Efficient computation of inviscid flow fields around complex configurations using a multiblock multigrid method

The efficient implementation of a multigrid technique for use on block-structured, body-fitted meshes is investigated. The algorithm employed for the solution of inviscid flow fields uses central differences with artificial dissipation, and time integration is performed by a five-stage Runge—Kutta scheme. A major point of concern is the amount of work which may be performed within a block before switching to the next block. In this study three different strategies are under consideration. In the first strategy data are exchanged between blocks in each stage of the Runge—Kutta time-stepping scheme. This keeps a possible time lag between blocks to a minimum, but requires a large amount of I/O operations and storage. The second strategy performs a complete Runge—Kutta cycle within a block before switching to the next. Having completed one time step in all blocks, a second sweep through all blocks is done in order to evaluate residuals necessary for the restriction to coarser meshes. In the third strategy both a complete Runge—Kutta cycle and the residual evaluation for the restriction operator are done within a block, allowing a minimum of I/O and storage. A primary application of all three strategies to a two-block mesh around a wing-body combination showed no significant differences in the convergence of the multigrid algorithm. To investigate the impact of the different strategies on complex configurations, computations were carried out on an 11-block mesh around a wing-body—engine-pylon configuration. Both the first and second strategies delivered converged results, but the third failed due to the larger time lag between blocks. Full multigrid was then used to obtain a preconditioned starting solution for the finest grid. This alleviated the time lag to such an extent that even the third strategy yielded convergence.