A three-dimensional immersed boundary method based on an algebraic forcing-point-searching scheme for water impact problems

Abstract

A new three-dimensional immersed boundary method combined with the level set method for the interface capturing is developed to simulate the interaction between the fixed∖moving structure and the two-phase fluid flow. The concept of the forcing point searching scheme developed for the two-dimensional situations in Yan et al. (2018) is extended in the present study to three dimensions, where the determination of intersections between the arbitrary body surface and the Cartesian background grid system is the major issue. This problem can be converted to the prediction of triangle–triangle intersection, which was traditionally solved from the geometrical point of view. Here, an algebraic algorithm is adopted for the triangle–triangle intersection, based on which the forcing points can be determined in the three-dimensional immersed boundary method. This algebraic algorithm is robust for any body geometry and easy for implementation. To demonstrate the accuracy and capability of the developed numerical model, three benchmark testing cases for water impact problems are conducted, including dam break over a fixed obstacle, water entry of a wedge and free decay of a bobber. Extensive comparisons with the experimental data and the numerical results obtained by other immersed boundary methods suggest that the developed immersed boundary method is accurate and effective for both fixed and moving bodies with complex geometries.