Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 229, Issue 11, Pages 4017-4032Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2010.01.035
Keywords
Advection-diffusion equation; Finite volume method; Discrete maximum principle; Monotone method; Unstructured mesh; Polygonal mesh
Funding
- National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory [DE-AC52-06NA25396]
- DOE Office of Science Advanced Scientific Computing Research (ASCR) [LA-UR 09-03209]
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We present a new second-order accurate monotone finite volume (FV) method for the steady-state advection-diffusion equation. The method uses a nonlinear approximation for both diffusive and advective fluxes and guarantees solution non-negativity. The interpolation-free approximation of the diffusive flux uses the nonlinear two-point stencil proposed in Lipnikov [23]. Approximation of the advective flux is based on the second-order upwind method with a specially designed minimal nonlinear correction. The second-order convergence rate and monotonicity are verified with numerical experiments. Published by Elsevier Inc.
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