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

By Zhijian Wang. 2002

568 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/4e9aef2784954f33505124a59c0e69d2248a2c96

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In Applied Mathematics

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

In Computational Mechanics

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

Citations in the corpus

• Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids (2002, methodology): “The spectral volume method [ 38 ] has been successfully extended to two-dimensional scalar conservation laws using unstructured triangular meshes.”
• Evaluation of discontinuous Galerkin and spectral volume methods for scalar and system conservation laws on unstructured grids (2004, methodology): “Following the arguments given in Reference [10], the surface integral must be exact for polynomials of degree 2k, while the volume integral must be exact for polynomials of degree 2k − 1, i.e.∮ @Ti jF · n dS= K∑ r=1 ∫ Ar jF · n dS∫ Ar jF · n dS≈ ns∑ s=1 wrs j(rrs)F̂(QL(rrs); QR(rrs); nr)Ar∫ Ti ∇ j ·”
• Connections between the filtered discontinuous Galerkin method and the flux reconstruction approach to high order discretizations (2011, methodology): “Kopriva and Kolias [8] introduced the staggered grid method, based on the differential form of the equation, later renamed spectral difference (SD) and thoroughly studied by Liu et al. [9] and Wang et al. [10].”
• 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 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].”
• 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 (finite) volume method for conservation laws on unstructured grids IV: extension to two-dimensional systems (2004, methodology): “For a more detailed review of the literature on the Godunov-type method, refer to [21], and the references therein.”