Second-order accurate monotone finite volume scheme for Richards' equation

Authors:
Oleksandr Misiats;Konstantin Lipnikov
Affiliations:
Department of Mathematics, The Pennsylvania State University, United States;MS B284, Los Alamos National Laboratory, Los Alamos, NM 87544, United States
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

In this work we perform a theoretical and numerical analysis of Richards' equation. For certain types of nonlinearities we provide explicit analytical solutions. These solutions are used to show that conventional unconditionally monotone finite volume schemes have only first-order accuracy. We derive necessary and sufficient conditions for the monotonicity of finite volume discretizations and use these conditions to construct a monotone finite volume discretization accurate to second-order.