Abstract:
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.
