高阶紧致格式在非线性数值模拟中的应用

Research on application of high order compact scheme in numerical simulation of nonlinear

对比分析迎风型格式及中心耗散格式优劣性,采用傅里叶分析方法分析显式格式及紧致格式在波数空间可准确模拟的波数范围。通过编程研究6种紧致格式,其中为保证紧致格式在内点及边界点的一致性,采用高精度边界格式,加入了滤波运算和采用更小的CFL数来控制紧致格式的稳定性。数值试验表明,中心紧致格式有更小的耗散误差及色散误差;通过4阶Pade格式计算模型绕流,验证了边界处理的正确性,也更加认识到紧致格式有非常严格的稳定性限制。

The article analyzed the merits of the upwind scheme and central dissipation scheme. Using the Fourier analysis method to analyze the wave number range of explicit and compact format, it can be accurately simulated in wave number space. Through programming on six compact scheme, In order to ensure consistency of formats, including compact point and boundary points, the program use high-precision format border. Filtering operation and the use of a smaller number of CFL compact format to control the stability. Numerical experiments show：the centre compact format has smaller error of dissipation and dispersion. Through fourth-order Pade format to compute the flow around airfoil, It verifies the correctness of the boundary treatment. Morely, we recognize the compact scheme has very strict stability limit.