| The immersed boundary methods (IBMS) are a class of methods in Computational Fluid Dynamics where the grids do not conform to the shape of the body. Instead they employ cartesian meshes and alternative ways to incorporate the boundary conditions in the (discrete) governing equations. The simple grids and data structure are very well suited to handle complex geometries and moving boundaries.In this thesis, a 2D Navier-Stokes code based on the immersed boundary methods is developed to solve unsteady flow and validated by several typical examples.This thesis is composed of five chapters.The first chapter is the introduction. The significance to study the immersed boundary methods is introduced. Also introduced are the development of this method and the approaches adopted by the present thesis. The outline of the thesis is presented in the introduction too.In the second chapter, the numerical algorithm used in the thesis is presented. The implicit scheme dual-time stepping LUSGS method is adopted to solve unsteady Navier-Stokes equations. The spatial discrete is treated using the Jameson central difference scheme.In the third chapter, the boundary treatment is presented. The interpolation stencil is introduced and a bilinear interpolation is employed in the computational domain to satisfy the boundary condition.In the forth chapter, several simple 2D examples of validation such as the viscous and unsteady flows of cylinder and NACA0012 airfoil are simulated in low Mach number.In the fifth chapter, the conclusions are presented .The summary of work in this thesis and the future work is presented.
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