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

Part of: Numerical methods

Published online by Cambridge University Press:  31 January 2018

Zhonghua Yao ,
Gang Li  and
Jinmei Gao
Zhonghua Yao*
Affiliation:
School of Mathematics and Statistics, Qingdao University, Qingdao, Shandong 266071, PR China
Gang Li*
Affiliation:
School of Mathematics and Statistics, Qingdao University, Qingdao, Shandong 266071, PR China
Jinmei Gao*
Affiliation:
School of Mathematics and Statistics, Qingdao University, Qingdao, Shandong 266071, PR China
*
*Corresponding author. Email addresses:yaozhonghuavip@163.com (Z. Yao), gangli1978@163.com (G. Li), gjinmei1979@163.com (J. Gao)
*Corresponding author. Email addresses:yaozhonghuavip@163.com (Z. Yao), gangli1978@163.com (G. Li), gjinmei1979@163.com (J. Gao)
*Corresponding author. Email addresses:yaozhonghuavip@163.com (Z. Yao), gangli1978@163.com (G. Li), gjinmei1979@163.com (J. Gao)
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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 modelfinite volume schemeWENO schemewell-balanced propertyhigh order accuracysource term

MSC classification

Secondary: 74S10: Finite volume methods
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 4 , November 2017 , pp. 852 - 866
Copyright
Copyright © Global-Science Press 2017 

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