Application of the Multigrid Method and a Flexible Hybrid Coordinate in a Nonhydrostatic Model

Abstract

A fully compressible, three-dimensional, nonhydrostatic model is developed using a semi-implicit scheme to avoid an extremely small time step. As a result of applying the implicit scheme to high-frequency waves, an elliptic partial differential equation (EPDE) has been introduced. A multigrid solver is applied to solve the EPDEs, which include cross-derivative terms due to terrain-following coordinate transformation. Several experiments have been performed to evaluate the model as well as the performance of the scheme with respect to tolerance number, relaxation choice, sweeps of prerelaxation and postrelaxation, and a flexible hybrid coordinate (FHC). An FHC with two functions (base and deviation functions) is introduced. The basic function provides constant vertical grid spacing required in the multigrid solver, while the deviation function helps to adjust the vertical resolution.