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 wellbalanced with respect to the priorly known isothermal and isentropic hydrostatic states. To ensure positivity of the density and pressure throughout the whole computation, we introduce interpolation-based and flux-based positivity-preserving limiters to both the density and pressure. Meanwhile, modifications are made to the discretization of the pressure equilibrium to restore well-balancedness. We point out that by using the Si-WENO operator we can compute all ingredients in the discretization of the source term prior to the time evolution, and the well-balanced and positivity-preserving modifications are made based on these ingredients, which can improve computational efficiency. Moreover, we carefully derive the positivity-preserving CFL conditions in one and two dimensions. Finally, the accuracy, robustness, effectiveness and numerical symmetry of our approach are demonstrated by a variety of numerical examples, where the time-marching strategy is used in two-dimensional problems to avoid strong dependence on p/.in the CFL conditions. (c) 2023 Elsevier Inc. All rights reserved.