An algebraic multigrid solver for transonic flow problems

This article presents the latest developments of an algebraic multigrid (AMG) based on full potential equation (FPE) solver for transonic flow problems with emphasis on advanced applications. The mathematical difficulties of the problem are associated with the fact that the governing equation changes its type from elliptic (subsonic flow) to hyperbolic (supersonic flow). The flow solver is capable of dealing with flows from subsonic to transonic and supersonic conditions and is based on structured body-fitted grids approach for treating complex geometries. The computational method was demonstrated on a variety of problems to be capable of predicting the shock formation and achieving residual reduction of roughly an order of magnitude per cycle both for elliptic and hyperbolic problems, through the entire range of flow regimes, independent of the problem size (resolution).