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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2/2018

12.02.2018

Monotone Finite Volume Schemes for Diffusion Equation with Imperfect Interface on Distorted Meshes

verfasst von: Fujun Cao, Zhiqiang Sheng, Guangwei Yuan

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2018

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Abstract

In this paper, we prove the solution of diffusion equation with imperfect interface is positivity-preserving and a monotone finite volume method is presented to obtain the nonnegative solution on distorted mesh. Motivated by Sheng and Yuan (J Comput Phys 231:3739–3754, 2012), the discrete normal flux on interface is defined by using an extended stencil and introducing two auxiliary points to distinguish the discontinuities of the unknowns on both sides of the interface. The resulting finite volume scheme is locally conservative and has only cell-centered unknowns. Moreover, it is proved to be monotone. The numerical results show that the method obtains second order convergent rate in \(L_2\) norms for solutions on quadrilateral and triangular meshes.
Vorheriger Artikel An HDG Method with Orthogonal Projections in Facet Integrals
Nächster Artikel A General Selective Averaging Method for Piecewise Constant Signal and Image Processing

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Metadaten
Titel
Monotone Finite Volume Schemes for Diffusion Equation with Imperfect Interface on Distorted Meshes
verfasst von
Fujun Cao
Zhiqiang Sheng
Guangwei Yuan
Publikationsdatum
12.02.2018
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-018-0651-8

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