Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 227, Issue 12, Pages 6288-6312Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2008.03.007
Keywords
monotonicity; finite volume scheme; diffusion equation; polygonal meshes
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We construct a nonlinear finite volume (FV) scheme for diffusion equation on star-shaped polygonal meshes and prove that the scheme is monotone, i.e., it preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficients. Our scheme has only cell-centered unknowns, and it treats material discontinuities rigorously and offers an explicit expression for the normal flux. Numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes for both smooth and non-smooth highly anisotropic solutions. And numerical results show that our scheme appears to be approximate second-order accuracy for the solution and first-order accuracy for the flux. (c) 2008 Elsevier Inc. All rights reserved.
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