论文部分内容阅读
高分辨率激波捕捉格式对含激波流场的数值模拟具有重要意义。在三阶WENO-Z格式(WENO-Z3)基础上,通过构造不同形式的全局光滑因子得到WENO-Z3N1,WENO-Z3N2,WENO-Z3N3格式。选取Sod激波管、双爆轰波碰撞、激波与熵波相互作用等经典算例,考察了上述格式(WENO-Z3,WENO-Z3N1,WENO-Z3N2,WENO-Z3N3)的计算性能。根据泰勒级数展开,理论推导给出上述格式的精度分析。通过探讨各格式理论精度与实际计算精度之间的关系得到如下结论:上述格式在连续解非极值点处的理论精度对实际计算性能起决定性的作用,并通过双马赫反射问题进一步验证该结论的可靠性。本文的研究给出一种三阶WENO-Z格式的改进方法:合理构造全局光滑因子使得格式在连续解非极值点处满足设计精度的要求。
High-resolution shock capture format is of great importance to the numerical simulation of flow field with shock. Based on the third-order WENO-Z format (WENO-Z3), WENO-Z3N1, WENO-Z3N2 and WENO-Z3N3 formats are obtained by constructing different forms of global smoothing factors. The classical numerical examples of Sod shock tube, double detonation collision and the interaction between shock wave and entropy wave were selected to investigate the computational performance of the above WENO-Z3, WENO-Z3N1, WENO-Z3N2 and WENO-Z3N3. According to Taylor series expansion, the theoretical derivation gives the accuracy analysis of the above format. By discussing the relationship between theoretical accuracy of each format and actual calculation accuracy, the following conclusions are reached: The theoretical accuracy of the above format at the non-extreme point of continuous solution plays a decisive role in the actual calculation performance, and the conclusion is further verified by the double Mach problem The reliability. The research in this paper gives an improved method for the third-order WENO-Z format: a reasonable construction of the global smoothing factor makes the format meet the design accuracy requirements at non-extremal points.