1887

Abstract

A new family of cell-centered finite-volume schemes is presented for solving the general full-tensor pressure equation on arbitrary unstructured triangulations. The new schemes are flux continuous and have full pressure support (FPS) over each subcell with continuous pressure imposed across each control-volume sub-interface, in contrast to earlier formulations. The earlier methods are point-wise continuous in pressure and flux with triangle-pressure-support (TPS) leading to a limited quadrature range. An M-matrix analysis identifies bounding limits for the schemes to posses a local discrete maximum principle. Positive definite conditions are also given. Comparisons show that the earlier pointwise TPS methods can induce strong spurious oscillations in solutions for problems involving strong full-tensor anisotropy where the M-matrix conditions are violated, leading to unstable solutions in such cases. The earlier unstructured cell-centered TPS schemes are investigated in terms of stability and are shown to be decoupled at high anisotropy ratio. In contrast to TPS, the new FPS formulation leads to well resolved stable solutions that are essentially free of spurious oscillations. A substantial degree of improved convergence behavior, for both pressure and velocity, is observed in all convergence tests.

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/content/papers/10.3997/2214-4609.20144952
2010-09-06
2024-04-19
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http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20144952
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