Adaptive Mesh Redistibution Method Based on Godunov's Scheme
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Abstract:
ÇÅź Å ÌÀº Ë Áº ¾¼¼¿ ÁÒØ ÖÒ Ø ÓÒ Ð ÈÖ ×× ÎÓкKeywords:
Godunov's scheme
Adaptive Mesh Refinement
Robustness
Solver
Interpolation
We perform adaptive mesh refinement (AMR) using the Residual error estimation method for two dimensional laminar backward-facing step flow and three dimensional turbulent flow around a low-rise building. In addition to that we make parametric studies about control parameters for AMR and examine relationship between error of calculated flow and number of ells on meshes generated by AMR. Consequently we reveal that we can generate cost-effective grid automatically for the above flow cases by performing directional AMR using appropriate control parameters even if we have very few knowledge about mesh generation technique for computational fluid dynamics simulation.
Adaptive Mesh Refinement
Regular grid
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In the present paper, high-order finite volume schemes on unstructured grids developed in our previous papers are extended to solve three-dimensional inviscid and viscous flows. The high-order variational reconstruction technique in terms of compact stencil is improved to reduce local condition numbers. To further improve the efficiency of computation, the adaptive mesh refinement technique is implemented in the framework of high-order finite volume methods. Mesh refinement and coarsening criteria are chosen to be the indicators for certain flow structures. One important challenge of the adaptive mesh refinement technique on unstructured grids is the dynamic load balancing in parallel computation. To solve this problem, the open-source library p4est based on the forest of octrees is adopted. Several two- and three-dimensional test cases are computed to verify the accuracy and robustness of the proposed numerical schemes.
Inviscid flow
Stencil
Adaptive Mesh Refinement
Robustness
Unstructured grid
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Water hammer
Godunov's scheme
Transient flow
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Aims. In this paper, we present a new method to perform numerical simulations of astrophysical MHD flows using the Adaptive Mesh Refinement framework and Constrained Transport.
Adaptive Mesh Refinement
Godunov's scheme
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In order to obtain good results from the finite element method the mesh used should suit the behaviour of the field. The adaptive mesh generation offers an automatic way to generate meshes fitting the problem. In this paper the effectiveness of the adaptive mesh generation is measured by comparing the error in the field solution of uniformly and adaptively generated meshes both for the 2D and the 3D case.
Adaptive Mesh Refinement
Volume mesh
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Godunov's scheme
Stencil
Tetrahedron
Flux limiter
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Adaptive Mesh Refinement
Laplacian smoothing
T-vertices
Triangle mesh
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In this paper, the use of adaptive mesh generation is proposed as a method of streamer simulation. The error estimation scheme is also presented. The employed adaptive scheme can refine the mesh where needed. In addition, it is possible to coarsen the unnecessarily dense mesh. For a numerical example, the propagation of a negative streamer was simulated and the results were shown. Through the adaptive mesh generation, we can obtain not only higher resolution but also more efficient grid distribution with a smaller number of grids.
Adaptive Mesh Refinement
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ÇÅź Å ÌÀº Ë Áº ¾¼¼¿ ÁÒØ ÖÒ Ø ÓÒ Ð ÈÖ ×× ÎÓк
Godunov's scheme
Adaptive Mesh Refinement
Robustness
Solver
Interpolation
Cite
Citations (33)
To efficiently solve the extended Boussinesq equations,a hybrid finite-difference and finite-volume scheme is developed. The one-dimensional governing equations are kept in conservation form. The flux term is discretized using the finite volume method,while the remaining terms are discretized using the finite difference method. A Godunov-type high resolution scheme,in conjunction with the Harten-Lax and van Leer( HLL) Riemann solver and the higher accuracy MUSCL( Monotone Upwind Schemes for Scalar Conservation Laws) method for variable reconstruction,is adopted to compute the interface flux. High order central difference formulas are used to discretize the remaining terms. The third order Runge-Kutta method with total variation diminishing( TVD) property is adopted for time marching. Numerical tests are conducted for model validation,and the computed results agree well with experimental data.
Total variation diminishing
Conservation law
Godunov's scheme
Finite difference
Flux limiter
Upwind scheme
Courant–Friedrichs–Lewy condition
Roe solver
Shallow water equations
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