Two Problems Existing in the Split Algorithm
分解算法中的两个问题

It is pointed out in this paper that there exist two problems to be settled in the split algorithm. They are: a) In addition to splitting the original equations according to fast and slow processes, which principle should be based on to split the equations again in order to get optimal efficiency? b) Whether or not the form of time discretization is allowed to be arbitrary, or in which form time discretization should be taken? The research to solve the first problem shows that the secondly split equation should preserve the important physical properties of the original equations, especially their overall properties (such as conservation of energy and mass) and the solutions of the secondly split equations should be consistent with those of the original equations, at least be consistent with some important ones of them. The result for settling the second problem indicates that in the case of finite difference scheme, two-time-level scheme is desirable; if three-time-level scheme is adopted, inconsistency would happen between the scheme and the corresponding set of partial differential equations.