An immersed-boundary method based on the gas kinetic BGK scheme for incompressible viscous flow

• Expanding the immersed-boundary (IB) method to the finite-volume gas kinetic Bhatnagar–Gross–Krook (BGK) scheme.
• The flux across the cell's interface will be influenced by the immersed-boundary force.
• The flow penetration to the immersed boundary is completely eliminated.
• The present method can be conveniently applied to problems with moving objects.

In this paper, an immersed-boundary (IB) method based on the gas kinetic Bhatnagar–Gross–Krook (BGK) scheme is proposed to simulate the incompressible viscous flow around stationary and moving rigid bodies. In the presented IB method, a set of Lagrangian points represent the solid boundary and will exert force on the surrounding Eulerian points which are the cell centers within the finite-volume framework. This force is calculated by a special iterative procedure and has an effect on the flux at the interface of cell, which guarantees the fulfillment of the no-slip boundary condition and entirely avoids the flow penetration. The flow field is obtained from the BGK scheme with local grid refinement. Without complex mesh generation and transformation, the present technique can be conveniently applied to simulations with complex and moving solid boundaries. The second-order temporal accuracy and better than first-order spatial accuracy in L2L2 norm are testified by the simulation of Stokes' first problem. Other three different test cases, including flows around a stationary circular cylinder, two circular cylinders in tandem and an oscillating circular cylinder, demonstrate the good capability of the present method.