High-order methods for computational fluid dynamics: A brief review of compact differential formulations on unstructured grids

HT Huynh, ZJ Wang, PE Vincent - Computers & fluids, 2014 - Elsevier
Popular high-order schemes with compact stencils for Computational Fluid Dynamics (CFD)
include Discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV) …

[HTML][HTML] PyFR: An open source framework for solving advection–diffusion type problems on streaming architectures using the flux reconstruction approach

FD Witherden, AM Farrington, PE Vincent - Computer Physics …, 2014 - Elsevier
High-order numerical methods for unstructured grids combine the superior accuracy of high-
order spectral or finite difference methods with the geometric flexibility of low-order finite …

A review of flux reconstruction or correction procedure via reconstruction method for the Navier-Stokes equations

ZJ Wang, HT Huynh - Mechanical Engineering Reviews, 2016 - jstage.jst.go.jp
Abstract Computational Fluid Dynamics (CFD) methods that are third-order accurate or
higher are generally considered high-order methods in the aerospace community. These …

Connections between the discontinuous Galerkin method and high‐order flux reconstruction schemes

D De Grazia, G Mengaldo, D Moxey… - … journal for numerical …, 2014 - Wiley Online Library
With high‐order methods becoming more widely adopted throughout the field of
computational fluid dynamics, the development of new computationally efficient algorithms …

Accuracy, stability, and performance comparison between the spectral difference and flux reconstruction schemes

C Cox, W Trojak, T Dzanic, FD Witherden, A Jameson - Computers & Fluids, 2021 - Elsevier
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 …

Energy stable flux reconstruction schemes for advection–diffusion problems on triangles

DM Williams, P Castonguay, PE Vincent… - Journal of Computational …, 2013 - Elsevier
The Flux Reconstruction (FR) approach unifies several well-known high-order schemes for
unstructured grids, including a collocation-based nodal discontinuous Galerkin (DG) method …

Development of an implicit high-order Flux Reconstruction solver for high-speed flows on simplex elements

R Dhib, FB Ameur, R Vandenhoeck, A Lani… - Computer Physics …, 2024 - Elsevier
In this study, a significant emphasis is placed on the extension of high-order Flux
Reconstruction (FR) schemes to cater to high-speed flows, specifically those involving high …

Implicit high-order flux reconstruction solver for high-speed compressible flows

R Vandenhoeck, A Lani - Computer Physics Communications, 2019 - Elsevier
The present paper addresses the development and implementation of the first high-order
Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD …

[图书][B] High-order energy stable flux reconstruction schemes for fluid flow simulations on unstructured grids

P Castonguay - 2012 - search.proquest.com
Nowadays, most commercial CFD software relies exclusively on low-order methods
(methods for which the spatial order of accuracy is at most two) for the simulation of flows …

High-order flux reconstruction schemes

FD Witherden, PE Vincent, A Jameson - Handbook of numerical analysis, 2016 - Elsevier
There is an increasing desire among industrial practitioners of computational fluid dynamics
to undertake high-fidelity scale-resolving simulations of unsteady flows within the vicinity of …