A monotone finite volume method for advection-diffusion equations on unstructured polygonal meshes

Authors:
K. Lipnikov;D. Svyatskiy;Y. Vassilevski
Affiliations:
Applied Mathematics and Plasma Physics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, United States;Applied Mathematics and Plasma Physics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, United States;Institute of Numerical Mathematics, Russian Academy of Sciences, 8, Gubkina, 119333 Moscow, Russia
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

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.