 Positive Scharfetter-Gummel finite volume method for convection-diffusion equations on polygonal meshesEl Houssaine Quenjel Applied Mathematics and Computation, 2022, vol. 425, issue C Abstract: In this paper, we develop and study a fully implicit positive finite volume scheme that allows an accurate approximation of the nonlinear highly anisotropic convection-diffusion equations on almost arbitrary girds. The key idea is to relate the oscillatory fluxes, including the convective ones, to the normal monotonic diffusive flux thanks to a technique used in the Scharfetter-Gummel discretizations. Then, we obtain a nonlinear two-point-like scheme with positive coefficients on primal and dual meshes. We check that the structure of the scheme naturally ensures the nonnegativity of the approximate solutions. We also establish energy estimates, which leads to a proof of existence of the numerical solutions. This analytical study is accompanied with a series of numerical results and simulations. They highlight the fulfillment of the discrete maximum principle, the optimal accuracy of our scheme, and its robustness with respect to the mesh and to high ratios of anisotropy. Keywords: Degenerate parabolic equations; Finite volume method; Scharfetter-Gummel scheme; Generic meshes; Positivity; Coercivity; Second order accuracy (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001552 DOI: 10.1016/j.amc.2022.127071 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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