A Level Set Based Geometry Handling Approach Used in the Immersed Boundary Methods for Fluid-Structure Interaction

Immersed boundary methods have gained increasing attention in modeling fluid-solid body interaction using non-body conforming computational fluid dynamics, due to their robustness and simplicity. They usually do this by adding a body force term in the momentum equation. The magnitude and direction of this body force ensure that the boundary condition on the solid-fluid interface is satisfied without invoking complicated body-conforming numerical methods to impose the boundary condition. The body force is usually calculated and imposed using some interpolation or extrapolation around the solid-fluid interface. It can also be calculated based on the solid volume fraction in the cells around the solid-fluid interface. Therefore, it is critical to have a robust method to represent or track arbitrary solid bodies immersed in a fluid field and facilitate the needed interpolation, extrapolation, or calculation of solid volume fraction. To that end, the level set method has been used as a robust method to represent and track arbitrary solid bodies in a fluid field. In the presented paper, the level set based approaches used to handle arbitrary solid bodies in a fluid field are reviewed, and a new higher order method is presented to resolve the solid-fluid interface using the given level sets at each grid point.