直接的矩阵分裂计算跨音速喷管流场

DIRECT COEFFICIENT MATRIX SPLITTING FOR NUMERICAL COMPUTATION OF TRANSONIC NOZZLE FLOW

关键词:  跨音速喷管  喷管气流  流动分布  矩阵算法  数值模拟

Key words:  Transonic nozzle  Nozzle gas flow  Flow distribution  Matrix algorithm  Numerical simulation

摘要:

给出了分离系数矩阵（ＳＣＭ）求解欧拉方程组时系数矩阵的直接分离公式，减少和简化了应用该方法时的矩阵运算。参照Ｂｅａｍ－Ｗａｒｍｉｎｇ显式格式构造与ＳＣＭ方法一致的内点差分格式，并分析了它的数值特性。对有斜激波的跨音速内流场进行了数值仿真。计算中采用变系数的当地时间步长，加快了流场达到稳态的收敛速度。计算无需引入任何人工参数，计算值与实验结果吻合。

Abstract:

he split coefficient matrix (SCM) method is improved for the numerical computation of Euler gas dynamic equations in nonconservative forms to simulate the transonic nozzle flowfields. Concise expressions for the direct coefficient matrix splitting are derived and presented in the paper, the related matrix splitting computation work is consequently greatly reduced and simplified. By referring to Beam-Warming’s explicit finite difference scheme, a second-order accurate scheme in consistence with SCM method is constructed and analysed. Besides conventional local time stepping to accelerating the convergence of steady state calculation, an additional option is switched on to setting the parameter C differently at each mesh point according to its local Mach number. The measure results a quicker convergence. Although there is an oblique shock within the nozzle supersonic flow region, it revealed that the algorithm being used is still robust even if without any artificial parameter to control the numerical instability. Computational results are in good agreement with experiments in a wide range of Mach number.