New fifth order WENO scheme based on mapping functions [基于映射函数的新型五阶WENO格式]

作者：Liu B.; Li S.; Chen J.; Cheng Q.; Shi X.^*

来源：Acta Aeronautica et Astronautica Sinica, 2022, 43(12): 126155.

DOI：10.7527/S1000-6893.2021.26155

• Euler equation
• high precision
• high resolution
• mapping function
• WENO

Differential formats with high accuracy and high resolution are critical for numerical simulation of complex flow fields. To overcome the degradation defects of WENO-JS and WENO-Z at the first and second order extreme points of the flux function, a new mapping Pe) is designed and applied to the fifth order WENO scheme based on the idea of weighted coefficient reconstruction. The analyses of Approximate Dispersion Relations (ADR) indicate a smaller dispersion error and numerical dissipation of WENO-Pe than WENO-JS, WENO-Z, and other mapping function-based WENO schemes. We conduct numerical simulation in the new scheme and other schemes for 1D cases of the deformed Gaussian wave problem, Sod excitation tube problem, Lax excitation tube problem, and Shu-Osher problem, and 2D cases of the Riemann problem, Rayleigh-Taylor shock-density instability problem, and double Mach reflection problem. The results show that WENO-Pe has stronger ability to capture intermittency and higher resolution with the same order, thereby suitable for numerical simulation of complex flow fields.

• 单位
  天津大学; 水利工程仿真与安全国家重点实验室; 中国科学院大学; 高温气体动力学国家重点实验室