# Modified symmetry technique for mitigation of flow leak near corners for compressible inviscid fluid flow

## TL;DR

This paper introduces a modified symmetry technique to address flow leak issues near corners in compressible inviscid fluid flow simulations, improving accuracy in pressure prediction and shock structure modeling.

## Contribution

The paper proposes a novel modification to the standard symmetry boundary condition technique to mitigate flow leaks near corners in Euler equation simulations.

## Key findings

- Reduced flow leak near corners in numerical solutions.
- Improved shock structure prediction on coarse meshes.
- Enhanced accuracy in pressure estimation.

## Abstract

Using the standard symmetry technique for applying boundary conditions for free slip and flat walls with corners will lead to flow leak through the wall near corners (violation of no penetration condition) and a corresponding error in prediction of pressure. Also, prescribing a state at the corner as a boundary condition is not possible. In this paper, a method for tackling the `corner point state' problem is given and modifications to the standard symmetry technique are proposed to mitigate flow leak near the corner. Using this modified symmetry technique, numerical solutions to the Euler equations for flows over forward facing and backward facing step are computed employing the Shu-Osher conservative finite difference scheme with WENO-NP3 reconstruction (with a formal order of accuracy in space of 3), Lax-Freidrichs flux splitting, and TVD-RK3 time discretisation. It is shown that using this modified symmetry technique leads to mitigation of flow leak near the corner and a better prediction of shock structure even on coarse meshes.