| Summary: | 碩士 === 國立中央大學 === 數學系 === 106 === The main purpose of this thesis is to implement an artificial compressibility-immersed boundary method with
direct forcing proposed in [22] for simulating 2-D unsteady flows interacting with rigid solid objects.
This approach is based on the artificial compressibility method and the direct-forcing immersed boundary method combined with a prediction-correction strategy.
Following the ideas in [22], we employ the penalty technique to weaken the incompressibility condition in the incompressible Navier-Stokes equations and introduce a virtual force distributed on the whole solid object and imposed to the fluid momentum equations to accommodate the no-slip boundary condition at the immersed solid boundary. We then use the first-order implicit Euler scheme to discretize the temporal variable in the resulting system of equations and apply the explicit first-order approximation to linearize the nonlinear convection term. After that, we employ a direct forcing immersed boundary method with a prediction-correction strategy to solve the system of time-discretized equations. For the spatial discretization in this approach, we take the second-order central differences on the staggered grids. We illustrate the performance of the algorithm by performing several 2-D numerical experiments of unsteady flow interacting with solid object. From the numerical results, we find that this simple artificial compressibility immersed boundary method with direct forcing can achieve reasonable results for 2-D fluid-solid interaction problems.
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