An immersed boundary-gas kinetic flux solver for simulation of incompressible flows

Abstract

Abstract In this paper, an immersed boundary-gas kinetic flux solver (IB-GKFS) is presented for simulation of incompressible viscous flows. In the present scheme, a simple Cartesian mesh is applied for the flow field and a set of Lagrangian points are used to represent the solid boundary. The solution process of the IB-GKFS can be separated into two steps, the predictor step and the velocity correction step. In the predictor step, the intermediate flow field is obtained by applying the gas kinetic flux solver. As the solid boundary is not considered in this step, there is no external force added in gas distribution function during the evaluation of numerical flux at each cell interface. In the velocity correction step, no-slip boundary condition is imposed at all boundary points to make velocity correction on the surrounding Eulerian points. The implicit boundary condition-enforced immersed boundary method is applied so that no-slip boundary condition can be accurately fulfilled and flow penetration is entirely avoided. The decoupled feature of the predictor step and velocity correction step makes the current scheme simple and efficient because the flux on each cell interface only needs to be calculated once in every time step. With a simple Cartesian mesh and flexible boundary condition treatment, the IB-GKFS can be conveniently applied to solve complex and moving boundary problems. Several numerical experiments are conducted to validate the present scheme, including the flow past a stationary circular cylinder and the NACA0012 airfoil, flow past an in-line oscillating cylinder with prescribed motions. After that, the typical fluid-structure interaction problem of one particle sedimentation in a rectangular domain is further considered. The numerical results of those test cases demonstrate the good capability of the present scheme.