Finite difference method on 1D and 2D Riemann problems for Euler equations with different state of equations

Abstract

We discussed the finite difference WENO5 scheme on the 1D and 2D compressible Euler equations. The 1D Chaplygin gas system with a constant external force led to two kinds of solutions: contact discontinuity and delta shock. A convex set and a limiter were applied to the 2D pressureless system to preserve the positivity of the density function and the boundedness of the velocity field. A global condition on the density function was applied to maintain the scheme’s high order of accuracy, as well as to reduce the computational cost.