Year: 2018
Author: Shouguo Qian, Gang Li, Xianqing Lv, Fengjing Shao
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 1 : pp. 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 well-balanced 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2016-0151
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 1 : pp. 22–40
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Blood flow model finite difference scheme WENO scheme high order accuracy well-balanced property.