||In general, we usually impose the no-slip boundary condition when simulating the problem of fluid dynamics. But recently, some experimental evidences this condition is not applicable in small-scale system or other situations. Many researchers propose to use the slip boundary condition instead. Then the result would be consistent with real appearance. Thus, we speculate the typical appearance would change when we apply the slip boundary condition. Therefore, we assume there exist slip behavior. We simulate with slip boundary condition to observe the difference between no-slip.|
In this thesis, we first introduce the background of slip boundary condition and the model we used. Then we derive the variational formulation of the Navier-Stokes equation with the slip boundary condition and the resulting large, sparse nonlinear system of equations is solved by the parallel Newton-Krylov-Schwarz algorithm. We validate our parallel fluid code by considering a test case with an available analytical solution. We apply parallel Galerkin/least squares finite element flow code with the slip boundary condition to two benchmark problems -- lid-driven cavity flows and sudden expansion flows. We investigate numerically how the slip condition effects the physical behavior of the fluid flows, including the critical Reynolds number for the pitchfork bifurcation and the performance of the nonlinear and linear iterative methods for solving resulting linear sparse nonlinear system of equations.
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