A fast mapping method to evaluate immersed boundary hydrodynamic forces

Immersed boundary method is a crucial method to deal with particle suspension flow. Particle shapes involved in such flow are usually simple geometry, such as sphere and ellipsoid, which can be conveniently represented by the triangular surface grid. When the number of particles and resolution of the surface grid increase, calculating the hydrodynamic force on the particle surface through integration can be time-consuming. Hence, the present paper establishes a fast mapping method to evaluate immersed boundary hydrodynamic force. Firstly, the particle surface grid is generated by an initial triangular element grid. Subsequently, the initial surface grid is refined by bisection refinement to the desired resolution. The final step is to find the triangular element index on the particle triangular surface grid, which contains the projective point. Test cases show that the present mapping algorithm has good accuracy and efficiency for calculating hydrodynamic forces of particles.