On the Connections Between Discontinuous Galerkin and Flux Reconstruction Schemes: Extension to Curvilinear Meshes

On the Connections Between Discontinuous Galerkin and Flux Reconstruction Schemes: Extension to Curvilinear Meshes
DOI: 10.1007/s10915-015-0119-z/fulltext.html
Abstract: This paper investigates the connections between many popular variants of the well-established discontinuous Galerkin method and the recently developed high-order flux reconstruction approach on irregular tensor-product grids.

Dealiasing techniques for high-order spectral element methods on regular and irregular grids

Dealiasing techniques for high-order spectral element methods on regular and irregular grids
DOI: 10.1016/j.jcp.2015.06.032
Abstract: High-order methods are becoming increasingly attractive in both academia and industry, especially in the context of computational fluid dynamics. However, before they can be more widely adopted, issues such as lack of robustness in terms of numerical stability need to be addressed, particularly when treating industrial-type problems where challenging geometries and a wide range of physical scales, typically due to high Reynolds numbers, need to be taken into account.

Linear dispersion-diusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods

Linear dispersion–diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods
DOI: 10.1016/j.jcp.2015.06.020
Abstract: We investigate the potential of linear dispersion–diffusion analysis in providing direct guidelines for turbulence simulations through the under-resolved DNS (sometimes called implicit LES) approach via spectral/hp methods. The discontinuous Galerkin (DG) formulation is assessed in particular as a representative of these methods. We revisit the eigensolutions technique as applied to linear advection and suggest a new perspective to the role of multiple numerical modes, peculiar to spectral/hp methods.