A Space-Time Discontinuous Galerkin Method for Navier-Stokes with Recovery.

Computational Fluid Dynamics;Recovery-based Discontinuous Galerkin Method (RDG);Space-time Advection-diffusion;High Order;Aerospace Engineering;Engineering;Aerospace Engineering

Lo, Kwok Ho MarcusRoe, Philip L. ;

University of Michigan

关键词: Computational Fluid Dynamics;    Recovery-based Discontinuous Galerkin Method (RDG);    Space-time Advection-diffusion;    High Order;    Aerospace Engineering;    Engineering;    Aerospace Engineering;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/86313/khlo_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This thesis tells the story of two new members of a new generation of discontinuous Galerkin (DG)methods. Although DG, as a spatial discretization, has exhibited unparalleled success in handling advection-dominated problems on unstructured grids, DG;;s development in diffusion and time-marching schemes haslagged far behind in comparison. The first part of this thesis contributes to a newly introduced diffusionscheme, and the second part to an arbitrarily high-order explicit time-marching scheme.Interface-centered recovery-based DG (RDG) was first introduced by Van Leer and Nomura (2005) asa new DG discretization for diffusion. The recovery concept is attractive because it is easily understoodand can be extended beyond diffusion. The idea is to recover a smooth solution across a cell interface thatshares all moments with the discontinuous solutions in the two cells adjacent to that interface. RDG provesto be a scheme of fine pedigree: its order of accuracy, 3p + 1 for odd p (p is the order of the solutionpolynomial), and 3p + 2 for even p, is unmatched on a Cartesian grid by any existing method for diffusion.For unstructured grids, the order of accuracy is reduced to the standard p+1, but RDG still allows of muchlarger time steps due to smaller eigenvalues. The extension to nonlinear problems with cross-derivative termsand two-dimensional structured and unstructured grids is described. Numerical tests for a range of diffusionequations, including Navier-Stokes, conrm the high-order accuracy of RDG.Van Leer (1977) coupled spatial and temporal operators to produce an exact shift in the solution foradvection at a Courant-Friedrich-Lewy (CFL) number of unity. Huynh (2005) successfully implemented thisconcept in the ;;moment scheme;; (p = 1) for the Euler equations. We extend this method to arbitrarily highorder, and incorporate RDG for handling diffusion. The method is currently called Hancock-Huynh discon-tinuous Galerkin (HH-DG). We have tested it on Euler problems and linear advection-diffusion problems.