Abstract 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.

中文翻译：

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不可压缩流迭代计算快速鲁棒收敛的通用自适应欠松弛策略

摘要 连续欠松弛(SUR)方法是数值求解控制流体流动和传热的非线性方程组的一种有效方法，可实现稳定收敛。到目前为止，还没有任何可行的应用方法来确定 SUR 的最佳松弛因子。在本文中，扩散项、对流项和欠松弛项之间的相互关系被视为计算欠松弛因子的关键。然后，提出了自适应欠松弛因子策略。基于所提出的自适应欠松弛策略，对盖子驱动的腔体流动和反向台阶上的流动两个典型问题进行了测试计算。证明与固定欠松弛因子方法相比，本方法是有效和稳健的。