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Volume 34, Issue 2
Monotonic Diamond and DDFV Type Finite-Volume Schemes for 2D Elliptic Problems

Xavier Blanc, Francois Hermeline, Emmanuel Labourasse & Julie Patela

DOI: 10.4208/cicp.OA-2023-0081

Commun. Comput. Phys., 34 (2023), pp. 456-502.

Published online: 2023-09

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  • Abstract

The DDFV (Discrete Duality Finite Volume) method is a finite volume scheme mainly dedicated to diffusion problems, with some outstanding properties. This scheme has been found to be one of the most accurate finite volume methods for diffusion problems. In the present paper, we propose a new monotonic extension of DDFV, which can handle discontinuous tensorial diffusion coefficient. Moreover, we compare its performance to a diamond type method with an original interpolation method relying on polynomial reconstructions. Monotonicity is achieved by adapting the method of Gao et al [A finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes] to our schemes. Such a technique does not require the positiveness of the secondary unknowns. We show that the two new methods are second-order accurate and are indeed monotonic on some challenging benchmarks as a Fokker-Planck problem.

  • Keywords

Finite volume method, anisotropic diffusion, monotonic method, DDFV scheme.

  • AMS Subject Headings

65N08, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-34-456, author = {Blanc , XavierHermeline , FrancoisLabourasse , Emmanuel and Patela , Julie}, title = {Monotonic Diamond and DDFV Type Finite-Volume Schemes for 2D Elliptic Problems}, journal = {Communications in Computational Physics}, year = {2023}, volume = {34}, number = {2}, pages = {456--502}, abstract = {

The DDFV (Discrete Duality Finite Volume) method is a finite volume scheme mainly dedicated to diffusion problems, with some outstanding properties. This scheme has been found to be one of the most accurate finite volume methods for diffusion problems. In the present paper, we propose a new monotonic extension of DDFV, which can handle discontinuous tensorial diffusion coefficient. Moreover, we compare its performance to a diamond type method with an original interpolation method relying on polynomial reconstructions. Monotonicity is achieved by adapting the method of Gao et al [A finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes] to our schemes. Such a technique does not require the positiveness of the secondary unknowns. We show that the two new methods are second-order accurate and are indeed monotonic on some challenging benchmarks as a Fokker-Planck problem.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0081}, url = {http://global-sci.org/intro/article_detail/cicp/21975.html} }
TY - JOUR T1 - Monotonic Diamond and DDFV Type Finite-Volume Schemes for 2D Elliptic Problems AU - Blanc , Xavier AU - Hermeline , Francois AU - Labourasse , Emmanuel AU - Patela , Julie JO - Communications in Computational Physics VL - 2 SP - 456 EP - 502 PY - 2023 DA - 2023/09 SN - 34 DO - http://doi.org/10.4208/cicp.OA-2023-0081 UR - https://global-sci.org/intro/article_detail/cicp/21975.html KW - Finite volume method, anisotropic diffusion, monotonic method, DDFV scheme. AB -

The DDFV (Discrete Duality Finite Volume) method is a finite volume scheme mainly dedicated to diffusion problems, with some outstanding properties. This scheme has been found to be one of the most accurate finite volume methods for diffusion problems. In the present paper, we propose a new monotonic extension of DDFV, which can handle discontinuous tensorial diffusion coefficient. Moreover, we compare its performance to a diamond type method with an original interpolation method relying on polynomial reconstructions. Monotonicity is achieved by adapting the method of Gao et al [A finite volume element scheme with a monotonicity correction for anisotropic diffusion problems on general quadrilateral meshes] to our schemes. Such a technique does not require the positiveness of the secondary unknowns. We show that the two new methods are second-order accurate and are indeed monotonic on some challenging benchmarks as a Fokker-Planck problem.

Blanc , XavierHermeline , FrancoisLabourasse , Emmanuel and Patela , Julie. (2023). Monotonic Diamond and DDFV Type Finite-Volume Schemes for 2D Elliptic Problems. Communications in Computational Physics. 34 (2). 456-502. doi:10.4208/cicp.OA-2023-0081
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