在生物體內的傳輸現象. 直接耦合方法求解流固耦合問題.

Abstract

The present work aims at developing a numerical solver for fluid–structure interac- tion (FSI) problems, especially those encountered in biology such as blood circulation in valved veins. Blood flow is investigated using anatomically and physically relevant models. Computational procedures are conceived, designed, and implemented in a platform that couples the cheapest cost and the fastest processing using high-performance comput- ing. The first aspect of FSI problems is related to management of algorithm stability. An Eulerian monolithic formulation based on the characteristic method unconditionally achieves stability and introduce a first order in time approximation with two distinct hy- perelastic material models. The second aspect deals with between-solid domain contact such as that between valve leaflets during closure and in the closed state over a finite surface, which avoid vcusp tilting and back flow. A contact algorithm is proposed and validated using benchmarks. Computational study of blood flow in valved veins is investigated, once the solver was verified and validated. The 2D computational domain comprises a single basic unit or the ladder-like model of a deep and superficial veins communicating by a set of perforating veins. A 3D mesh of the basic unit was also built. Three-dimensional computation relies on high performance computing. Blood that contains cells and plasma is a priori a heterogeneous medium. However, it can be assumed homogeneous in large blood vessels, targets of the present study. Red blood capsules that represent the vast majority of blood cells (97%) can deform and aggregate, influencing blood rheology. However, in large veins, in the absence of stagnant flow regions, blood behaves as a Newtonian fluid. Blood flow dynamics is strongly coupled to vessel wall mechanics. Deformable vascular walls of large veins and arteries are composed of three main layers (intima, media, and adventitia) that consist of composite material with a composition specific to each layer. In the present work, the wall rheology is assumed to be a Mooney–Rivlin material.