An efficient temporal multiscale algorithm for simulating a long-term plaque growth problem in relation to power-law blood flows

This paper discusses the problem of non-Newtonian fluids with time multiscale characteristics, especially considering the type of power-law blood flow in a narrowed blood vessel due to plaque growth. In the vessel, the blood flow is considered as a fast-scale periodic motion, while the vessel wall grows on a slow scale. We use an auxiliary temporal periodic problem and an effective time-average equation to approximate the original problem. The approximation error is analyzed only for a largely simplified linear system, where the simple front-tracking technique is used to update the slow vessel wall growth. An effective multiscale method is then designed based on the approximation problem. The front-tracking technique also makes the implementation of the multiscale algorithm easier. Compared with the traditional direct solving process, this method shows a strong acceleration effect. Finally, we present a concrete numerical example. Through comparison, the relative error between the results of the multi-scale algorithm and the direct solving process is small, which is consistent with the theoretical analysis.