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A NEW multigrid relaxation scheme is developed for thesteady-state solution of the Euler and Navier-Stokes equa-tions. The lower-upper Symmetric-Gauss-Seidel method (LU-SGS) does not require flux splitting for approximate Newton iteration. The present method, which is vectorizable and uncon-ditionally stable, needs only scalar diagonal inversions. Appli-cation to transonic flow shows that the new method is efficient and robust. Contents Recently, several implicit schemes have been developed suc-cessfully in conjunction with a multigrid method for steady-state solution of the unsteady Euler equations.12 Although the alternating direction implicit scheme could be improved to
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