Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection–diffusion problems: insights into spectral vanishing viscosity

Eigensolution analysis of spectral/hp continuous Galerkin approximations to advection–diffusion problems: Insights into spectral vanishing viscosity
DOI: 10.1016/j.jcp.2015.12.009
Abstract: This study addresses linear dispersion–diffusion analysis for the spectral/hp continuous Galerkin (CG) formulation in one dimension.

Nektar++ on the Mira Cluster

Mira is a Blue Gene/Q supercomputer ran by the Argonne national laboratory. As of 2016, it is ranked as the fifth-fastest supercomputer in the world. If you are interested in using Nektar++ on Mira, please read on. Users of Mira often have access to Cetus, a smaller  cluster with the same architecture as Mira. The […]

Formula 1

Nektar++ has been used to investigate the flow dynamics and vortex generation behind the front section of a Formula 1 racing car. The above image shows the flow trajectory, coloured by pressure, at a Reynolds number of 220,000, based on the chord of the main-plane of the front-wing. The simulation has 13 million degrees of […]

Profiling using Solaris Studio

Oracle Solaris Studio is a free proprietary development suite that includes compilers and analysis tools. It is available ​from here for free download upon a quite non-restrictive license agreement and it can be used locally on Linux machines with Java installed. On the internal Nektar++ compute nodes it is made available by running This pages describes how to use […]

Compressible flow

Nektar++ includes a solver for simulating the dynamics of compressible inviscid/viscous flow on unstructured two-dimensional and three-dimensional meshes. Specifically, the solver solves two system of equations: Euler equations; Navier-Stokes equations. The systems are provided with a comprehensive set of boundary conditions (1) for specifying inflow/outflow variables as well as wall conditions. In both the systems appropriate techniques for […]

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.