Temporal Stabilisation of Flux Reconstruction on Linear Problems

TL;DR

This paper investigates the use of reference domain filtering in Flux Reconstruction for linear problems, demonstrating its stabilizing effect, impact on accuracy, and influence on turbulence transition in simulations.

Contribution

It introduces a novel approach of applying filtering in the reference domain of high order Flux Reconstruction and analyzes its effects on stability, accuracy, and turbulence transition.

Findings

Filtering stabilizes the scheme temporally by up to 25% for fourth order FR.

Filtering reduces convective velocity and affects the order of accuracy.

The filter Reynolds number helps understand filtering effects on turbulence simulations.

Abstract

Filtering is often used in Large Eddy Simulation with a global filter width, instead here a filter width in the reference domain of high order Flux Reconstruction is considered. It is shown via Von Neumann analysis how filtering effects the dispersion and dissipation of the scheme when spatially and temporally discretised. With it being shown that filtering stabilises the scheme temporally by upto $25\%$ for forth order FR. The impact of filtering on error production is calculated, highlighting the reduction in convective velocity caused and showing numerically the impact on order of accuracy. Finally, the turbulent Taylor-Green case is used to understand the effect of reference domain filtering on the transition to turbulence, and a filter Reynolds number is defined that is shown to be useful in understanding the effect of filtering on simulations.