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Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model
Xiaofei Wang1, Jose-Maria Fullana, Pierre-Yves Lagrée
1a Sorbonne Universités , UPMC Univ Paris 6, UMR 7190, Institut Jean le Rond d'Alembert, Paris , France.
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.
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