Feasibility of the Direct Method to Solve the Anelastic Pressure Equation in Nonhydrostatic Two-Dimensional Mesoscale Models

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  • 1 Institute of Earth Sciences, Free University, Amsterdam, The Netherlands
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Abstract

For anelastic nonhydrostatic mesoscale models, the pressure has to be solved from the Poisson partial differential equation. This can be done in various ways. Here the usually neglected direct method is compared to widely used (iterative) relaxation methods. The feasibility of the direct method is limited to the two-dimensional (2D) case. For this case, the direct method appears to compare favorably, provided the number of grid levels is sufficiently small.

Furthermore, it is shown that nonhydrostatic calculations can proceed faster than hydrostatic ones in certain cases, in spite of the fact that the amount of computation time per time stop is longer for the former. The reason is that the time step can often be chosen much larger for the nonhydrostatic than for the hydrostatic calculations without violating stability requirements.

Abstract

For anelastic nonhydrostatic mesoscale models, the pressure has to be solved from the Poisson partial differential equation. This can be done in various ways. Here the usually neglected direct method is compared to widely used (iterative) relaxation methods. The feasibility of the direct method is limited to the two-dimensional (2D) case. For this case, the direct method appears to compare favorably, provided the number of grid levels is sufficiently small.

Furthermore, it is shown that nonhydrostatic calculations can proceed faster than hydrostatic ones in certain cases, in spite of the fact that the amount of computation time per time stop is longer for the former. The reason is that the time step can often be chosen much larger for the nonhydrostatic than for the hydrostatic calculations without violating stability requirements.

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