Abstract
THE transonic full potential equation in strong conservation form is solved on a body-fitted coordinate system using a strongly implicit procedure enhanced by the multigrid procedure. Weak viscous effects are accounted for by computing the displacement thickness using the NashMcDonald integral boundary-layer equation. The convergence speed of the multigrid procedure is found to be comparable to the state-of-the-art multigrid-alternating direction implicit procedures on identical grids. Several numerical cases, some involving weak viscous effects, are presented and compared with published results. Contents Recently the author and his co-workers developed a relaxation procedure for the solution of the steady transonic full potential equation in a body-fitted coordinate system.1 This procedure has the following steps. The governing equation is linearized at each step of the iteration by lagging the density by one iteration. The density is biased in supersonic regions using the artificial compressibility concept.2'3 Standard central differences are used to discretize the governing equation and the transformation metrics. The above steps lead to the following system of equations:
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