Verification, conservation, stability and efficiency of a finite volume method for the 1D Richards equation

SummaryRichards equation is a non-linear partial differential equation that describes flow in porous media. To solve it, numerical methods that need to be conservative, stable, accurate and efficient, are required. Finite volume methods have not been reported as widely as finite difference or finite element methods. This work is focused on providing numerical results and analysis of several finite volume schemes in one dimension. The formulation of time discretization schemes is revisited, a stability analysis is performed, and analytical and experimental benchmakrs are provided.

► A finite volume scheme for the solution of Richards equation is formulated. ► Several time discretization techniques and their numerical properties are studied. ► Verification is done with a 1D analytical solution and an academic test case. ► Numerical solutions are validated against four experimental cases.