Nonlinear wave interactions for a flux perturbed model in non-ideal gas dynamics

This work explores the Riemann problem for a pressureless gas dynamics Cargo–LeRoux model with constant gravity governing a 3 by 3 system of conservation laws in the absence of external forces of Euler equations. Introducing flux perturbation of a van der Waals isothermal gas, the elementary waves of the Riemann problem are derived and establish the existence-uniqueness of the Riemann solution for arbitrary initial data locally. We develop a series of test cases to design these waves, where the Newton-Raphson method of two variables is used to determine the unknown densities. Moreover, the influence of van der Waals excluded volume on physical quantities such as density, potential, velocity and total pressure is analyzed and illustrated graphically using MATLAB. Finally, we extensively study the elementary wave interactions with and without involving contact discontinuity and the possible combination of waves is demonstrated thoroughly.