In this Ph.D. thesis, a novel high-resolution Godunov-type numerical procedure has been developed for solving the unsteady, incompressible Navier-Stokes equations for constant and variable density flows. The proposed FSAC-PP approach encompasses both artificial compressibility (AC) and fractional step (FS) pressure-projection (PP) methods of Chorin [3, 4] in a unified solution concept. To take advantage of different computational strategies, the FS and AC methods have been coupled (FSAC formulation), and further a PP step has been employed at each pseudo-time step. To provide time-accurate solutions, the dual-time stepping procedure is utilized. Taking the advantage of the hyperbolic nature of the inviscid part of the AC formulation, high-resolution characteristics-based (CB) Godunov-type scheme is employed to discretize the non-linear advective fluxes. Highorder of accuracy is achieved by using from first- up to ninth-order interpolation schemes. Time integration is obtained from a fourth-order Runge-Kutta scheme. A non-linear fullmultigrid, full-approximation storage (FMG-FAS) acceleration technique has been further extended to the FSAC-PP solution method to increase the efficiency and decrease the computational cost of the developed method and simulations. Cont/d
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