Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

By Yen Liu, Marcel Vinokur, Zhijian Wang. 2004

158 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/db82db3bb04e6d86d7b561d0b43e3ec65bbb65a2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Haiyang Gao
2. Zhijian Wang
3. Yen Liu
4. Antony Jameson
5. Michael Yang
6. Y. Allaneau
7. Yuzhi Sun
8. Takanori Haga

In Computational Mechanics

1. Zhijian Wang
2. Haiyang Gao
3. Hung T. Huynh
4. Takanori Haga
5. Antony Jameson
6. Y. Allaneau
7. Yuzhi Sun
8. Yen Liu

Citations in the corpus

• A review of flux reconstruction or correction procedure via reconstruction method for the Navier-Stokes equations (2016, unknown): “…Galerkin (Reed & Hill, 1973, Cockburn & Shu, 1998, Bassi & Rebay, 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…”
• Differential Formulation of Discontinuous Galerkin and Related Methods for the Navier-Stokes Equations (2013, background): “Commonly usedmethods of this type include discontinuous Galerkin (DG) [2, 3, 5–7], staggered-grid (SG) [15], spectral volume (SV) [24–27], and spectral difference (SD) [17–19].”
• High-Order Multidomain Spectral Difference Method for the Navier-Stokes Equations on Unstructured Hexahedral Grids (2006, methodology): “An incomplete list of notable examples includes the spectral element method [25], multi-domain spectral method [16,17], k-exact finite volume method [3], WENO methods [13], discontinuous Galerkin method [4, 7, 8], high-order residual distribution methods [1], spectral volume (SV) [21, 31, 36, 37] an”
• A Parameter-Free Generalized Moment Limiter for High- Order Methods on Unstructured Grids (2009, methodology): “Examples of such methods include the discontinuous Galerkin (DG) method [4, 5, 30], the multi-domain staggered- grid method [16, 17], the spectral volume method [41, 42], the spectral difference (SD) method [22, 34].”
• Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations (2011, methodology): “…Allanea a b s t r a c t The purpose of this paper is to provide new insights on the connections that exist between the discontinuous Galerkin method (DG), the flux reconstruction method (FR) and the recently identified energy stable flux reconstruction method (ESFR) when solving time dependent…”
• 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.”
• Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations (2007, unknown): “[15,16] for conservation laws on unstructured grids.”
• A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids (2009, methodology): “There are also significant research activities in other methods, such as the k-exact finite volume method [2,6,12,32], streamline-upwind Petrov–Galerkin (SUPG) method [21,46], spectral and spectral-element type methods [15,5,19,24], the residual distribution (RD) or fluctuation splitting method [1],”
• High‐order CFD methods: current status and perspective (2013, methodology): “Other methods were developed for unstructured meshes, for example, [6, 9–18].”
• A Reconstruction Approach to High -Order Schemes Including Discontinuous Galerkin for Diffusion (2009, background): “(3.21) Note that this g results in a scheme very similar to the staggered-grid scheme of Kopriva and Kolias (1996) as well as the spectral-difference method of Liu et al. (2006).”