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

TY - JOUR

T1 - An efficient temporal multiscale algorithm for simulating a long-term plaque growth problem in relation to power-law blood flows

AU - Li, Xinyu

AU - Lin, Ping

AU - Zhao, Weifeng

N1 - Publisher Copyright: © 2025 Elsevier B.V.

PY - 2025/12/1

Y1 - 2025/12/1

N2 - 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.

AB - 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.

KW - Blood flow

KW - Fluid–structure interaction

KW - Non-newtonian fluid

KW - Power law flow

KW - Temporal multiscale

U2 - 10.1016/j.cam.2025.116666

DO - 10.1016/j.cam.2025.116666

M3 - Article

AN - SCOPUS:105001737095

SN - 0377-0427

VL - 469

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 116666

ER -