title: Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model.
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, 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.
authors.affiliation: a Sorbonne Universités , UPMC Univ Paris 6, UMR 7190, Institut Jean le Rond d'Alembert, Paris , France.
authors.forename: Xiaofei
authors.initials: X
authors.lastname: Wang
authors.forename: Jose-Maria
authors.initials: JM
authors.lastname: Fullana
authors.forename: Pierre-Yves
authors.initials: PY
authors.lastname: Lagrée
mesh_terms: D001158:Arteries / Q000502:physiology*; D001775:Blood Circulation; D004058:Diffusion; D004548:Elasticity; D018056:Hemorheology; D006801:Humans; D008955:Models, Cardiovascular; D009716:Numerical Analysis, Computer-Assisted; D011312:Pressure; D013997:Time Factors; D014783:Viscosity
keywords: 1D flow modeling; blood flow; numerical simulation; vascular network