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Comparison of reduced models for blood flow using Runge–Kutta discontinuous Galerkin methods

机译:使用Runge-Kutta不连续Galerkin方法简化的血流模型的比较

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摘要

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.
机译:一维血流模型采用非线性双曲线系统的一般形式,但其公式不同。一类模型考虑质量和动量的物理守恒量,而另一类模型描述质量和速度。此外,模型推导中使用的平均过程需要指定轴向速度分布;此选择可区分每个类别中的模型。不同模型之间的差异尚待调查。在本文中,我们对模型之间的一些理论差异进行评论,并系统地比较它们在生理上相关的血管参数,网络拓扑和边界数据。特别是,在光滑和不连续溶液的情况下都研究了速度分布的影响,并提供了生理模型的建议。通过一类Runge–Kutta不连续Galerkin方法离散化模型。

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