A Fast, Matrix-free Implicit Method for Computing Low Mach Number Flows on Unstructured Grids

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Abstract
A fast, matrix-free implicit method has been developed to solve low Mach number flow problems on unstructured grids. The preconditioned compressible Euler and Navier-Stokes equations are integrated in time using a linearized implicit scheme. A newly developed fast, matrix-free implicit method, GMRES + LU−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 in viscid and viscous flows, in both 2D and 3D to validate the developed method and to evaluate the effectiveness of the GMRES + LU−SGS method. 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 method, while maintaining memory requirements similar to its explicit counterpart. An overall speedup factor from one to more than two order of magnitude for all test cases in comparison with the explicit method is demonstrated.