一种求解欧拉方程改进的通量分裂方法

本文以Steger-Warming提出求解Euler方程的通量分裂方法为基础,利用改进的特征值分裂方法,建立了一种连续的通量分裂方法。该方法克服了Steger-Warming通量分裂法存在的分裂后的通量在个别点导数不连续的问题,同时方法简单,便于推广。对于通量分裂后的Euler方程,采用迎风格式,建立了相应的二阶隐式有限体积方程。为了减少求解所得块矩阵方程组所需要的工作量,本文利用特征变换,在不改变原方程组离散化精度的前提下,将所得块矩阵方程组化为分离的代数方程组进行求解,从而大大减少了计算量。文中分别对一维管流,二维绕NACA-0012和NACA64A-10翼型在亚声速和超声速来流的跨声速流场进行了计算,并将所得结果与有关实验和计算结果进行了比较,均符合良好。 本文所建立的方法具有占机内存小,计算时间短的优点。在普通中小型计算机上亦可使用。

A Kind of Improved Flux-Split Method for Solving the Euler Equations

A new continuous flux-split method for solving the Euler equations is given in this paper.In the method, the idea in Steger-Warming's flux splitting method is used, while the improved eigenvalue split method is presented with which the split flux slope discontinuity which appeared in the Steger-Warming's approach at some critical points in the flow field is eliminated. Practical application indicates that this method is rather simple and robust. For the flux split Euler equations, the MUSCL type upwind difference scheme is used and the second order implicit finite volume formulations are built.These formulations are block matrix structures.In order to reduce the computer time,the eigenvector matrix transformation is used so the induced block matrix equations are transformed into separate algebriac equations.lt is much easier to solve this kind of equations than the former one, espacially in medium or microl computers.As examples, an quasi-one-dimensional nozzle flow with shock and the subsonic and transonic flow about NACA-0012 and NACA64A-10 airfoils are calculated.The results are compared with the experimental data and the other computed results. Numerical application shows that the present method needs less computer storage volume and CPU time.