Volume 7, Issue 4
A High Order Well-Balanced Finite Volume WENO Scheme for a Blood Flow Model in Arteries

Zhonghua Yao, Gang Li & Jinmei Gao

East Asian J. Appl. Math., 7 (2017), pp. 852-866.

Published online: 2018-02

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  • Abstract

The numerical simulations for the blood flow in arteries by high order accurate schemes have a wide range of applications in medical engineering. The blood flow model admits the steady state solutions, in which the flux gradient is non-zero and is exactly balanced by the source term. In this paper, we present a high order finite volume weighted essentially non-oscillatory (WENO) scheme, which preserves the steady state solutions and maintains genuine high order accuracy for general solutions. The well-balanced property is obtained by a novel source term reformulation and discretisation, combined with well-balanced numerical fluxes. Extensive numerical experiments are carried out to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.

  • Keywords

Blood flow model, finite volume scheme, WENO scheme, well-balanced property, high order accuracy, source term.

  • AMS Subject Headings

74S10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-852, author = {}, title = {A High Order Well-Balanced Finite Volume WENO Scheme for a Blood Flow Model in Arteries }, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {4}, pages = {852--866}, abstract = {

The numerical simulations for the blood flow in arteries by high order accurate schemes have a wide range of applications in medical engineering. The blood flow model admits the steady state solutions, in which the flux gradient is non-zero and is exactly balanced by the source term. In this paper, we present a high order finite volume weighted essentially non-oscillatory (WENO) scheme, which preserves the steady state solutions and maintains genuine high order accuracy for general solutions. The well-balanced property is obtained by a novel source term reformulation and discretisation, combined with well-balanced numerical fluxes. Extensive numerical experiments are carried out to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.181016.300517f}, url = {http://global-sci.org/intro/article_detail/eajam/10725.html} }
TY - JOUR T1 - A High Order Well-Balanced Finite Volume WENO Scheme for a Blood Flow Model in Arteries JO - East Asian Journal on Applied Mathematics VL - 4 SP - 852 EP - 866 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.181016.300517f UR - https://global-sci.org/intro/article_detail/eajam/10725.html KW - Blood flow model, finite volume scheme, WENO scheme, well-balanced property, high order accuracy, source term. AB -

The numerical simulations for the blood flow in arteries by high order accurate schemes have a wide range of applications in medical engineering. The blood flow model admits the steady state solutions, in which the flux gradient is non-zero and is exactly balanced by the source term. In this paper, we present a high order finite volume weighted essentially non-oscillatory (WENO) scheme, which preserves the steady state solutions and maintains genuine high order accuracy for general solutions. The well-balanced property is obtained by a novel source term reformulation and discretisation, combined with well-balanced numerical fluxes. Extensive numerical experiments are carried out to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.

Zhonghua Yao, Gang Li & Jinmei Gao. (2019). A High Order Well-Balanced Finite Volume WENO Scheme for a Blood Flow Model in Arteries . East Asian Journal on Applied Mathematics. 7 (4). 852-866. doi:10.4208/eajam.181016.300517f
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