Numerical scheme for solving the soil-water coupling problems based on finite volume method with unstructured mesh

In this paper, a novel matrix-free finite volume (FV) numerical scheme with unstructured mesh is proposed for simulating unsaturated seepage-stress coupling problems in earth science. The proposed model solves Richards Equation (RE) for unsteady unsaturated infiltration flow and Cauchy Equation (CE) for soil dynamics. A universal finite volume (FV) numerical scheme is developed for solving the governing equations mentioned above with unstructured mesh. The techniques of matrix-free and fully implicit time stepping algorithm are utilized in the numerical discretization in order to avoiding for the calculation and storage of large matrices. The new model is assessed and evaluated by benchmarks and test infiltration cases. Comparing with the solutions of commercial software packages called GEO-Studio and AutoBANK, the accuracy of the proposed model is assessed and verified. A slope infiltration simulation case is carried out as the engineering application of the current model at last. With the advantage of novel numerical scheme and high accuracy, the proposed model shows its potential value in engineering application.