Back to Search
Start Over
The finite volume scheme preserving maximum principle for diffusion equations with discontinuous coefficient
- Source :
- Computers & Mathematics with Applications. 79:2168-2188
- Publication Year :
- 2020
- Publisher :
- Elsevier BV, 2020.
-
Abstract
- We construct a new scheme whose primary unknowns include both cell-centered unknowns and edge unknowns on discontinuous line to solve diffusion equations with discontinuous coefficient. First, two linear fluxes are given on both sides of the cell edge, respectively. In order to deal with the defect of the existing scheme preserving maximum principle for solving diffusion problem with discontinuous coefficient, in addition to cell-centered unknowns, we also introduce cell-edge unknowns on discontinuous line as basic unknowns. Second, the conservative flux is constructed by using nonlinear weighted combination of these two linear fluxes. For the cell-edge unknowns on discontinuous line, we add an equation by using the continuity of normal flux. Compared to the classical cell-centered nonlinear finite volume scheme, the introduction of cell-edge unknowns on discontinuous edge is the key point for our scheme to solve diffusion equations with discontinuous coefficient. Then we prove that the scheme satisfies the discrete maximum principle. Based on this, the existence of a solution for the scheme is also obtained. Numerical results are presented to show that our scheme obtains almost second order accuracy for solution on random meshes, preserves discrete maximum principle, and is superior to the existing scheme (in Sheng and Yuan (2011)) preserving the maximum principle on dealing with the problems with strong anisotropic discontinuous coefficient on distorted meshes.
- Subjects :
- Finite volume method
Mathematical analysis
010103 numerical & computational mathematics
Edge (geometry)
01 natural sciences
010101 applied mathematics
Computational Mathematics
Nonlinear system
Maximum principle
Computational Theory and Mathematics
Modeling and Simulation
Line (geometry)
Polygon mesh
0101 mathematics
Diffusion (business)
Anisotropy
Mathematics
Subjects
Details
- ISSN :
- 08981221
- Volume :
- 79
- Database :
- OpenAIRE
- Journal :
- Computers & Mathematics with Applications
- Accession number :
- edsair.doi...........d27c6e0ef06230ee85e7c36c8efea4ea