Adv. Appl. Math. Mech., 10 (2018), pp. 22-40.
Published online: 2018-10
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0151}, url = {http://global-sci.org/intro/article_detail/aamm/10499.html} }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.