流动模拟二阶精度的简易保持研究

Convenient Maintenance of Second-order Numerical Accuracy in Fluid Flow Simulation

首先分析了各类低阶和高阶差分格式,指出二阶精度格式具有综合优势.接着以二维对流扩散方程为例,推导出延迟修正的CDS格式,并定义为DCDS格式.通过标量绕静点输运、自然对流及混合对流等实例,并与UDS,CDS及QUICK格式比较,论证了CCDS 格式不仅能维持计算结果的二阶精度,而且极大地约束了CDS格式所固有的振荡和越界行为,边界处理也很简单.总之,在程序的效率、调试、边界处理、计算精度及稳定性等因素权衡下,DCDS格式是保持二阶数值精度的简易途径.

After analyzing the characteristics of different low-order and high-order schemes, it was pointed out that the schemes of second-order numerical accuracy were the optimum way in numerical simulation. Taking, the general two-dimensional steady convection-diffusion equation as an example, the deferred correction CDS scheme was derived based on the first-order upwind scheme, which we defined as DCDS scheme, The performance of DCDS scheme was compared with UDS, CDS and QUICK schemes via studying scalar transport in a stagnation point flow, thermal-driven and lid-driven fluid flow in square cavities. It was proved that DCDS scheme could maintain second-order numerical accuracy on single grid and reduce the oscillations and overshoots, and the boundary treatments of DCDS were consistent with those of UDS and CDS. Compromising the programming efficiency, debugging, boundary treatments, numerical accuracy and stability, the DCDS scheme is a convenient and optimum way to maintain the second-order numerical accuracy.