Abstract
A specially combined lower–upper factored implicit scheme based on the lower–upper symmetric-Gauss–Seidel (LU-SGS) implicit scheme in conjunction with diagonalization and Gaussian elimination (GE) is proposed for solving the compressible, three-dimensional Navier–Stokes equations and the two-equation q– ω turbulence model. The present scheme, LU-SGS-GE, contains all features of the LU-SGS scheme. Because the similarity transforms are used to construct upstream Jacobian matrices of flux vectors, it leads to much faster convergence and better stability without improper numerical dissipation and free-parameters; besides, the block-diagonal matrix inversions are still eliminated partly, and the implicit operator can also be vectorized completely. The new implicit scheme can be used for solving the unsteady three-dimensional flows.
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