High-order accurate entropy stable adaptive moving mesh finite difference schemes for (multi-component) compressible Euler equations with the stiffened equation of state

TL;DR

This paper develops high-order entropy stable adaptive moving mesh finite difference schemes for multi-component compressible Euler equations with a stiffened equation of state, improving accuracy and stability in complex simulations.

Contribution

It extends existing entropy stable schemes to multi-dimensional multi-component Euler equations with adaptive moving meshes and high-order accuracy.

Findings

Validated through 2D and 3D numerical tests.

Demonstrated effective capture of localized structures.

Achieved high-order accuracy and stability.

Abstract

This paper extends the high-order entropy stable (ES) adaptive moving mesh finite difference schemes developed in [14] to the two- and three-dimensional (multi-component) compressible Euler equations with the stiffened equation of state. The two-point entropy conservative (EC) flux is first constructed in the curvilinear coordinates. The high-order semi-discrete EC schemes are given with the aid of the two-point EC flux and the high-order discretization of the geometric conservation laws, and then the high-order semi-discrete ES schemes satisfying the entropy inequality are derived by adding the high-order dissipation term based on the multi-resolution weighted essentially non-oscillatory (WENO) reconstruction for the scaled entropy variables to the EC schemes. The explicit strong-stability-preserving Runge-Kutta methods are used for the time discretization and the mesh points are adaptively redistributed by iteratively solving the mesh redistribution equations with an appropriately chosen monitor function. Several 2D and 3D numerical tests are conducted on the parallel computer system with the MPI programming to validate the accuracy and the ability to capture effectively the localized structures of the proposed schemes.