

Bioflows in pipelike domains: qualitative analysis, reduction to monodimensional models and numerical simulations


Piotr B. Mucha (MIM University of Warsaw) and Milan Pokorny (Faculty
of Mathematics and Physics Charles University in Prague)


The project is carried out by Joanna Skonieczna at University of Warsaw


Our interest is directed to the flows appearing in biology and medicine, socalled bioflows,
such as blood flows or motions of chemical ingredients in plants. We concentrate on models
based on incompressible nonNewtonian flows with suitable viscoelastic stress tensor involving
rules/laws describing the transport of chemical, alimentary or medically active particles [1]. A good example is Oldroyd model [2].
The project will be divided into three stages: (1) precise analysis of the original equations/solutions, (2)
reducing the three dimensional equations to monodimensional models describing the most important
quantities of the system (e.g. in the blood flow, we are interested more in concentration of the chemical
ingredients than in the very velocity) and (3) numerical analysis of one dimensional model in order to obtain
richer qualitative results (such as blowups or effects of stabilizations).
The precise analysis will allow to control the difference between original and simplified model investigating the admissibility of the second one.
Analysis of the obtained monodimensional model will be similar to results for the compressible NavierStokes
system in 1D [4]. This part will be realized under the supervision of Piotr Mucha and Milan Pokorny. The numerical
simulations and experiments should deliver us representative picture of behaviour of the original 3D system as in [3]
and will be conducted in collaboration with Maria Lukacova.
Cardiosurgeon Jeremi Mizerski MD, Ph.D. of ICM will be available for medical consultancy to this project.
[1] M. Anand and K.R. Rajagopal, (2004) Int. J. Cardiovascular Medicine and Science, 4: 5968.
[2] J.Y. Chemin and N. Masmoudi, (2001) SIAM J. Math. Anal., 33: 84112.
[3] M.LukacovaMedvidova and A. Zauskova, (2008) J. Num. Meth. Fluids, 56: 14091415.
[4] X. Qin, Z. Yao and H. Zhao, (2008) Commun. Pure Appl. Anal., 7: 373381.




