Temporal Second-order Accuracy of Simple-type Methods for Incompressible Unsteady Flows

SIMPLE-type methods are presented in a more concise formulation. This formulation is used to analyze temporal accuracy for unsteady flows. Detailed error formulations are given. Analysis shows that SIMPLE-type methods have second-order temporal accuracy if a second-order temporal updating technique is employed to update both the convective and diffusion terms. Two algorithms for unsteady flows are presented. Algorithm A is an iteration method, which will cost more time than algorithm B, a noniteration algorithm. Also several second-order updating techniques are presented. A classical validation example is employed to validate the temporal accuracy in this article. A new four-step SIMPLE-type method is presented, in which the pressure Poisson equation, not the pressure difference Poisson equation is solved.