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    Numerical method of characteristics for one-dimensional blood flow

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    Author
    Acosta, Sebastian; Puelz, Charles; Riviére, Béatrice; Penny, Daniel J.; Rusin, Craig G.
    Date
    2015
    Abstract
    Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.
    Citation
    Acosta, Sebastian, Puelz, Charles, Riviére, Béatrice, et al.. "Numerical method of characteristics for one-dimensional blood flow." Journal of Computational Physics, 294, (2015) Elsevier: 96-109. http://dx.doi.org/10.1016/j.jcp.2015.03.045.
    Published Version
    http://dx.doi.org/10.1016/j.jcp.2015.03.045
    Keyword
    blood flow; computational hemodynamics; characteristics; wave propagation
    Type
    Journal article
    Publisher
    Elsevier
    Citable link to this page
    https://hdl.handle.net/1911/94228
    Rights
    This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.
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    • CAAM Publications [71]
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    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map