Numerical simulation of unsteady three dimensional incompressible flows in complex geometries.

摘要

Unsteady, three dimensional, incompressible flows in arbitrarily complex, multi-connected geometries are encountered in a number of areas of engineering interest, such as in hydraulics, hydrodynamics, aerodynamics, hemodynamics, biofluid mechanics, etc. This thesis deals with the numerical simulation of the flows and makes novel contributions as follows. The unsteady, three dimensional, incompressible Navier-Stokes equations are integrated in time using a novel second-order accurate artificial-compressible (AC) formulation. The proposed approach modifies the standard, dual time-stepping AC method by incorporating ideas from fractional-step, pressure-based formulations. Numerical experiments are carried out to compare the new and the standard AC formulations. It is shown that the new method gives second-order accurate solutions and, compared with the standard AC method, requires considerably less CPU time. A general domain decomposition method is developed for simulating flows in complex geometries. Chimera overset grids are adopted and a novel algorithm, based on mass conservation, is developed to facilitate communication at grid interfaces. The numerical method is validated by applying it to simulate a variety of flows, such as lid driven cavity flow and pipe bend flow. Compared to standard interface treatment techniques, based on straightforward interpolation, the new grid interface algorithm enhances the efficiency of the iterative solver and practically eliminates spurious oscillations at the interface even for subdomains with discontinuous grid spacing.; The numerical method is applied to simulate unsteady vortex shedding from a circular cylinder mounted between two endplates and the computed results compare well with available experiments and previous numerical computations. Lagrangian particle tracking and techniques for visualizing coherent structures are employed to elucidate the dynamics of the wake flow. Subsequently, the flow in a domain inspired by the geometry of abutment-pier configurations encountered in bridge sections is modeled. Simulations are carried out for different Reynolds number and geometrical parameters. Analysis of the calculated flow fields sheds new light into the three-dimensional structure of such flows and contributes toward the understanding of the dynamics of large-scale, organized vortices documented experimentally in turbulent bridge foundation flows.