvers, which requires high-order numerical methods to avoid artificial wave damping. The numerical model is fully parallelized based on the domain decomposition, using MPI (message passing interface) for internode communication.