A least squares based diamond scheme for anisotropic diffusion problems on polygonal meshes

2021 ◽  
Author(s):  
Cheng Dong ◽  
Tong Kang
Keyword(s):  
Least Squares ◽  
Anisotropic Diffusion ◽  
Polygonal Meshes ◽  
Diffusion Problems

ON VERTEX RECONSTRUCTIONS FOR CELL-CENTERED FINITE VOLUME APPROXIMATIONS OF 2D ANISOTROPIC DIFFUSION PROBLEMS

2007 ◽  
Vol 17 (01) ◽  
pp. 1-32 ◽  
Author(s):  
ENRICO BERTOLAZZI ◽  
GIANMARCO MANZINI
Keyword(s):  
Boundary Conditions ◽  
Least Squares ◽  
Finite Volume ◽  
Anisotropic Diffusion ◽  
Neumann Boundary ◽  
Linear Constraints ◽  
Neumann Boundary Conditions ◽  
Benchmark Problems ◽  
New Variant ◽  
Diffusion Problems

The accuracy of the diamond scheme is experimentally investigated for anisotropic diffusion problems in two space dimensions. This finite volume formulation is cell-centered on unstructured triangulations and the numerical method approximates the cell averages of the solution by a suitable discretization of the flux balance at cell boundaries. The key ingredient that allows the method to achieve second-order accuracy is the reconstruction of vertex values from cell averages. For this purpose, we review several techniques from the literature and propose a new variant of the reconstruction algorithm that is based on linear Least Squares. Our formulation unifies the treatment of internal and boundary vertices and includes information from boundaries as linear constraints of the Least Squares minimization process. It turns out that this formulation is well-posed on those unstructured triangulations that satisfy a general regularity condition. The performance of the finite volume method with different algorithms for vertex reconstructions is examined on three benchmark problems having full Dirichlet, Dirichlet-Robin and Dirichlet–Neumann boundary conditions. Comparison of experimental results shows that an important improvement of the accuracy of the numerical solution is attained by using our Least Squares-based formulation. In particular, in the case of Dirichlet–Neumann boundary conditions and strongly anisotropic diffusions the good behavior of the method relies on the absence of locking phenomena that appear when other reconstruction techniques are used.

A stabilized linearity-preserving scheme for the heterogeneous and anisotropic diffusion problems on polygonal meshes

2012 ◽  
Vol 231 (21) ◽  
pp. 7152-7169 ◽  
Author(s):  
Jiming Wu ◽  
Zhiming Gao ◽  
Zihuan Dai
Keyword(s):  
Anisotropic Diffusion ◽  
Polygonal Meshes ◽  
Diffusion Problems

A metamorphic positivity-preserving conservative formulation applied to the solution of general anisotropic diffusion problems in distorted 2-D grids

2020 ◽  
Author(s):  
Emerson W. D. Magalhães ◽  
Márcio R. A. Souza ◽  
Igor F. Gomes
Keyword(s):  
Anisotropic Diffusion ◽  
Positivity Preserving ◽  
Diffusion Problems

scholarly journals Robust numerical schemes for anisotropic diffusion problems, a first step for turbulence modeling in Lagrangian hydrodynamics

2009 ◽  
Vol 28 ◽  
pp. 80-99
Author(s):  
Julien Dambrine ◽  
Philippe Hoch ◽  
Raphaël Kuate ◽  
Jérôme Lohéac ◽  
Jérôme Métral ◽  
...  
Keyword(s):  
Anisotropic Diffusion ◽  
Turbulence Modeling ◽  
Numerical Schemes ◽  
Lagrangian Hydrodynamics ◽  
Diffusion Problems
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