A novel vertex-centered finite volume method for solving Richards' equation and its adaptation to local mesh refinement

Abstract

Accurate and efficient numerical simulations of soil water movement, as described by the highly nonlinear Richards' equation, often require local refinement near recharge or sink/source terms. In this paper, we present a novel numerical scheme for solving Richards' equation. Our approach is based on the vertex-centered finite volume method (VCFVM) and can be easily adapted to locally refined meshes. The proposed scheme offers some key features, including the definition of all unknowns over vertices of the primary mesh, expression of flux crossing dual edges as combinations of hydraulic heads at the vertices of the primary cell, and the capability to handle nonmatching meshes in the presence of local mesh refinement. For performance evaluation, soil water content and soil water potential simulated by the proposed scheme are benchmarked against results produced from HYDRUS (a widely used soil water numerical model) and the observed values in four test cases, including a convergence test case, a synthetic case, a laboratory experiment case and a field experiment case. The comparison results demonstrate the effectiveness and applicability of our scheme across a wide range of soil parameters and boundary conditions.