A high-efficiency sharp-interface immersed boundary method based on multi-linear interpolation

Abstract

The sharp-interface immersed boundary method (IBM) reconstructs the flow locally to achieve the precise identification of solid boundaries and their consequential influences on the fluid dynamics. However, the computational accuracy and efficiency are notably impacted by the diverse interaction between the fluid's Euler grid and the solid's Lagrange mesh. Taking the two-dimensional (2D) case as an example, we analyze the characteristics of various grid cutting classes, with a particular focus on how they reduce the solution speed and computational precision. To address these challenges, we propose a multi-linear interpolation method that enriches flow field information by expanding the interpolation template. Computational results of 2D flow past a stationary cylinder and airfoil, and the takeoff of airfoil takeoff demonstrate that the multi-linear interpolation method increases computational efficiency by up to 20%, while maintaining accuracy. Furthermore, we extend this method to three-dimensional (3D) calculations, enhancing efficiency by about 5% and improving accuracy. Finally, by simulating the full-body motion of a penguin swimming, we showcase the robustness of the method in simulating complex geometric moving boundary problems.