烧蚀外形方程差分计算方法研究

Finite difference schemes for solution of the nosetip shape change equation

分析了烧蚀外形方程的性质,研究了人工粘性项对烧蚀外形计算结果的影响,发现人工粘性在抹平非物理波动的同时,会严重影响计算精度。借鉴于CFD中NND格式的思想,构造了求解烧蚀外形方程的无波动、无自由参数的耗散差分格式,得到了满意的计算结果。

In this paper, the characteristics of the nosetip shape change equation are analysed, and the effects of the artificial viscous term on the solution of the shape change finite difference equation are investigated thoroughly. The numerical results show that the artificial viscous term could eliminiate the spurious osciliations, but have a great influence on the accuracy of the final results. A new scheme which has properties of non-oscillatory and non-free-parameter dissipation is used to solve the nosetip shape change equation. It is shown that the new algorithm is efficient and robust.