Институт вычислительной математики
и математической геофизики

Abstracts

Numerical solution of differential and integral equations

documentstyle[12pt]{article} title{Computational techniques for blood flow through arteries} author{A.R. Ansari, T. McGloughlin, G.I. Shishkin, M. Walsh} date{} begin{document} maketitle

We develop a mathematical model based on flow of an incompressible fluid through a pipe, which is driven by a pulsatile type pressure gradient. Blood flow in arteries which are driven by a pulsatile pressure gradient have wide applications in cardiovascular surgery. This type of flow usually shows boundary layer phenomena, this can be the source of difficulty for experimental study. The layer thickness for such a problem can depends on the ratio $ u/n$ where $n$ is the frequency of the pulsatile source and $ u$ is the viscosity of blood. The periodic solution of this problem is a solution of the Navier-Stokes equations with cylindrical symmetry.

Standard numerical methods for this problem have large errors for high frequencies $n$. Our ultimate aim is the construction of a numerical method for which the errors are independent with respect to the ratio $ u/n$, extit{i.e.,} parameter-robust with respect the parameter $ u/n$ (in short, with respect to the frequency $n$).

Here our aim is to develop an appropriate mathematical model which is an adequate representation of the pulsatile flow of blood through arteries.

Acknowledgements. This work was supported by the Russian Foundation for Basic Research under grant No. 04-01-00578. end{document}

Note. Abstracts are published in author's edition

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