Well-balanced finite difference WENO schemes for the blood flow model

Zhenzhen Wang (1) , Gang Li (1) , Olivier Delestre (2)

1 QDU - Qingdao University
2 LJAD - Laboratoire Jean Alexandre Dieudonné

The blood flow model maintains the steady state solutions, in which the flux gradients are non-zero but exactly balanced by the source term. In this paper, we design high order finite difference weighted non-oscillatory (WENO) schemes to this model with such well-balanced property and at the same time keeping genuine high order accuracy. Rigorous theoretical analysis as well as extensive numerical results all indicate that the resulting schemes verify high order accuracy, maintain the well-balanced property, and keep good resolution for smooth and discontinuous solutions.

Mots clés: Blood flow model; Finite difference schemes; WENO schemes; Well-balanced property; High order accuracy; Source term

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Zhenzhen Wang, Gang Li, Olivier Delestre. Well-balanced finite difference WENO schemes for the blood flow model. International Journal for Numerical Methods in Fluids, 2016, ⟨10.1002/fld.4232⟩. ⟨hal-01334841v2⟩