Commun. Comput. Phys., 6 (2009), pp. 978-996.

An Implicit LU-SGS Scheme for the Spectral Volume Method on Unstructured Tetrahedral Grids

Takanori Haga 1*, Keisuke Sawada 1, Z. J. Wang 2

1 Department of Aerospace Engineering, Tohoku University, Sendai 980-8579, Japan.
2 Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA.

Received 2 October 2008; Accepted (in revised version) 4 February 2009
Available online 5 May 2009


An efficient implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solution approach has been applied to a high order spectral volume (SV) method for unstructured tetrahedral grids. The LU-SGS solver is preconditioned by the block element matrix, and the system of equations is then solved with a LU decomposition. The compact feature of SV reconstruction facilitates the efficient solution algorithm even for high order discretizations. The developed implicit solver has shown more than an order of magnitude of speed-up relative to the Runge-Kutta explicit scheme for typical inviscid and viscous problems. A convergence to a high order solution for high Reynolds number transonic flow over a 3D wing with a one equation turbulence model is also indicated.

AMS subject classifications: 65M70, 76M12, 76M22

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Key words: High-order, unstructured grid, spectral volume, implicit method.

*Corresponding author.
Email: (T. Haga), (K. Sawada), (Z. J. Wang)

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