改进的3阶WENO-N3格式及其在内爆炸载荷计算中的应用

  目的  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，其不但可以降低网格的规模，而且能较好地分辨出流场中复杂的波系结构。  方法  通过在权函数公式中增加额外项的方式构造出WENO-N+3格式，并采用泰勒级数展开的方法对WENO-N3和WENO-N+3格式在极值点处的精度进行理论推导和精度数值测试。选用激波与熵波相互作用、双爆轰波碰撞、瑞利—泰勒不稳定性等问题验证改进格式WENO-N+3与WENO-JS3，WENO-Z3和WENO-N3格式的区别。最后，将改进格式WENO-N+3应用于内爆炸载荷的数值计算。  结果  研究表明，改进格式WENO-N+3相较其他格式耗散低，并且在相同的计算网格下能给出较高的冲击波峰值。  结论  该方法可用于内爆炸载荷的数值计算。

Weighted essentially non-oscillatory schemes

  Objectives  In this paper, an improved third-order WENO scheme named 'WENO-N+3' is constructed by adding a suitable term to the weights of the conventional WENO-N3 scheme.  Methods  The precision near the critical points of WENO-N3 and the WENO-N+3 schemes is derived using the Taylor expansion, and accuracy tests are also conducted. Shock-entropy wave interaction, interacting blast waves and Rayleigh-Taylor instability problems are selected in order to verify that the improved scheme WENO-N+3 has less dissipation than the conventional WENO-JS3, WENO-Z3 or WENO-N3 schemes, with high-resolution flow field structures. Finally, the proposed WENO-N+3 scheme is applied to simulations of explosion loads in a confined space.  Results  The simulation results indicate that the present scheme can provide a higher shockwave peak.  Conclusions  The findings of this paper can provide valuable references for research into the numerical calculation of internal explosion loads.