The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations
The stability of time-split numerical methods for the hydrostatic and the nonhydrostatic elastic equations
复制标题
静水和非静水弹性方程时分数值方法的稳定性
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
J. Klemp
中科院分区：
文献类型：
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作者：
W. Skamarock;J. Klemp
二维线性浅水系统和二维声平流系统在数学上的等价性有力地表明，在非静力模式中可以采用为静力方程设计的时间分裂格式，反之亦然。给出了积分这两个系统的几种时间分裂数值方法的稳定性分析。主要的兴趣是非静力系统和不产生多维椭圆型方程的显式数值格式；因此，详细分析了Klemp和Wilhelmson(KW)用于积分时间分裂的非静力系统的显式技术。研究发现，传播声模和平流声模之间的相互作用会对最大允许时间步长产生严格的限制。适当的过滤可以消除这些限制。对其他显式时间分裂格式进行了分析，认为KW时间分裂方法具有最好的计算效率。
Abstract The mathematical equivalence of the linearized two-dimensional (2D) shallow-water system and the 2D acoustic-advection system strongly suggests that time-split schemes designed for the hydrostatic equations can be employed in nonhydrostatic models and vice versa. Stability analyses are presented for several time-split numerical methods for integrating the two systems. The primary interest is in the nonhydrostatic system and in explicit numerical schemes where no multidimensional elliptic equations arise; thus, a detailed analysis of the Klemp and Wilhelmson (KW) explicit technique for integrating the time-split nonhydrostatic system is undertaken. It is found that the interaction between propagating and advecting acoustic modes can introduce severe constraints on the maximum allowable time steps. Proper filtering can remove these constraints. Other explicit time-split schemes are analysed, and, of all the explicit schemes considered, it is believed that the KW time-split method offers the best co...