This paper proposes and implements the Random Choice Method (RCM) based on a direct Eulerian generalized Riemann problem (GRP) scheme for one-dimensional Euler equations in gas dynamics. It is an application of the second order accurate GRP scheme proposed by Ben-Artzi et al. (2006) [6]. Since the RCM was introduced as a numerical tool in the gas dynamics and it has the advantage of capturing discontinuities with sharp resolution, we here implement the RCM by choosing the GRP scheme as the “building block”. The initial data are assumed to be piecewise linear function, and the local GRP is resolved directly and analytically at each interface. Special attention is paid to the treatment of resolving smooth wave. Numerical simulations on some typical problems show that the proposed method achieves good performance.

本文针对一维气体动力学欧拉方程，提出并实现了一种基于直接欧拉广义Riemann问题（GRP）方案的随机选择方法（RCM）。这是Ben-Artzi等人提出的二阶精确GRP方案的应用。（2006）[6]。由于RCM是作为气体动力学中的数值工具引入的，它具有捕获具有清晰分辨率的不连续性的优势，因此我们在这里通过选择GRP方案作为“构建块”来实施RCM。假定初始数据为分段线性函数，并且在每个接口处直接解析地解析局部GRP。要特别注意解决平滑波的处理。对一些典型问题的数值模拟表明，该方法具有良好的性能。