Red Blood Cell Dynamics on Non-Uniform Grids using a Lattice Boltzmann Flux Solver and a Spring-Particle Red Blood Cell Model

The Computational Haemodynamics Research Group (CHRG) in Technological University Dublin is developing a computational fluid dynamics (CFD) software package aimed specifically at physiologically-realistic modelling of blood flow. A physiologically-realistic model of blood flow involves calculating the deformation of individual red blood cells (RBCs) and the contribution of this deformation to the overall blood flow. The CHRG has developed an enhanced spring-particle RBC structural model that is capable of modelling the full stomatocyte-discocyteechinocyte (SDE) transformation. This RBC model, incorporated into a fluid dynamics solver, will provide a physiologically-realistic blood flow model. In this work the overall plasma flow is modelled using a novel technique: the lattice Boltzmann flux solver (LBFS). This is an innovative approach to solving the NavierStokes (N-S) equations for fluid flow. It involves solving the macroscopic equations using the finite volume method (FVM) and calculating the flux across the cell interfaces via a local reconstruction of the lattice Boltzmann equation (LBE). Fluidstruture interaction between the RBC and the plasma is captured by coupling the RBC solver to the LBFS via the immersed boundary method (IBM). Numerical experiments investigating RBC dynamics are performed using non-uniform grids and validated against existing experimental data in the literature. Finally all numerical solvers are developed using general purpose GPU programming (GPGPU) and this is shown to accelerate simulation runtimes significantly