Generalised Lebesgue Stable Flux Reconstruction

A unique set of correction functions for Flux Reconstruction is presented, with there derivation stemming from proving the existence of energy stability in the Lebesgue norm. The set is shown to be incredibly arbitrary with the only union to existing correction function sets being show to be for DG. Von Neumann analysis of both advection and coupled advection-diffusion is used to show that once coupled to a temporal integration method, good CFL performance can be achieved and the correction function may have better dispersion and dissipation for application to implicit LES. Lastly, the turbulent Taylor-Green vortex test case is then used to show that correction functions can be found that improve the accuracy of the scheme when compared to the error levels of Discontinuous Galerkin.