High order well-balanced positivity-preserving scale-invariant AWENO scheme for Euler systems with gravitational field

In this paper, we propose a fifth order well-balanced positivity-preserving finite difference scale-invariant AWENO scheme for the compressible Euler equations with gravitational fields. By using the scale-invariant WENO (Si-WENO) operator and well-balanced modification of the interpolated conservative variables, the finite difference discretization is well-balanced with respect to the priorly known isothermal and isentropic hydrostatic states. …