Application of defined auxiliary system in the method of layer potentials for solving the stokes flow problem

Abstract

In this article, we apply an error estimation technique to assess the numerical error of seven kinds of method of layer potentials for solving the Stokes flow problem governed by the biharmonic equation. The new error estimation technique allows us to estimate numerical errors in situations where analytical solutions are not available. Additionally, it enables us to determine the optimal solution for the seven methods, making them applicable in various engineering problems. We validate the developed algorithm through four numerical experiments on 2D flows: (1) a gear cavity, (2) a circular cavity, (3) a lid-driven square cavity, and (4) an amoeba-shaped cavity. The results demonstrate close agreement with previous research, affirming that the error estimation technique can guarantee the method of layer potentials an accurate and versatile approach to solving the Stokes flow problem.