Host: The Japan Society of Mechanical Engineers
Name : [in Japanese]
Date : November 11, 2020 - November 13, 2020
In the recent development of the micro- and nanofluidics, the prediction of the flow with the slip velocity on the walls plays a significant role. However, the computational methods that deal with the arbitrarily shaped slip boundaries have not been established. The immersed boundary method is one of the most popular method to simulate the flows with the arbitrarily shaped surfaces where the no-slip boundary conditions are imposed. In the immersed boundary method, the boundary forces defined on the immersed surfaces are added to the Navier-Stokes equations to impose the boundary conditions. Since the immersed surfaces are not fitted on the fixed grid where the flow fields are solved, the boundary conditions are described with the interpolation operator and the boundary forces are smeared on the fixed grid with the regularization operator. These operators compose of the discrete delta functions. In the case of the Navier slip boundary condition containing the velocity gradient, however, the conventional combination of these operators cannot appropriately evaluate the velocity gradient. In order to impose the Navier slip boundary condition on the immersed boundaries, we introduce a new regularization operator based on the immersed boundary projection method, in which the boundary force are determined implicitly to satisfy the boundary conditions. The flow inside two concentric cylinders are calculated to validate the present method. The resulting velocity profile shows a good agreement with the analytical solution.
