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Formaggia, L., Gerbeau, J., Nobile, F. and Quarteroni, A. (2001) On the Coupling of 3D and 1D Navier-Stokes Equations for Flow Problems in Compliant Vessels. Computer Methods in Applied Mechanics and Engineering, 191, 561-582.

has been cited by the following article:

• TITLE: Approximate and Invariant Solutions of a Mathematical Model Describing a Simple One-Dimensional Blood Flow of Variable Density

  AUTHORS: Ranis Ibragimov, Nail Ibragimov, Pirooz Mohazzabi

  KEYWORDS: Blood Flow, Variable Density, Approximate, Invariant, Solution

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.6, June 29, 2017

  ABSTRACT: We examine governing equations that could be used to model a one-dimensional blood flow within a pulsating elastic artery that is represented by a tube of varying cross-section. The model is considered from two perspectives. The first represents a singular perturbation theory providing explicit approximate solutions to the model, and the second is based on group theoretical modeling that provides exact solutions in implicit form. The main goal is to compare these two approaches and lay out the advantages and disadvantages of each approach.