改进的高阶加权紧致非线性差分格式

Improved High Order Weighted Compact Nonlinear Difference Scheme

基于中心紧致三对角系数矩阵的四阶、六阶格式,通过非线性组合五阶WENO差分格式大模板和两个对称小模板对网格半节点函数值的插值计算,得到求解双曲守恒律方程的四阶、五阶加权紧致非线性差分格式。线性对流方程的计算结果验证了格式的计算精度和计算效率;一维无粘Burgers方程的计算结果验证了格式分辨率;一、二维欧拉方程的计算结果验证了格式对非线性问题中激波间断的捕捉能力。所有数值实验均表明,构造的新格式是一个高效、高精度、高分辨率的激波捕捉格式。

Based on the fourth-and sixth-order central compact schemes with tridiagonal coefficient matrix,the fourth-and fifth-order weighted compact nonlinear difference schemes are obtained for solving hyperbolic conservation law equations,the function values of half-node are interpolated with the nonlinear combination of the fifth-order WENO difference scheme of large template and two small symmetrical templates.The computational accuracy and efficiency of the new scheme are verified by the results of linear convection equation.The resolution of the new scheme is verified by the results of one-dimensional inviscid Burgers equation.The ability of the new scheme to capture the shock discontinuity in nonlinear problems is verified by one-and two-dimensional Euler equations.The numerical experiments show that the proposed scheme is an efficient,high-order and high-resolution shock capturing scheme.