research partners    
Ph.D. students    
consortium members    

Piotr Gwiazda
Institute of Applied Mathematics and Mechanics
University of Warsaw
Banacha 2,
02-097 Warsaw
phone: +48 22 5544551
fax: +48 22 5544700

Bio-flows in pipe-like 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, so-called bio-flows, such as blood flows or motions of chemical ingredients in plants. We concentrate on models based on incompressible non-Newtonian 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 blow-ups 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 Navier-Stokes 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.

Cardio-surgeon 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: 59-68.
[2] J.Y. Chemin and N. Masmoudi, (2001) SIAM J. Math. Anal., 33: 84-112.
[3] M.Lukacova-Medvidova and A. Zauskova, (2008) J. Num. Meth. Fluids, 56: 1409-1415.
[4] X. Qin, Z. Yao and H. Zhao, (2008) Commun. Pure Appl. Anal., 7: 373-381.