Monotone Finite Volume Scheme for Three Dimensional Diffusion Equation on Tetrahedral Meshes. (5th December 2016)

• Record Type: Journal Article
• Authors: Lai, Xiang; Sheng, Zhiqiang; Yuan, Guangwei
• Is Part Of: Communications in computational physics. Volume 21:Number 1(2017:Jan.)
• Page Start: 162
• Page End: 181
• Publication Date: 2016-12-05
• Subjects: 65M06, -- 65M12, -- 65M55; Monotonicity, -- finite volume scheme, -- diffusion equation, -- tetrahedral meshes; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.220415.090516a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: We construct a nonlinear monotone finite volume scheme for three-dimensional diffusion equation on tetrahedral meshes. Since it is crucial important to eliminate the vertex unknowns in the construction of the scheme, we present a new efficient eliminating method. The scheme has only cell-centered unknowns and can deal with discontinuous or tensor diffusion coefficient problems on distorted meshes rigorously. The numerical results illustrate that the resulting scheme can preserve positivity on distorted tetrahedral meshes, and also show that our scheme appears to be approximate second-order accuracy for solution.