以沉浸邊界方法求解具複雜外型之不可壓縮黏性流

Abstract

In this thesis, a discrete-time direct forcing method in Cartesian grids is applied to the numerical simulation of the flow over a circular cylinder, flow over two cylinders in tandem, backward-facing step flow and flow over the label of 'SCCS'. A collocated finite-difference method for CDR (convection-diffusion-reaction) equation with nodally exact discrete scheme in non-staggered uniform Cartesian grids is used. The momentum forcing is applied on the body surface or inside the body to satisfy the no-slip boundary condition on the immersed boundary (body-fluid interface). For immersed boundary method, the choice of an accurate interpolation scheme satisfying the no-slip condition on the immersed boundary is very important because the grid lines generally do not coincide with the immersed boundary. Therefore, a novel interpolation technique for evaluating the momentum forcing on the body surface or inside the body is presented. The benchmark problem of flow over a circular cylinder, is simulated using the proposed immersed boundary method. The results agree very well with other numerical and experimental results in the literatures.