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Dispersion-diffusion analysis for variable coefficient advection problems, with application to alternative DG formulations and under-resolved turbulence
Dispersion-diffusion analysis for variable coefficient advection problems, with application to alternative DG formulations and under-resolved turbulence (PDF)
Dispersion-diffusion analysis for variable coefficient advection problems, with application to alternative DG formulations and under-resolved turbulence (Other)
Dispersion-diffusion analysis for variable coefficient advection problems, with application to alternative DG formulations and under-resolved turbulence (Other)
Dispersion-diffusion analysis for variable coefficient advection problems, with application to alternative DG formulations and under-resolved turbulence (Other)
Dispersion-diffusion analysis for variable coefficient advection problems, with application to alternative DG formulations and under-resolved turbulence (Other)
Dispersion-diffusion analysis for variable coefficient advection problems, with application to alternative DG formulations and under-resolved turbulence (Other)
In this thesis, the Von Neumann analysis to analyse diffusion and dispersion errors is extended for variable coefficient linear advection equations. This new approach will be used to analyse the theoretical behaviour exhibited by Discontinuous Galerkin (DG) methods in the wavenumber domain. Variable coefficient linear advection equations are highly relevant as they can be com- pared with the metric terms added when considering curvilinear meshes. Using standard DGSEM algorithm, aliasing errors arising from a deficient interpolation of the non-homogeneous coefficient advective flux may lead to instabilities and early divergence. This features can be predicted with the proposed analysis, and also other DGSEM strategies can be explored in order to counteract this effects. Firstly, this method will be applied to compare the behaviour of Gauss nodes ver- sus Gauss-Lobatto nodes, as well as to compare dispersion and diffusion errors with upwind and central fluxes. Then, this analysis has been also applied to the recently studied branch of Energy Stable DGSEM algorithms, also called skew-symmetric split formulations, which are designed to be aliasing free. Numerical solutions will be carried out in order to confirm the predicted solutions by the Von Neumann test. Several analysis will be then carried in 1D Burgers turbulence, which will serve as a first step before extending this algorithms to Navier-Stokes 3D equations.
2016-07-10
Dispersion-diffusion analysis for variable coefficient advection problems, with application to alternative DG formulations and under-resolved turbulence
Aeronautics
Aeronáutica
Física
Physics
Computer Science
Informática
Matematica_aplicada_2014, Espacio
Espacio
Ferrer Vaccarezza
Esteban
Esteban Ferrer Vaccarezza
Valero Sánchez
Eusebio
Eusebio Valero Sánchez
Manzanero Torrico
Juan
Juan Manzanero Torrico