The generalized Riemann problem for the Chaplygin gas equation

Abstract

The main motive of the present study is to determine the closed form solution of the generalized Riemann Problem (GRP) for the 1-D Euler's equation for Chaplygin gas by using the Differential Constraint Method (DCM). The consistency conditions and differential constraint for the governing model is determined. Also, the compatibility condition between differential constraints and Chaplygin gas model is computed here. Further, to obtain an exact (closed form) solution of Generalized Riemann Problem (GRP), we characterize the solution for a smooth arbitrary function as initial data. Ultimately, we solve the GRP with generalized discontinuous initial data. © 2020 Elsevier Masson SAS