Abstract
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.
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