A boundary condition capturing immersed interface method for 3D rigid objects in a flow

To simulate the flow around an object, we can replace the object with the fluid enclosed by a singular force. We can then simulate the flow on a fixed domain with a fluid–fluid interface supporting the singular force. In this paper, we present a boundary condition capturing approach to determine the singular force for a 3D rigid object. We apply a discontinuous body force to enforce the rigid motion of the fluid replacing the object and compute the singular force based on the kinematics of the object. Due to the singular force and the body force, the flow is not smooth across the interface. We solve the flow using the immersed interface method. Our boundary condition capturing immersed interface method is very efficient and stable, and its accuracy based on the infinity norm is near second order for the velocity and above first order for the pressure.