A fast, matrix-free implicit method for computing low Mach number flows onunstructured grids

A fast, matrix-free implicit method has been developed to solve low Mach nu mber how problems on unstructured grids. The preconditioned compressible Eu ler and Navier-Stokes equations are integrated in time using a linearized i mplicit scheme. A newly developed fast, matrix-free implicit method, GMRESLU-SGS, is then applied to solve the resultant system of linear equations. A variety of computations has been made for a wide range of flow conditions , for both inviscid and viscous flows, in both 2D and 3D to validate the de veloped method and to evaluate the effectiveness of the GMRES + LU-SGS meth od. The numerical results obtained indicate that the use of the GMRES + LU- SGS method leads to a significant increase in performance over the LU-SGS m ethod, while maintaining memory requirements similar to its explicit counte rpart. An overall speedup factor from one to more than two order of magnitu de for all test cases in comparison with the explicit method is demonstrate d.