An efficient numerical scheme based on the lattice Boltzmann method for a temporal multiscale plaque growth problem

In this work, we propose an efficient numerical scheme based on the lattice Boltzmann method (LBM) to solve the fluid-structure interaction (FSI) problem of plaque growth in blood vessels. For this problem, the blood flow is approximated as a fast-scale periodic motion while the boundary deforms on a slow scale so that we can evolve the fast-scale problem with a large time step. Specifically, the unknown initial value at each macro-time step is obtained by solving a time-periodic solution of the incompressible Navier-Stokes equations, which is discretized by the LBM. Since the LBM is easy for boundary treatment of complex geometry, we realize the dynamic growth of the plaque by using interpolation and fast tracking of reshaped grid at each step, instead of the traditional ALE mapping method. In this way, we obtain an efficient numerical scheme for plaque growth with multiscale characteristics. Numerical examples demonstrate that our scheme shows a strong acceleration effect compared with the traditional direct solving process. The relative errors of results of the time multiscale scheme with respect to those of the direct solving process are small, which is consistent with the theoretical analysis.