Numerical scheme for solving the Richard's equation based on finite volume model with unstructured mesh and implicit dual-time stepping

In this paper, a novel finite volume model with unstructured mesh and implicit dual time stepping is proposed for simulating unsaturated infiltration flows based on Richards's equation (RE), which is one of the most challenging problems in earth science. In time, a matrix-free fully implicit dual time stepping algorithm is developed to discrete the equation, and in space, the equation is discretized by the finite volume model with unstructured grid. The new method is assessed and evaluated by benchmark and engineering water infiltration cases. Both numerical solutions in the literature and solutions of a commercial package called GEO-Studio are used to verify the accuracy of the proposed algorithm. An unsteady water infiltration simulation case is carried out as the application of the current model by using the topographic dataset of the Monterey Bay in California. The results demonstrate that the new algorithm is robust and practical, with fast convergence and high accuracy.