On the connection between the spectral volume and the spectral difference method

Journal of Computational Physics

Volumn 227, Issue 2, 2007, Pages 877-885

  Van den Abeele, Kris ^a   Lacor, Chris ^a   Wang, Z J ^b  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^b Iowa State University of Science and Technology   (United States)

Author keywords

Spectral difference method; Spectral volume method

Indexed keywords

SPECTRAL DIFFERENCE METHODS; SPECTRAL VOLUME METHOD; SPECTRAL VOLUMES;

EID: 36148968111     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.08.030     Document Type: Article

References (16)

1. Cockburn B., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II: general framework. Mathematics of Computation 52 (1989) 411-435
2. Wang Z.J. Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation. Journal of Computational Physics 178 (2002) 210-251
3. Wang Z.J., and Liu Y. Spectral (finite) volume method for conservation laws on unstructured grids. II: extension to two-dimensional scalar equation. Journal of Computational Physics 179 (2002) 665-697
4. Wang Z.J., and Liu Y. Spectral (finite) volume method for conservation laws on unstructured grids. III: one dimensional systems and partition optimization. Journal of Scientific Computing 20 (2004) 137-157
5. Wang Z.J., Zhang L., and Liu Y. Spectral (finite) volume method for conservation laws on unstructured grids. IV: extension to two-dimensional Euler equations. Journal of Computational Physics 194 2 (2004) 716-741
6. Liu Y., Vinokur M., and Wang Z.J. Spectral (finite) volume method for conservation laws on unstructured grids. V: extension to three-dimensional systems. Journal of Computational Physics 212 (2006) 454-472
7. Sun Y., Wang Z.J., and Liu Y. Spectral (finite) volume method for conservation laws on unstructured grids. VI: extension to viscous flow. Journal of Computational Physics 215 (2006) 41-58
8. Wang Z.J., and Liu Y. Extension of the spectral volume method to high-order boundary representation. Journal of Computational Physics 211 (2006) 154-178
9. Liu Y., Vinokur M., and Wang Z.J. Spectral difference method for unstructured grids. I: basic formulation. Journal of Computational Physics 216 (2006) 780-801
10. Wang Z.J., Liu Y., May G., and Jameson A. Spectral difference method for unstructured grids. II: extension to the Euler equations. Journal of Scientific Computing (2006) 10.1007/s10915-006-9113-9
11. Kopriva D.A. A conservative staggered-grid Chebyshev multidomain method for compressible flows. II: semi-structured method. Journal of Computational Physics 128 (1996) 475
12. Chen Q.-Y. Partitions of a simplex leading to accurate spectral (finite) volume reconstruction. SIAM Journal on Scientific Computing 27 4 (2006) 1458-1470
13. Q.-Y. Chen, Partitions for spectral (finite) volume reconstruction in the tetrahedron, IMA Preprint Series # 2035, April 2005.
14. Van den Abeele K., Broeckhoven T., and Lacor C. Dispersion and dissipation properties of the 1D spectral volume method and application to a p-multigrid algorithm. Journal of Computational Physics 224 2 (2007) 616-636
15. Van den Abeele K., and Lacor C. An accuracy and stability study of the 2D spectral volume method. Journal of Computational Physics 226 1 (2007) 1007-1026
16. Shu C.-W. Total variation diminishing Runge-Kutta schemes. SIAM Journal of Scientific and Statistical Computing 9 (1988) 1073-1084