Direct 0D‐3D coupling of a lattice Boltzmann methodology for fluid–structure aortic flow simulations

Abstract

AbstractThis work introduces a numerical approach and implementation for the direct coupling of arbitrary complex ordinary differential equation‐ (ODE‐)governed zero‐dimensional (0D) boundary conditions to three‐dimensional (3D) lattice Boltzmann‐based fluid–structure systems for hemodynamics studies. In particular, a most complex configuration is treated by considering a dynamic left ventricle‐ (LV‐)elastance heart model which is governed by (and applied as) a nonlinear, non‐stationary hybrid ODE‐Dirichlet system. Other ODE‐based boundary conditions, such as lumped parameter Windkessel models for truncated vasculature, are also considered. Performance studies of the complete 0D‐3D solver, including its treatment of the lattice Boltzmann fluid equations and elastodynamics equations as well as their interactions, is conducted through a variety of benchmark and convergence studies that demonstrate the ability of the coupled 0D‐3D methodology in generating physiological pressure and flow waveforms—ultimately enabling the exploration of various physical and physiological parameters for hemodynamics studies of the coupled LV‐arterial system. The methods proposed in this paper can be easily applied to other ODE‐based boundary conditions as well as to other fluid problems that are modeled by 3D lattice Boltzmann equations and that require direct coupling of dynamic 0D boundary conditions.