Volume 50, Issue 2
A Well-Balanced Discontinuous Galerkin Method for the Blood Flow Model

Zhonghua Yao, Gang Li & Lina Song

J. Math. Study, 50 (2017), pp. 174-189.

Published online: 2017-06

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  • Abstract

Numerical simulations by high order methods for the blood flow model in arteries have wide applications in medical engineering. This blood flow model admits the steady state solutions, for which the flux gradient is non-zero, and is exactly balanced by the source term. In this paper,we design a high order discontinuous Galerkin method to this model by means of a novel source term approximation as well as wellbalanced numerical fluxes. Rigorous theoretical analysis as well as extensive numerical results all suggest that the resulting method maintains the well-balanced property, enjoys high order accuracy and keeps good resolutions for smooth and discontinuous solutions.

  • Keywords

Blood flow model discontinuous Galerkin method well-balanced property high order accuracy source term

  • AMS Subject Headings

65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yaozhonghuavip@163.com (Zhonghua Yao)

gangli1978@163.com (Gang Li)

lnsong365@gmail.com ( Lina Song)

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@Article{JMS-50-174, author = {Yao , Zhonghua and Li , Gang and Song , Lina }, title = {A Well-Balanced Discontinuous Galerkin Method for the Blood Flow Model}, journal = {Journal of Mathematical Study}, year = {2017}, volume = {50}, number = {2}, pages = {174--189}, abstract = {

Numerical simulations by high order methods for the blood flow model in arteries have wide applications in medical engineering. This blood flow model admits the steady state solutions, for which the flux gradient is non-zero, and is exactly balanced by the source term. In this paper,we design a high order discontinuous Galerkin method to this model by means of a novel source term approximation as well as wellbalanced numerical fluxes. Rigorous theoretical analysis as well as extensive numerical results all suggest that the resulting method maintains the well-balanced property, enjoys high order accuracy and keeps good resolutions for smooth and discontinuous solutions.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v50n2.17.04}, url = {http://global-sci.org/intro/article_detail/jms/10008.html} }
TY - JOUR T1 - A Well-Balanced Discontinuous Galerkin Method for the Blood Flow Model AU - Yao , Zhonghua AU - Li , Gang AU - Song , Lina JO - Journal of Mathematical Study VL - 2 SP - 174 EP - 189 PY - 2017 DA - 2017/06 SN - 50 DO - http://dor.org/10.4208/jms.v50n2.17.04 UR - https://global-sci.org/intro/jms/10008.html KW - Blood flow model KW - discontinuous Galerkin method KW - well-balanced property KW - high order accuracy KW - source term AB -

Numerical simulations by high order methods for the blood flow model in arteries have wide applications in medical engineering. This blood flow model admits the steady state solutions, for which the flux gradient is non-zero, and is exactly balanced by the source term. In this paper,we design a high order discontinuous Galerkin method to this model by means of a novel source term approximation as well as wellbalanced numerical fluxes. Rigorous theoretical analysis as well as extensive numerical results all suggest that the resulting method maintains the well-balanced property, enjoys high order accuracy and keeps good resolutions for smooth and discontinuous solutions.

Zhonghua Yao, Gang Li & Lina Song. (2019). A Well-Balanced Discontinuous Galerkin Method for the Blood Flow Model. Journal of Mathematical Study. 50 (2). 174-189. doi:10.4208/jms.v50n2.17.04
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