Analysis of a geometrical multiscale blood flow model based on the coupling of ODEs and hyperbolic PDEs

被引:65
作者
Fernández, MA [1 ]
Milisic, V [1 ]
Quarteroni, A [1 ]
机构
[1] Ecole Polytech Fed Lausanne, IACS, CH-1015 Lausanne, Switzerland
关键词
multiscale modeling; hyperbolic systems; lumped parameters models; blood flow modeling; fixed-point techniques;
D O I
10.1137/030602010
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For the numerical simulation of the circulatory system, geometrical multiscale models based on the coupling of systems of differential equations with different spatial dimensions are becoming common practice [L. Formaggia et al., Comput. Vis. Sci., 2 (1999), pp. 75-83, A. Quarteroni and A. Veneziani, Multiscale Model. Simul., 1 (2003), pp. 173-195, L. Formaggia et al., Comput. Methods Appl. Mech. Engrg., 191 (2001), pp. 561-582]. In this paper we address the mathematical analysis of a coupled multiscale system involving a zero-dimensional (0D) model, describing the global characteristics of the circulatory system, and a one-dimensional (1D) model giving the pressure propagation along a straight vessel. We provide a local-in-time existence and uniqueness of classical solutions for this coupled problem. To this purpose we reformulate the original problem in a general abstract framework by splitting it into subproblems (the 0D system of ODEs and the 1D hyperbolic system of PDEs); then we use fixed-point techniques. The abstract result is then applied to the original blood flow case under very realistic hypotheses on the data. This work represents the 1D-0D counterpart of the 3D-0D mathematical analysis reported in [A. Quarteroni and A. Veneziani, Multiscale Model. Simul., 1 (2003), pp. 173-195].
引用
收藏
页码:215 / 236
页数:22
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