二维非定常有涡流动的数值模拟方法

为有效地模拟二维有分离现象的粘性流动,发展了求解涡量流函数方程的数值方法。对涡量输运方程的时间项运用四阶Runge-Kutta法离散,从而将方程分解为4个计算步分别求解。在每一计算步对方程进行Steger-Warming近似因式分解,从而使涡量的计算在空间的两个方向上分别进行。对流项采用Chakravaythy-Oscher总变差减少(TVD)格式离散。流函数的Poisson方程运用Tschebyscheff SLOR方法交替方向迭代求解。运用该方法对突然起动圆柱和高雷诺数时弯曲薄翼的非定常有涡流动进行了数值模拟,并将计算结果与其它方法的计算结果和试验结果进行了对比,结果表明本方法具有精度高、数值稳定性好和计算效率高的优点。

Numerical simulation method of unsteady vortical flows

A vorticity-stream function method was developed to simulate unsteady vortical flows. The solution of the vorticity transport equation was split into four steps using the fourth-order Runge-Kutta method. At each step, the equation was solved in two computational directions after factorization using the Steger-Warming approximate factorization scheme with the convective term discretized with the Chakravaythy-Oscher total variation diminishing (TVD) scheme. The stream function Poisson equation was solved with the Tschebyscheff successive linear over-relaxation (SLOR) method in alternating directions. The unsteady vortical flows past an impulsively started cylinder and flows around a thin cambered airfoil at high Reynolds numbers were simulated using the method. The results compare well with experimental data and previous calculations.