The finite volume particle method: Toward a meshless technique for biomedical fluid dynamics

Biomedical fluid dynamics often involves large wall motions, which greatly complicate computational modeling. Meshless methods offer the potential to model moving walls in a natural manner because computational points (particles) simply move with the fluid and follow any wall or moving interface. In this chapter, one such approach, the finite volume particle method, is described. It combines some of the rigorous mathematical properties of mesh-based finite volume methods with the flexibility of meshless methods. We describe some the problems encountered in development and application of the method and their solutions. The capability to model fluid-structure interaction accurately is demonstrated with validation for a vortex-induced vibration problem. Finally, an application to an idealized heart valve is presented.