Commun. Comput. Phys., 2 (2007), pp. 310-333.


High-Order Multidomain Spectral Difference Method for the Navier-Stokes Equations on Unstructured Hexahedral Grids

Yuzhi Sun 1, Z. J. Wang 1*, Yen Liu 2

1 Department of Aerospace Engineering, Iowa State University, 2271 Howe Hall, Ames, IA 50011, USA.
2 NASA Ames Research Center, Mail Stop T27B-1, Moffett Field, CA 94035, USA.

Received 15 May 2006; Accepted (in revised version) 9 August 2006
Available online 30 September 2006

Abstract

A high order multidomain spectral difference method has been developed for the three dimensional Navier-Stokes equations on unstructured hexahedral grids. The method is easy to implement since it involves one-dimensional operations only, and does not involve surface or volume integrals. Universal reconstructions are obtained by distributing solution and flux points in a geometrically similar manner in a unit cube. The concepts of the Riemann solver and high-order local representations are applied to achieve conservation and high order accuracy. In this paper, accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. High order of accuracy and spectral convergence are obtained for the propagation of an isotropic vortex and Couette flow. The capability of the method for both inviscid and viscous flow problems with curved boundaries is also demonstrated.

AMS subject classifications: 65M70, 76M20, 76M22

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Key words: High order, unstructured grids, spectral difference, Navier-Stokes.

*Corresponding author.
Email: sunyuzhi@iastate.edu (Y. Sun), zjw@iastate.edu (Z. J. Wang), Yen.Liu@nasa.gov (Y. Liu)
 

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