Fifth-Order Bound-, Positivity-, and Equilibrium-Preserving Affine-Invariant AWENO Scheme for Two-Medium γ-based Model of Stiffened Gas
ABSTRACT
We describe a quasi-conservative finite difference AWENO scheme with the affine-invariant Z-type nonlinear weights (Ai-AWENO) for the γ-based model. The shock-capturing scheme should always but often fail to preserve the constant velocity and pressure. One leading cause is that switching the equation of state between different mediums generates numerical oscillations around the medium interface. In the Ai-AWENO scheme, the conservative variables, instead of the primitive variables, are used, and the equilibriums of velocity and pressure are preserved. A hybrid flux-based bound-and positivity-preserving (BP-P) limiter, which is a convex combination of the high-order (for resolution) and first-order (for BP-P) numerical fluxes, is also implemented to enforce the physical constraints. The theoretical analysis yields the exact CFL conditions of the first-order Lax-Friedrichs numerical flux for the stiffened gas. The numerical diffusion coefficient depends nonlinearly on the local Mach number. Various one-, two-, and three-dimensional benchmark two-medium shock-tube problems illustrate the proposed scheme’s high-order accuracy and enhanced robustness.