A two-dimensional geometric multigrid model for Poisson equation with interface on structured adaptive mesh refinement grid

Abstract In this study, a two-dimensional Geometric Multigrid (GMG) model for Poisson equation with interface on Structured Adaptive Mesh Refinement (SAMR) grid is developed. The model is designed to be combined with Navier-Stokes solvers with staggered arrangements of variables, although solvers with collocated arrangement are also applicable. Based on a general GMG method, special attention for flux conservation is taken on the coarse-fine interface. As large density ratios commonly exist in interface flows such as free surface flows, Galerkin Coarse grid Approximation (GCA) method is adopted to generate coefficients on coarse grids to enhance the robustness and efficiency of the model. Benchmark case is carried out for the validation of the model, and it is demonstrated to obtain 2nd-order accuracy and acceptable efficiency for even the density ratio reaches 104. Point iteration and line relaxation iteration of Gauss-Seidel methods are compared to obtain a better performance. Furthermore, the model is implemented in a developed Navier-Stokes solver to validate its performance in simulating interface problems. The numerical results are compared with theoretical solution or experimental data from reliable sources.