An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

Abstract

We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed sphere. This approach combines a Runge–Kutta time discretization with a fourth-order-accurate spatial discretization and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy but with many fewer operations.