Volume 10, Issue 1
An Efficient High Order Well-Balanced Finite Difference WENO Scheme for the Blood Flow Model

Shouguo Qian, Gang Li, Xianqing Lv & Fengjing Shao

Adv. Appl. Math. Mech., 10 (2018), pp. 22-40.

Published online: 2018-10

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  • Abstract

The blood flow model admits the steady state, in which the flux gradient is non-zero and is exactly balanced by the source term. In this paper, we present a high order well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which exactly preserves the steady state. In order to maintain the wellbalanced property, we propose to reformulate the equation and apply a novel source term approximation. Extensive numerical experiments are carried out to verify the performances of the current scheme such as the maintenance of well-balanced property, the ability to capture the perturbations of such steady state and the genuine high order accuracy for smooth solutions.

  • Keywords

Blood flow model, finite difference scheme, WENO scheme, high order accuracy, well-balanced property.

  • AMS Subject Headings

65L12, 74S20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-22, author = {}, title = {An Efficient High Order Well-Balanced Finite Difference WENO Scheme for the Blood Flow Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {1}, pages = {22--40}, abstract = {

The blood flow model admits the steady state, in which the flux gradient is non-zero and is exactly balanced by the source term. In this paper, we present a high order well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which exactly preserves the steady state. In order to maintain the wellbalanced property, we propose to reformulate the equation and apply a novel source term approximation. Extensive numerical experiments are carried out to verify the performances of the current scheme such as the maintenance of well-balanced property, the ability to capture the perturbations of such steady state and the genuine high order accuracy for smooth solutions.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0151}, url = {http://global-sci.org/intro/article_detail/aamm/10499.html} }
TY - JOUR T1 - An Efficient High Order Well-Balanced Finite Difference WENO Scheme for the Blood Flow Model JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 22 EP - 40 PY - 2018 DA - 2018/10 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2016-0151 UR - https://global-sci.org/intro/article_detail/aamm/10499.html KW - Blood flow model, finite difference scheme, WENO scheme, high order accuracy, well-balanced property. AB -

The blood flow model admits the steady state, in which the flux gradient is non-zero and is exactly balanced by the source term. In this paper, we present a high order well-balanced finite difference weighted essentially non-oscillatory (WENO) scheme, which exactly preserves the steady state. In order to maintain the wellbalanced property, we propose to reformulate the equation and apply a novel source term approximation. Extensive numerical experiments are carried out to verify the performances of the current scheme such as the maintenance of well-balanced property, the ability to capture the perturbations of such steady state and the genuine high order accuracy for smooth solutions.

Shouguo Qian, Gang Li, Xianqing Lv & Fengjing Shao. (2020). An Efficient High Order Well-Balanced Finite Difference WENO Scheme for the Blood Flow Model. Advances in Applied Mathematics and Mechanics. 10 (1). 22-40. doi:10.4208/aamm.OA-2016-0151
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