Riemann问题基于双激波近似的激波捕捉格式

Riem ann问题迭代求解的计算量很大 ,为了提高效率 ,减小计算量 ,提出一种 Riemann问题的近似解法。把Riem ann问题中的膨胀波看成是“膨胀激波”,认为左右状态之间存在由两个激波围成的相似解区域。该方法的优点是保留了 Riem ann问题的非线性特征 ,且保证左右波之间的自相似解区域的熵不减少。该方法在一维及多维无粘可压缩流动求解中取得了较好的结果。

Shock capturing scheme based on two-shock approximation to Riemann problem

Riemann problem is a "building block" of modern high resolution shock capturing schemes. The exact solution of Riemann problem can not be written in close form. Certain iteration procedures are needed to get the explicit solution. Therefore, numerical schemes based on exact Riemann solver are computationally very expensive. In order to improve the computational efficiency, a shock capturing scheme to the original Riemann problem is proposed based on the two shock approximation procedure. In the scheme, all waves in the structure of Riemann problem solution are treated as shock waves. This method keeps non linear feature for Riemann problem, and the entropy does not decrease. Numerical tests indicate that the proposed scheme is efficient and of high resolution to shocks and contact discontinuities.