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。 Riem ann problem is computationally intensive, and in order to improve the efficiency and reduce the computational complexity, an approximate solution to the Riemann problem is proposed. Expanded waves in the Riem ann problem are considered as “dilatant shock waves”, and there is a similar solution region between the left and right states formed by two shocks. The advantage of this method is that it preserves the non-linear features of the Riem ann problem and guarantees that the entropy of the self-similar solution region between left and right waves does not decrease. The proposed method achieves good results in solving one-dimensional and multi-dimensional non-viscous and compressible flow.