A High-Order Accurate Godunov Method for Modified and Pure Chaplygin Gas Dynamics

We present a high-order accurate Godunov method for solving both modified and pure Chaplygin gas dynamics equations. The approach involves analyzing and applying an exact Riemann solver to construct the Godunov fluxes for both types of gas dynamics. To effectively resolve discontinuities in numerical simulations, we employ a classical weighted essentially nonoscillatory (WENO) scheme and a monotonicity-preserving scheme for the reconstruction of cell averages. A series of numerical tests in both one and two dimensions are conducted to demonstrate the accuracy and robustness of the proposed numerical scheme. Additionally, we examine the behavior of numerical solutions for the modified Chaplygin gas equations. Our results confirm that as the parameter A in the modified Chaplygin gas equation of state approaches zero, the solutions of the modified Chaplygin gas equations converge to those of the pure Chaplygin gas equations, potentially exhibiting delta shock waves.