An economical method of difference computation in evolution equation (Q1210252)

In this note, the splitting method, which is applied to the difference schemes of explicit and complete square conservation, is described according to the separability of the adjustment stage (the fast process) and the advection stage (the slow process) in atmospheric motion. Some further tests have been performed on the adjustment term, from which a kind of instable factor to influence the computation is found and a corresponding computational method that is the compensated computation in the deducted region is introduced to restrict the computational instability. The stable conditions for the difference scheme of explicit and complete square conservation are given. Some numerical tests have been done on the four-wave Rossby-Haurwitz waves by using the spherical barotropic primitive equations, and the results are satisfactory.