A direct Eulerian GRP scheme for a blood flow model in arteries

TL;DR

This paper introduces a novel Eulerian GRP scheme tailored for blood flow in arteries, utilizing Riemann invariants and Rankine-Hugoniot conditions, achieving second-order accuracy and extending to 2D via dimensional splitting.

Contribution

It presents a new direct Eulerian GRP scheme for arterial blood flow modeling, incorporating Riemann invariants and handling complex wave interactions with second-order accuracy.

Findings

Scheme successfully resolves rarefaction and shock waves.

Achieves second-order accuracy in numerical tests.

Extends effectively to two-dimensional blood flow simulations.

Abstract

In this paper, we propose a direct Eulerian generalized Riemann problem (GRP) scheme for a blood flow model in arteries. It is an extension of the Eulerian GRP scheme, which is developed by Ben-Artzi, et. al. in J. Comput. Phys., 218(2006). By using the Riemann invariants, we diagonalize the blood flow system into a weakly coupled system, which is used to resolve rarefaction wave. We also use Rankine-Hugoniot condition to resolve the local GRP formulation. We pay special attention to the acoustic case as well as the sonic case. The extension to the two dimensional case is carefully obtained by using the dimensional splitting technique. We test that the derived GRP scheme is second order accuracy.