Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids

By Zhijian Wang, Yen Liu. 2002

365 citations recorded by the source corpus.

Subfields: Atmospheric Science, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/3c08ca10f9caaa9ab392b217a25f260b75b7fc9e

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Citations in the corpus

Spectral difference method for unstructured grids I: Basic formulation (2006, methodology): “A TVD limiter implemented here is very similar to that for the SV method [41].”
A High-Order Unifying Discontinuous Formulation for the Navier-Stokes Equations on 3D Mixed Grids (2011, methodology): “Other methods assuming element-wise discontinuous solution are staggered-grid (SG) multi-domain spectral method [20], spectral volume (SV) [12, 14, 24, 39, 43, 46, 47, 48] and spectral difference (SD) [22, 23, 27, 40] methods.”
A review of flux reconstruction or correction procedure via reconstruction method for the Navier-Stokes equations (2016, neutral): “…1997a, 1997b, Cockburn, Karniadakis, and Shu, 2000), 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…”
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, background): “This is a classical reconstruction or recovery problem of a higher order polynomial from known cell averages, which typically arises within the finite volume context and also in spectral finite volume methods [111, 72, 110].”
Spectral (finite) volume method for conservation laws on unstructured grids IV: extension to two-dimensional systems (2004, methodology): “We continue the development of the spectral (finite) volume (SV) method for hyperbolic conservation laws on unstructured grids following the basic formulation [21], development for two-dimensional (2D) scalar conservation laws [ 22 ], and one-dimensional (1D) systems and partition optimization [23].”
Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials (2012, methodology): “Several strategies became very popular due to their intrinsic simplicity such that the MUSCL method [3,6,7,20,26,32] or their efficiency to achieve very high-order accuracy such that the ENO/WENO method [1,21,29,30,36,37,46,18,19,35,49,41], the Discontinuous Galerkin method [9– 12], the ADER method ”