Decoupled modified characteristics variational multiscale method for solving the blood solute dynamics model

In this article, we propose and analyze the robust modified characteristics variational multiscale (MCVMS) method for solving the blood solute dynamics model, which consists of the Navier–Stokes equations to describe the blood flow in the lumen, the advection–diffusion equation for the lumenal concentration and the pure-diffusion equation for the arterial wall concentration, separated by the endothelial layer as interface. This method is based on the combination of the characteristics temporal discretization to deal with the difficulty that arises by the nonlinear terms and the projection-based variational multiscale (VMS) technique to stabilize the spurious oscillation caused by the lower diffusivity of the solute concentration. The natural combination of these methods retains the best features and overcomes their deficits. The global problem is divided into three subproblems, standing on the full explicitly uncoupled VMS stabilization terms, by lagging the projection terms for the velocity and the lumenal concentration onto the previous time level, and the explicit treatment of the interface terms. The unconditional stability and the optimal error estimate are derived rigorously for the newly introduced method. The exclusive feature of the proposed method is demonstrated by performing four numerical experiments, which achieves optimal convergence order and illustrates the flow behavior, solute concentration, wall shear stress, pressure distribution in a curved arterial blood vessel and a 3D stenosis artery.