Resolving vortices with an isothermal HLLC Riemann solver

TL;DR

This paper introduces a new isothermal HLLC Riemann solver that improves vortex resolution in 2D flows, addressing limitations of existing solvers in capturing contact discontinuities.

Contribution

A novel contact resolving Riemann solver for isothermal Euler equations extending the HLL solver, enhancing vortex resolution while maintaining computational simplicity.

Findings

Significant improvement in vortex resolution demonstrated in simulations.

The new solver effectively captures contact discontinuities in 2D flows.

Discussion of Galilean invariance loss and its effects on contact resolution.

Abstract

The importance of contact discontinuities in 2D isothermal flows has rarely been discussed, since most Riemann solvers are derived for 1D Euler equations. We present a new contact resolving approximate Riemann solver for the isothermal Euler equations and show its performance for several one- and two-dimensional test problems. The new solver extends the well-known HLL solver, while retaining its computational simplicity. The significant gain in resolution of vortices is displayed by a simulation of the K\'arm\'an vortex street. We discuss the loss of Galilean invariance and its implications for the resolution of contact discontinuities, which is experienced by all modern numerical schemes for hydrodynamics in non-moving grids.