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• W3203138520 endingPage "110729" @default.
• W3203138520 startingPage "110729" @default.
• W3203138520 abstract "In this paper, a nonlinear positivity-preserving finite volume scheme for the heterogeneous and anisotropic diffusion problems is proposed. Firstly, a linear diamond finite volume scheme is introduced. This scheme has both cell-centered unknowns and vertex unknowns. The vertex unknowns are treated as auxiliary ones and are expressed as linear combinations of the surrounding cell-centered unknowns, which reduces the scheme to a pure cell-centered one. Two new interpolation algorithms are suggested through the linearity-preserving approach and a novel discretization of diffusion coefficient. The new vertex interpolation algorithms improve a great deal the numerical performance of the linear scheme on distorted meshes with strongly anisotropy. Secondly, a new positivity-preserving cell-centered scheme is constructed via the aforementioned linear scheme and a nonlinear correction technique proposed by [28]. This nonlinear scheme is different from most existing nonlinear two-point flux approximation schemes in the way that it is not based on the nonlinear two-point flux approximation and it doesn't require the positivity-preserving vertex interpolation. Its implementation is also very easy and simple. Numerical experiments conducted in this paper indicate that the new positivity-preserving scheme is efficient and has approximately second order accuracy in most extreme cases." @default.
• W3203138520 created "2021-10-11" @default.
• W3203138520 creator A5008756867 @default.
• W3203138520 creator A5073132805 @default.
• W3203138520 date "2022-01-01" @default.
• W3203138520 modified "2023-10-17" @default.
• W3203138520 title "A nonlinear correction scheme for the heterogeneous and anisotropic diffusion problems on polygonal meshes" @default.
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• W3203138520 doi "https://doi.org/10.1016/j.jcp.2021.110729" @default.
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