A computationally efficient method for simulating fluid flow in elastic pipes in three dimensions

We propose a new method for carrying out lattice-Boltzmann simulations of pulsatile fluid flow in three-dimensional elastic pipes. It is based on estimating the distances from sites at the edge of the simulation box to the wall along the lattice directions from the displacement of the closest point on the wall and the curvature there, followed by application of a nonequilibrium extrapolation method. Viscous flow in an elastic pipe is studied in three dimensions at a wall displacement of 5% of the radius of the pipe, which is realistic for blood flow through large cerebral arteries. The numerical results for the pressure difference, wall displacement and flow velocity agree well with the analytical predictions. At all sites, the calculation depends only on information from nearest neighbours, so the method proposed is suitable for efficient computation on multicore machines. Compared to simulations with rigid walls, simulations with elastic walls require only 13% more computational effort at the parameters chosen in this study.