Generalized mass-conservative finite volume framework for unified saturated–unsaturated subsurface flow

Abstract

Numerical modeling of saturated–unsaturated flow in porous media is very challenging due to the strong nonlinearity of the Richards Equation in the unsaturated flow zone. Robust and efficient numerical models are essential to simulate the flow dynamics of regional-scale subsurface systems accurately. In this paper, we have presented generalized mass-conservative Finite Volume solvers for pressure head-based and mixed forms of Richards Equation named subsurfaceFlowFOAM, developed using OpenFOAM® framework. The solution of Richards Equation often encounters numerical instabilities and convergence issues owing to the inherent nonlinearity of the soil–water characteristic relations and sharp variations in hydrological conditions over time. In this work, we have proposed a stabilized and adaptive time-stepping algorithm that adjusts the time-step size following the solution requirements ensuring smooth convergence. We have further implemented the parallel computation technique through the domain decomposition method to accelerate the computation process for large-scale simulations involved in regional-scale modeling. The numerical results of subsurfaceFlowFOAM depict excellent correspondence with the data presented in the literature for a wide variety of subsurface flow problems with deficient cumulative mass balance error. The solution accuracy and the computational efficiency of the solvers ensure their potential applicability to solve multi-dimensional regional-scale subsurface flow problems.