A general self-adaptive under-relaxation strategy for fast and robust convergence of iterative calculation of incompressible flow

The method of successive under-relaxation (SUR) is an effective way for numerically solving a nonlinear system of equations governing the fluid flow and heat transfer, resulting in stable convergence. So far, there is not any doable applied method to determine the best relaxation factor of SUR. In this article, the interrelation among the diffusion term, the convection term and the under-relaxation term is regarded as the key to calculate the under-relaxation factor. Then, the self-adaptive under-relaxation factor strategy is proposed. The test calculation of two typical problems, lid-driven cavity flow, and flow over a backward-facing step is carried out based on the proposed self-adaptive under-relaxation strategy. It is proved that the present method is efficient and robust compared to the fixed under-relaxation factor method.