Volume 6, Issue 5
An Implicit LU-SGS Scheme for the Spectral Volume Method on Unstructured Tetrahedral Grids

Takanori Haga, Keisuke Sawada & Z. J. Wang

DOI:

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

Published online: 2009-06

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  • Abstract

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.

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