Comparison of Some Schemes for Nonhydrostatic Models with Orography

[摘要] Three schemes for nonhydrostatic models with orography incorporated, consisting of an-elastic (AE), elastic horizontally and vertically implicit (E-HI-VI) and elastic horizontally explicit, vertically implicit (E-HE-VI), are compared in their formulation and performance.If sound waves are damped enough in the elastic models, the results of these schemes are similar, in spite of the use of the flux form of the advection term in AE. Efficient damping methods of sound waves are examined, and a linear analysis is made of their stability, where both sound and gravity waves are taken into account simultaneously.An iterative application of a direct method for solving the elliptic equation of pressure needed for the AE and some E-HI-VI schemes appears to be accurate. One application of a direct method increased the central processing unit (CPU) time by about 15%, which is comparable to the CPU time required for a small time step integration of the E-HE-VI scheme.For the E-HI-VI scheme, a partially implicit method was found to need no iteration in solving the pressure equation for the case of a low or moderate mountain, since the erroneous forcing at the boundary is practically negligible. However, for the case of a high and steep mountain, the method needs iteration to get rid of the erroneous forcing at the boundary which is no longer negligible. This method is found to be unstable for the case of a very steep mountain.

[学科分类] 大气科学