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Article Dans Une Revue Journal of Computational Physics Année : 2023

Arbitrary order positivity preserving finite-volume schemes for 2D elliptic problems

Résumé

The positivity preservation is very important in most applications solving elliptic problems. Many schemes preserving positivity has been proposed but are at most second-order convergent. Besides, in general, high-order schemes do not preserve positivity. In the present paper, we propose an arbitrary-order positivity preserving method for elliptic problems in 2D. We show how to adapt our method to the case of a discontinuous and/or tensor-valued diffusion coefficient, while keeping the expected order of convergence. We assess the new scheme on several test problems.
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Dates et versions

cea-04211874 , version 1 (20-09-2023)
cea-04211874 , version 2 (06-08-2024)

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Xavier Blanc, Francois Hermeline, Emmanuel Labourasse, Julie Patela. Arbitrary order positivity preserving finite-volume schemes for 2D elliptic problems. Journal of Computational Physics, 2023, ⟨10.1016/j.jcp.2024.113325⟩. ⟨cea-04211874v2⟩
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