Simple high order well-balanced finite difference WENO schemes for the Euler equations under gravitational fields

The compressible Euler equations coupled with the gravitational source terms admit a hydrostatic equilibrium state where the gradients of the flux terms can be exactly balanced by those in the source terms. This property of exact preservation of the equilibrium is highly desirable at the discrete level when they are numerically solved. In this study, we design the simple high order well-balanced finite difference weighted essentially …