Convergence and computational cost analysis of a boundary integral method applied to a rigid body moving in a viscous fluid in close proximity to a fixed boundary

The Boundary Integral Method (BIM) applied to the unsteady Stokes and continuity equations is a standard method used to simulate problems of bodies oscillating in fluids. Despite the technique providing accurate numerical results, current implementations are computationally expensive. In this work, we focus on the flow around an infinitely thin beam oscillating near a solid surface and we show that the convergence of the BIM depends on geometrical and flow parameters. By using a combination of closed-form expression and numerical integration of the kernel functions arising in the BIM, we demonstrate that much computational cost can be saved. For example, the same problem can be solved in 0.5% of the required computational time using a naive approach. The computational cost analysis of different approaches adopted is included. This work also includes a detailed analysis and validation for numerical methods by comparing them to closed-form solutions.