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

TL;DR

This paper develops high-order finite difference WENO schemes that are well-balanced for blood flow models, accurately preserving steady states and handling both smooth and discontinuous solutions.

Contribution

It introduces a novel high-order WENO scheme that maintains the well-balanced property for blood flow models, ensuring accuracy and stability.

Findings

Schemes verify high order accuracy

Maintain well-balanced property

Good resolution for smooth and discontinuous solutions

Abstract

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.