Affiliation:
1. Lomonosov Moscow State University
2. Moscow Center of Fundamental and Applied Mathematics
Abstract
The paper is devoted to the construction of a numerical algorithm for calculating the blood flow in a volume vessel. The derivation of the system of differential equations describing the dynamics of fluid in a single vessel with moving walls in cylindrical coordinates assuming axial symmetry in arbitrary eulerianlagrangian variables is given. Balance-characteristic scheme based on the CABARET methodology is constructed for the obtained system of equations. The results of calculations of test problems are given.
Publisher
The Russian Academy of Sciences
Reference26 articles.
1. Sherwin, S.J. One-dimensional modelling of a vascular network in space-time variables / S.J. Sherwin, V. Franke, J. Peiro, K. Parker // J. of Engineering Math. — 2003. — V. 47. — P. 217–250.
2. Formaggia, L. One-dimensional models for blood flow in arteries / L. Formaggia, D. Lamponi, A. Quarteroni // J. of Engineering Math. — 2003. — V. 47. — P. 251–276.
3. Симаков, С.С. Современные методы математического моделирования кровотока с помощью осредненных моделей / С.С. Симаков // Компьют. исследования и моделирование. — 2018. — Т. 10, № 5. — С. 581–604.
4. Вычислительный эксперимент в гемодинамике / А.Я. Буничева, С.И. Мухин, Н.В. Соснин, А.П. Фаворский // Дифференц. уравнения. — 2004. — Т. 40, № 7. — С. 920–935.
5. Multiscale modelling of the circulatory system: a preliminary analysis / L. Formaggia, F. Nobile, A. Quarteroni, A. Veneziani // Comput. Visual. Sci. — 1999. — V. 2. — P. 75–83.