Multigrid Code for Three-Dimensional Transonic Potential Flow about Inlets

Abstract

In recent years, new mathematical techniques, known as multigrid methods, have been increasingly advocated for the acceleration of relaxation calculations. When successful, they have been extremely effective. However, it has been questioned whether, in view of their complexity, these methods could ever be fruitfully applied to practical problems with complex geometry in three dimensions. An existing code for axisymmetric inlets at angles of attack has been modified to utilize a four-level multigrid method. The mesh follows cylindrical coordinates in the physical domain and is not fitted to the body. Order-of-magnitude improvements in speed and accuracy over the unmodified code are reported. The procedure maintains an overall convergence rate of 0.9. Because this rate is independent of the mesh spacing, an important conclusion is that the method makes possible the use of meshes too fine to have been considered previously. It is also observed that the coding of the algorithm can, as expected, require considerable effort. Further, the adaptation of existing codes is found to be difficult if the structure of the original is not amenable to multigrid procedures. Nevertheless, the method is shown to be of enormous value, when carefully applied, in spite of nonlinearities and complicated geometry. We conclude that its application in production codes will ultimately be deemed practical.