Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model
For researchers simulating blood flow in compliant vessels, this work provides a practical comparison of numerical schemes, but it is incremental as it applies existing methods to a known model.
This paper compares four numerical schemes (MacCormack, Taylor-Galerkin, MUSCL, local discontinuous Galerkin) for solving a 1D viscoelastic blood flow model. The schemes are tested on single vessel, bifurcation, and a 55-artery network, with favorable agreement against analytical or clinical data. No specific numerical results (e.g., error percentages) are provided.
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.