埋め込み境界射影法によるすべり境界を含む流れの計算手法に関する研究

抄録

The prediction of the flow confined by intricately shaped walls with slip velocity plays a significant role in the design of microfluidic or nanofluidic devices. Immersed boundary methods have been used to simulate flows with arbitrary-shaped boundaries on the Cartesian grid. The key concept of this approach is that the boundary force imposes the no-slip condition which is described with interpolation operator on the immersed boundaries. The boundary force is defined on the immersed boundaries, and smeared on the Cartesian grid by using the regularization operator which composes of the discrete delta functions as well as the interpolation operator. In the immersed boundary projection method which is used for flows over rigid bodies, the boundary force is determined to satisfy the no-slip condition in the same way that the pressure is obtained to satisfy the divergence-free constraint in the fractional step method. We extend this approach to simulations of the flows with partial slip boundaries. In order to impose the partial slip boundary condition on the immersed boundaries, we introduce a new regularization operator which allows the continuous velocity gradient on the immersed boundaries. The channel flow confined by the slip immersed boundaries is computed with the present method.

The resulting velocity profile shows a good agreement with the analytical solution.