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 and Fengjing Shao

10.4208/aamm.OA-2016-0151

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

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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.

  • History

Published online: 2018-10

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