正压涡度方程中考虑粘性项与平滑过程的一些意见

SOME OPINION FOR CONSIDERING FRICTIONAL TERM AND SMOOTHING PROCESS IN THE BAROTROPIC VORTICITY EQUATION

中文摘要:

      本文首先讨论了如何依据空间步长来选取平滑系数。其次考虑在涡度方程中加上粘性项后对微分方程解的影响,讨论如何选取适当的粘性系数。第三讨论涡度方程加粘性项后对差分格式计算稳定性的影响,证明了在常用时间中心差分格式中应把粘性项取在第(n-1)时间层,这样计算才是稳定的。反之,如把粘性项取在第n时间层,则差分格式计算不稳定。并且时间向前差的格式在加上粘性项后也可以稳定,但要求的粘性系数过大。最后讨论了用涡度方程作数值预告时加上平滑过程与加上粘性项之间的关系,从计算上看,二者并不等价。但可以把平滑过程与扩散方程类比,以确定适当的平滑系数。

英文摘要:

      First of all, this paper discusses how to choose smoothing coefficient in accordance with the grid size of space. Secondly we study the influence on the solution of the differential equation by adding frictional term in the vorticity equation, and then show how to choose suitable frictional coefficient in this case. Thirdly we discuss the influence for computational stability of the finite difference scheme after adding frictional term in the vorticity equation. It is shown that the computation is stable, if taking the frictional term in the(n-1) time layer in the normal centered time difference scheme. If taking the frictional term in the n time layer, then the computation of the difference scheme is unstable. At the same time, the time forward difference scheme may be stable also after adding frictional term, but the frictional coefficient required is then much larger. Finally, we discuss the relation between the smoothing process and frictional term for numerical prediction using the vorticity equation. From the viewpoint of computation, the two things are not equivalent. But we might determine suitable smoothing coefficient by comparing the smoothing process in a diffusion equation.