A Flux Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin Methods

By Hung T. Huynh. 2007

1,030 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3dd563b3ec1bc1c56f0ad9151b69a029b63403b5

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In Computational Mechanics

Citations in the corpus

Differential Formulation of Discontinuous Galerkin and Related Methods for the Navier-Stokes Equations (2013, methodology): “This reduction by a factor of 2 in the stability limit for the 2D diffusion equation is consistent with the reduction by a factor of √ 2 for advection equation in [13,14]: each derivative corresponds to a reduction by √ 2.”
Connections between the discontinuous Galerkin method and high‐order flux reconstruction schemes (2014, methodology): “Huynh in [4] proposed that one can recover a nodal DG scheme with the FR approach by using Radau polynomials for the correction functions.”
PyFR: An open source framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach (2013, background): “Various authors [4, 10] have shown FR schemes exhibit so-called ‘super accuracy’ (an order of accuracy greater than the expected ℘ + 1).”
A High-Order Unifying Discontinuous Formulation for the Navier-Stokes Equations on 3D Mixed Grids (2011, methodology): “It can be shown that the location of SPs does not affect the numerical scheme for linear conservation laws [40, 16].”
Deep Dynamical Modeling and Control of Unsteady Fluid Flows (2018, background): “Recent advances in computational fluid dynamics (CFD) have enabled the numerical simulation of previously intractable flow problems for complex geometries [7]–[11].”
A High-Order Lifting Collocation Penalty Formulation for the Navier-Stokes Equations on 2-D Mixed Grids (2009, methodology): “Huynh (2007) [14] unified all the above methods in 1D with the introduction of the flux reconstruction (FR) method.”
A Reconstruction Approach to High -Order Schemes Including Discontinuous Galerkin for Diffusion (2009, methodology): “The key difference is that the current scheme employs only one grid, and it is stable, whereas the staggered-grid and spectral-difference methods employ two grids, and they are mildly unstable (Huynh 2007).”
Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations (2011, methodology): “…t r a c t The purpose of this paper is to provide new insights on the connections that exist between the discontinuous Galerkin method (DG), the flux reconstruction method (FR) and the recently identified energy stable flux reconstruction method (ESFR) when solving time dependent conservation laws.”
A New Class of High-Order Energy Stable Flux Reconstruction Schemes (2011, methodology): “Also, it has been shown that SD type methods can be recovered (at least for a linear flux function) if the corrections gL and gR are set to zero at a set of k points within S (located symmetrically about the origin) [12].”
A review of flux reconstruction or correction procedure via reconstruction method for the Navier-Stokes equations (2016, methodology): “Various corrections functions are included in (Huynh, 2007).”