Energy stable flux reconstruction schemes for advection–diffusion problems

P Castonguay, DM Williams, PE Vincent… - Computer Methods in …, 2013 - Elsevier
High-order methods for unstructured grids provide a promising option for solving
challenging problems in computational fluid dynamics. Flux reconstruction (FR) is a …

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 …

Three-dimensional high-order least square-based finite difference-finite volume method on unstructured grids

YY Liu, LM Yang, C Shu, HW Zhang - Physics of Fluids, 2020 - pubs.aip.org
The least square-based finite difference-finite volume (LSFD-FV) method has been
developed and successfully applied to solve various two-dimensional flow problems with a …

Third-order Paired Explicit Runge-Kutta schemes for stiff systems of equations

SH Nasab, BC Vermeire - Journal of Computational Physics, 2022 - Elsevier
The ability to advance locally-stiff systems of equations in time depends on accurate and
efficient temporal schemes. Recently, a new family of Paired Explicit Runge-Kutta (P-ERK) …

Nonlinearly stable flux reconstruction high-order methods in split form

A Cicchino, S Nadarajah, DCDR Fernández - Journal of Computational …, 2022 - Elsevier
The flux reconstruction (FR) method has gained popularity in the research community as it
recovers promising high-order methods through modally filtered correction fields, such as …

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

DM Williams, A Jameson - Journal of Scientific Computing, 2014 - Springer
The flux reconstruction (FR) methodology provides a unifying description of many high-order
schemes, including a particular discontinuous Galerkin (DG) scheme and several spectral …

Optimal Runge-Kutta stability polynomials for multidimensional high-order methods

S Hedayati Nasab, CA Pereira, BC Vermeire - Journal of Scientific …, 2021 - Springer
In this paper we generate optimized Runge-Kutta stability polynomials for multidimensional
discontinuous Galerkin methods recovered using the flux reconstruction approach. Results …

A parallel, high-order direct discontinuous Galerkin method for the Navier-Stokes equations on 3D hybrid grids

J Cheng, X Liu, T Liu, H Luo - Communications in Computational …, 2017 - cambridge.org
A parallel, high-order direct Discontinuous Galerkin (DDG) method has been developed for
solving the three dimensional compressible Navier-Stokes equations on 3D hybrid grids …

Equivalence between the energy stable flux reconstruction and filtered discontinuous Galerkin schemes

P Zwanenburg, S Nadarajah - Journal of Computational Physics, 2016 - Elsevier
The aim of this paper is to demonstrate the equivalence between filtered Discontinuous
Galerkin (DG) schemes and the Energy Stable Flux Reconstruction (ESFR) schemes …

Provably stable flux reconstruction high-order methods on curvilinear elements

A Cicchino, DCDR Fernández, S Nadarajah… - Journal of …, 2022 - Elsevier
Provably stable flux reconstruction (FR) schemes are derived for partial differential
equations cast in curvilinear coordinates. Specifically, energy stable flux reconstruction …