A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes

By Michael Dumbser, Dinshaw S. Balsara, Eleuterio F. Toro, Claus-Dieter Munz. Journal of Computational Physics, 2008

622 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2d676116efd79653716db8d4999e297eeec16f4a

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In Computational Mechanics

Citations in the corpus

A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids (2014, methodology): “Yidong Xia a,⇑, Hong Luo a, Megan Frisbey a, Robert Nourgaliev b a Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, USA b B Division, Weapons and Complex Integration, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA a r t i c l e”
Numerical Methods for High-Speed Flows (2011, methodology): “Sample results of the calculations of Touber & Sandham (2009) are reported in Figure 5, showing a comparison between the mean LES field (in terms of streamwise velocity and turbulent shear stress), and reference experimental data (Dupont et al., 2008). Overall, the LES results are in very good agree”
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, methodology): “The iterative method (14) converges very efficiently to the unknown expansion coefficients q̂l of the local space-time predictor solution, see [35, 51, 41].”
Well-Balanced High-Order Centred Schemes for Non-Conservative Hyperbolic Systems. Applications to Shallow Water Equations with Fixed and Mobile Bed (2009, methodology): “For two more general and fully numerical alternatives to the semi-analytical Cauchy-Kovalewski procedure see [11] and [10], where local space-time finite element methods are used in order to compute the polynomial Qi(x, t).”
A review of flux reconstruction or correction procedure via reconstruction method for the Navier-Stokes equations (2016, background): “…spectral difference (Liu, Vinokur, and Wang, 2006, Kopriva and Kolias, 1996), spectral volume (Wang, Zhang, and Liu, 2004), and PnPm or hybrid DG/finite volume (Dumbser et al, 2008 and Zhang et al, 2012) methods, have been developed for many decades on both structured and unstructured meshes.”
Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter (2016, methodology): “The modification procedure is in a least square fashion [10].”