Spectral difference method for unstructured grids I: Basic formulation

By Yen Liu, Marcel Vinokur, Zhijian Wang. Journal of Computational Physics, 2006

597 citations recorded by the source corpus.

Subfields: Astronomy and Astrophysics, Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/09785bf7406ea22221f2131c5fd05dadc7e597c4

How researchers see this paper

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

In Astronomy and Astrophysics

1. Hung T. Huynh
2. Haiyang Gao
3. Zhijian Wang
4. Yuzhi Sun
5. Takanori Haga
6. Yen Liu

In Computational Mechanics

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

In Electrical and Electronic Engineering

1. Hung T. Huynh
2. Haiyang Gao
3. Zhijian Wang
4. Yuzhi Sun
5. Takanori Haga
6. 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…”
• A New Class of High-Order Energy Stable Flux Reconstruction Schemes (2011, background): “However, several years later in 2006 Liu, Wang and Vinokular [8] presented a more general formulation for both triangular and quadrilateral elements, which they termed the SD method (a name which has been retained to the present).”
• Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations (2007, background): “Figure 1 displays the placements of solution and flux points for the first to third-order SD schemes [16].”
• 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 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).”
• 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].”
• 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.”