Discrete Forcing Immersed Boundary Method Using Virtual Interpolation Points

As a method to solve flow problems on complicated domains, an immersed boundary (IB) method equipped with the discrete forcing based on the fluid-structure interaction (FSI) is proposed in which the virtual interpolation points are introduced. The discrete force to the background fluid due to the no-slip condition on the surface of a fixed rigid boundary is the instantaneous amount of momentum exchange, which is called the discrete FSI force. To implement this force, we employ the projection method using the virtual interpolation points for solving the incompressible Navier-Stokes flows, in which there is virtually staggered structure for the velocity and pressure but actually there is no explicit staggered structure for stability. The unstructured node distribution for computation is available due to the approximation method of the moving least squares. The use of the same nodes for computations of the velocity and pressure must be one of key advantages of this method. Indeed, the staggered grid in FVM often becomes burdensome. Additionally, it is another advantage that the implementation is easy compared to other methods for solving FSI problem. This means that it is readily extended to 3D without case-by-case changes. To validate the feasibility of the method, we solve the exterior flow passing around a circular cylinder and compare the numerical IB solution by our method with others well-known. Finally, performing the numerical computation of complicated flows in complex geometry, we will show that the proposed IB method is efficient and stable.