Abstract: A lower-upper implicit scheme is developed for the unsteady Euler equations. The scheme requires only two sweeps through the grid and it is unconditionally stable. Each factor represents an algebraic system which is either lower block diagonal or upperblock diagonal and hence the name LU. Inversion of such systems is relatively simple and efficient. A nonlinear multigrid algorithm,full approximation storage (FAS),is combined with LU implicit scheme to produce a rapidlyconvergent algorithm for calculating steady-state solutions of the Euler equations.

Key words: Jameson-Turkel LU scheme, FAS non-linear multigrid algorithm, Euler Equations