A new matrix-free implicit iteration algorithm based on finite volume method for simulating groundwater seepage flows

Purpose This study proposes a novel algorithm based on the finite volume method for simulating groundwater flows and presents the practical application of this method in geotechnical engineering. Design/methodology/approach The matrix-free implicit iteration method based on the finite volume method and preconditioning conjugate gradient algorithm was used to discretize and solve the groundwater seepage governing equation. Implicit residual smoothing and GPU parallel techniques were utilized to speed up the computation with the solver. Findings The new method was assessed and evaluated using benchmark and typical infiltration cases. Both the analytical solutions and solutions of the commercial software GEO-Studio were used to verify the accuracy of the proposed algorithm. The speedup performance of the GPU parallel algorithm was also well reflected. Originality/value The results demonstrate that the new algorithm is simple and practical, with fast convergence and high accuracy and can satisfy engineering application requirements.