High Order Flux Reconstruction on Stretched and Warped Meshes

TL;DR

This paper investigates the stability and performance of high-order Flux Reconstruction (FR) methods on stretched and warped meshes, demonstrating increased wave propagation resilience compared to traditional schemes, which is crucial for complex geometries.

Contribution

It provides a modified von Neumann analysis for FR on deformed grids and compares its performance with finite difference and finite volume methods on warped meshes.

Findings

Higher CFL limits in contracting mesh regions

FR shows increased wave propagating ability on warped meshes

FR is more resilient to mesh deformation than traditional methods

Abstract

High-order CFD is gathering a broadening interest as a future industrial tool, with one such approach being Flux Reconstruction (FR). However, due to the need to mesh complex geometries if FR is to displace current, lower order methods, FR will likely have to be applied to stretched and warped meshes. Therefore, it is proposed that the analytical and numerical behaviour of FR on deformed meshes for both the 1D linear advection and the 2D Euler equations is investigated. The analytical foundation of this work is based on a modified von Neumann analysis for linearly deformed grids that is presented. The temporal stability limits for linear advection on such grids are also explored analytically and numerically, with CFL limits set out for several Runge-Kutta schemes, with the primary trend being that contracting mesh regions give rise to higher CFL limits whereas expansion leads to lower CFL limits. Lastly, the benchmarks of FR are compared to finite difference and finite volumes schemes, as are common in industry, with the comparison showing the increased wave propagating ability on warped and stretched meshes, and hence, FR;s increased resilience to mesh deformation.