We report the development of a discontinuous spectral element flow solver that includes the
implementation of both spectral difference and flux reconstruction formulations. With this …

The flux reconstruction (FR) approach offers a flexible framework for describing a range of
high-order numerical schemes; including nodal discontinuous Galerkin and spectral …

The paper devises high-order energy stable flux reconstruction method towards first-order
hyperbolic linear advection-diffusion and nonlinear Navier-Stokes problems (HFR). The …

Theoretical methods are developed to understand the effect of non-uniform grids on Flux
Reconstruction (FR) in multi-dimensions. A better theoretical understanding of the effect of …

We provide a careful Fourier analysis of the Guermond–Pasquetti mass lumping correction
technique (Guermond and Pasquetti, 2013 [11]) applied to pure transport and convection …

We present a numerical analysis of linear multigrid operators for the high-order Flux
Reconstruction method. The non-modal analysis is used to assess the short-term numerical …

The purpose of this work is to describe in detail the development of the spectral difference
Raviart–Thomas (SDRT) formulation for two and three-dimensional tensor-product elements …

An extended range of energy stable flux reconstruction schemes, developed using a
summation-by-parts approach, is presented on quadrilateral elements for various sets of …

Flux reconstruction provides a framework for solving partial differential equations in which
functions are discontinuously approximated within elements. Typically, this is done by using …

High-order methods have become of increasing interest in recent years in computational
physics. This is in part due to their perceived ability to, in some cases, reduce the …