Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model

TL;DR

This paper compares four numerical schemes for simulating 1D viscoelastic blood flow, evaluating their accuracy, speed, and complexity on various vessel models, to identify the most suitable methods for clinical and research applications.

Contribution

It provides a comprehensive comparison of MacCormack, Taylor-Galerkin, MUSCL, and local discontinuous Galerkin schemes for 1D blood flow with viscoelastic walls, highlighting their strengths and limitations.

Findings

MUSCL scheme offers high accuracy and shock-capturing ability.

Local discontinuous Galerkin provides a good balance of speed and accuracy.

All schemes produce results consistent with analytical or clinical data.

Abstract

A reliable and fast numerical scheme is crucial for the 1D simulation of blood flow in compliant vessels. In this paper, a 1D blood flow model is incorporated with a Kelvin-Voigt viscoelastic arterial wall. This leads to a nonlinear hyperbolic-parabolic system, which is then solved with four numerical schemes, namely: MacCormack, Taylor-Galerkin, MUSCL (monotonic upwind scheme for conservation law) and local discontinuous Galerkin. The numerical schemes are tested on a single vessel, a simple bifurcation and a network with 55 arteries. The numerical solutions are checked favorably against analytical, semi-analytical solutions or clinical observations. Among the numerical schemes, comparisons are made in four important aspects: accuracy, ability to capture shock-like phenomena, computational speed and implementation complexity. The suitable conditions for the application of each scheme are discussed.