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Article Dans Une Revue Communications in Computational Physics Année : 2023

Monotonic diamond and DDFV type finite-volume schemes for 2D elliptic problems

Résumé

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 from [44, 19, 49, 18] 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.
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Dates et versions

cea-04137599 , version 1 (22-06-2023)

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Citer

Xavier Blanc, Francois Hermeline, Emmanuel Labourasse Null, Julie Patela. Monotonic diamond and DDFV type finite-volume schemes for 2D elliptic problems. Communications in Computational Physics, 2023, 34 (2), pp.456-502. ⟨10.4208/cicp.OA-2023-0081⟩. ⟨cea-04137599⟩
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