# An accurate and robust genuinely multidimensional Riemann solver for Euler equations based on TV flux splitting

## TL;DR

This paper introduces a new multidimensional Riemann solver for Euler equations that is robust, shock-stable, and preserves contact discontinuities, demonstrating superior performance on complex shock problems.

## Contribution

A novel genuinely multidimensional Riemann solver based on TV flux splitting that effectively handles shock stability and contact preservation in Euler equations.

## Key findings

- Solver is free of Carbuncle instability.
- Demonstrates superior shock stability in 2D tests.
- Effectively preserves contact discontinuities.

## Abstract

A simple robust genuinely multidimensional convective pressure split (CPS) , contact preserving, shock stable Riemann solver (GM-K-CUSP-X) for Euler equations of gas dynamics is developed. The convective and pressure components of the Euler system are separated following the Toro-Vazquez type PDE flux splitting [Toro et al, 2012]. Upwind discretization of these components are achieved using the framework of Mandal et al [Mandal et al, 2015]. The robustness of the scheme is studied on a few two dimensional test problems. The results demonstrate the efficacy of the scheme over the corresponding conventional two state version of the solver. Results from two classic strong shock test cases associated with the infamous Carbuncle phenomenon, indicate that the present solver is completely free of any such numerical instabilities albeit possessing contact resolution abilities.Such a finding emphasizes the pre-existing notion about the positive effects that multidimensional flow modelling may have towards curing of shock instabilities.