The Application of the Multigrid Method in a Nonhydrostatic Atmospheric Model

Shu-Hua Chen
Department of Earth and Atmospheric Sciences
Purdue University
West Lafayette, IN 47907, USA


A nonhydrostatic atmospheric model is developed. The use of the Semi-implicit scheme in this model has relaxed the constraint of exceedingly small time step, but it generates a huge sparse matrix (400,000 x 400,000) of the Elliptic Partial Differential Equations (EPDEs). This study attempts to apply the Multigrid method to solve these EPDEs and to address the performance and efflciency of the Multigrid method. Two experiments are examined. The model results are in good agreement with those in historical papers and the analytical solution. Furthermore, the Multigrid solver, mud3cr, applied in this model is very efflcient. These indicate the success of the Muitigrid method applied to nonhydrostatic atmospheric models.