許文翰臺灣大學：工程科學及海洋工程學研究所丁曉楓Ting, Hsung-FengHsung-FengTing2007-11-262018-06-282007-11-262018-06-282005http://ntur.lib.ntu.edu.tw//handle/246246/51056In 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.Acknowledgements i Abstract ii 1 Introduction 1 1.1 Research objectives(Background) 1 1.2 Governing equations 2 1.2.1 Governing equations for pure fluid 2 1.2.2 Governing equations for fluids in complex geometries 2 1.3 Literature review 3 1.4 Outlines of this study 5 2 Two-dimensional incompressible Navier-Stokes equations 6 2.1 Mathematical formulation 6 2.1.1 Generalized Navier-Stokes equation 6 2.1.2 Pressure Poisson Equation 7 2.1.3 Normalization 8 2.2 Discretization of equations on non-staggered grids 10 2.2.1 Five-point CDR scheme 11 2.2.2 Compact scheme 12 2.3 Numerical Studies 14 2.3.1 Validation for steady Navier-Stokes model 15 2.3.2 Validation for unsteady Navier-Stokes model 15 4 Immersed Boundary Method 20 4.1 Volume of fluid method 20 4.1.1 Volume-fraction field 21 4.1.2 Computational procedures 22 4.2 Direct forcing method 24 4.2.1 Momentum forcing 24 4.2.2 Interpolation method for the velocity 25 4.3 Extended direct forcing method 29 4.3.1 Interpolation method for the velocity 29 4.3.2 Computational procedures 30 5 Numerical Results 33 5.1 2-D flow over a circular cylinder 33 5.1.1 Computational domain and boundary condition 34 5.1.2 Results and discussion 35 5.2 2-D Flow over two cylinders in tandem 37 5.2.1 Computational Domain and Boundary Condition 38 5.2.2 Results and discussion 38 5.3 2-D backward facing-step flow 39 5.3.1 Computational Domain and Boundary Condition 40 5.3.2 Results and discussion 40 5.4 2-D flow over the label of "SCCS" 41 5.4.1 Computational Domain and Boundary Condition 42 5.4.2 Results and discussion 42 6 Conclusion 775521665 bytesapplication/pdfen-US沉浸邊界方法複雜外型不可壓縮黏性流Immersed Boundary MethodComplex GeometryIncompressible Viscous Flowthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/51056/1/ntu-94-R92525003-1.pdf