"The Study On Flow Past Stationary And Forced Systems With Multi-bodies"

The flow past multi-bodies, i.e. multi-cylinders or multi-shperes, is multi-connected and a number of natural and engineering applications exist. The study on the flow past multi-bodies focuses on the capturing of mode transitions, the identification of vortex structures, the dynamic response, etc. Due to the complexity introduced by 'multi-bodies', it is hard to achieve some analytical solution for such flow problems. The experimental and numerical methods have shown wonderful perspective to investigate the flow past multi-bodies. While the difficulty in the grid generation for multi-connected region make it impossible to solve the 'mulit-bodies' problem by using the traditional body-fitted grid system. Further more, the oscillating motion of multi-bodies challenge the CFD researchers to design a more powerful numerical technique. In this paper, two novel numerical techniques, i.e. Domain Decomposition and Overlapping method and Virtual Body method, have been applied to successfully compute the oscillating flow of multi-bodies. These two numerical techniques hold the high-accuracy and high-resolution behaviors as well as they solve the difficulty in grid generation for multi-bodies, which are important to simulate the fluid flow with multi-scales.The first part of this paper implemented high accurate domain decopmosition and overlapping method (DDM) code, which specially aims at imcopressible viscous fluid flow described with primitive N-S equations under arbitrary curvilinear coordinate system. We used fourth-order Pade scheme for viscous terms and the fourth-order Runge-Kutta scheme for time discretization. To guarantee the numerical stability, the third-order upwind scheme provided by Fu Dexun and Ma, Yanwen is applied to convective terms. In our code, two kind of means are designed to handle the message passing between two adjacent sub-regions: Dirichlet condition for one-layer-overlapping sub-regions and Dirichlet-Neumann condition for sub-regions with different grid direction. In virtue of the open MPI library, the parallel version of this code was writed and the most running cases were finished on the SGI Onyx3900 machine located in the Center for Engineering and Scientific Computation of Zhejiang University.The high accurate DDM was used to simulate the flow past a single spherefor Reynolds numbers between 20 and 1000. The exact vortex structures transitions were numerically discovered and the code proved to be feasible to simulate 3D fluid flow. The flow separation was captured at Re=25 which has good agreement with the available experimental result. The stable and plane-symmetric mode was computed at 210r~nted and the flow characteristics of two spheres in tandem arrangement were given as the function of the spacing ratio and Reynolds number. The flow transitions and the competition mechanism of vortex structures were obtained. As a typical case of more complicated fluid flows, the four spheres located in a cross-plane were studied and the interference between the vortex structures were analyzed, which will show important introduction to the study on the multiphase flow and the oscillating flow in engineering applications.