多项式拟合数值边界格式及其稳定性分析

根据构造无反射数值边界格式的基本思想,采用多项式拟合的方法,构造了一种高精度的数值边界格式(SFEBS).理论分析表明:SFEBS边界格式与4阶紧致差分格式相结合,既能保持格式的G-K-S稳定性,又能保持三对角矩阵是严格对角占优的.数值试验表明:2阶和3阶边界格式分别能够保持3阶和4阶的整体精度;4阶的SFEBS格式也能够保持4阶的整体精度,同时能够减小自由流出边界上的最大误差.

Polynomial Fitting Numerical Boundary Scheme and It's Stability Analysis

Based on the idea of non-reflection boundary scheme,a high order numerical boundary scheme (SFEBS) is proposed in this paper by using the polynomial fitting method. Theoretical analysis shows that,combined with the forth order compact scheme,not only the SFEBS boundary scheme is stable in G-K-S sense,but also the strictly diagonally dominant tridiagonal matrix can be obtained. Numerical experiments indicate that the global accuracy of the second (third,forth) order boundary scheme is third (forth,forth) order. Most significantly is the finding that the high order boundary scheme can decrease the error on the outflow boundary scheme.