The purpose of this research was to investigate the possibility of blood flow modelling in LS-DYNA using its SPH solver and SPH-FEM coupling. SPH and FEM methods are both based on the continuum mechanics, and SPH uses Lagrangian material framework, while FEM can use both Lagrangian for solid, and Eulerian formulation for fluid analysis. SPH implementation is mesh-free giving it the capability to model very large deformations without mesh distortions. However, this comes at a high computational price, so the number of SPH particles needs to be significantly lower in comparison to the number of FEM elements in the Eulerian analysis of the same fluid domain. In the case of combined SPH-FEM analysis, the blood vessel wall is modelled with FEM shell elements, while the blood inside is modelled with SPH particles. The contact between the two is done using nodes to surface algorithm, while if we use the SPH only, there is no need for the specific contact definition. The Lagrangian framework of the SPH method means that we need to generate particles at one end, and to destroy them on the other, in order to generate a continuous fluid flow. To do this we used activation and deactivation planes, which is a solution implemented in the commercial LS-Dyna SPH solver. In the results section of the paper, the velocity field of blood obtained by implementation of described modelling methodology is shown. SPH-FEM coupling offers greater possibilities to study the effects of wall deformations, tracking of movement of solid particle inclusion, or mixing two different fluids, but it requires elaborate contact definition, and prolonged analysis time in comparison to the FEM CFD analysis.
The nonlocal, local and mixed forms of the SPH method
