Puelz Charles, Čanić Sunčica, Rivière Béatrice, Rusin Craig G
Rice University, Department of Computational and Applied Mathematics.
University of Houston, Department of Mathematics.
Appl Numer Math. 2017 May;115:114-141. doi: 10.1016/j.apnum.2017.01.005. Epub 2017 Jan 11.
One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class describes mass and velocity. Further, the averaging process employed in the model derivation requires the specification of the axial velocity profile; this choice differentiates models within each class. Discrepancies among differing models have yet to be investigated. In this paper, we comment on some theoretical differences among models and systematically compare them for physiologically relevant vessel parameters, network topology, and boundary data. In particular, the effect of the velocity profile is investigated in the cases of both smooth and discontinuous solutions, and a recommendation for a physiological model is provided. The models are discretized by a class of Runge-Kutta discontinuous Galerkin methods.
一维血流模型具有非线性双曲系统的一般形式，但在其公式表述上有所不同。一类模型考虑质量和动量这些物理守恒量，而另一类模型描述的是质量和速度。此外，模型推导中采用的平均过程需要指定轴向速度分布；这种选择区分了每一类中的不同模型。不同模型之间的差异尚未得到研究。在本文中，我们阐述了模型之间的一些理论差异，并针对生理相关的血管参数、网络拓扑结构和边界数据对它们进行了系统比较。特别是，研究了速度分布在光滑解和间断解两种情况下的影响，并给出了一个生理模型的建议。这些模型通过一类龙格 - 库塔间断伽辽金方法进行离散化。
