\documentstyle[11pt]{article}

\setlength{\hoffset}{0mm}
\setlength{\voffset}{0mm}
\setlength{\textheight}{240mm}
\setlength{\textwidth}{160mm}

\setlength{\oddsidemargin}{0mm}
\setlength{\topmargin}{0mm}
\setlength{\headheight}{0mm}
\setlength{\headsep}{0mm}
\setlength{\evensidemargin}{0mm}
\setlength{\marginparsep}{0mm}
\setlength{\marginparwidth}{0mm}
\setlength{\footskip}{10mm}
\setlength{\footheight}{0pt}

\begin{document}
\thispagestyle{empty}

\begin{center}
{
A NUMERICAL METHOD FOR THERMAL-HYDRAULIC \\
ANALYSIS IN COMPLEX GEOMETRIES
}
\end{center}
%%%\vspace{\baselineskip}

\begin{center}
{
A.V.~VORONKOV, \quad A.A.~IONKIN \\[0mm]
Keldysh Institute of Applied Mathematics, Russian Ac.Sci., \\
4 Miusskaya Square, Moscow 125047, Russia \\[2mm]
A.N.~PAVLOV ~and~ A.G.~CHURBANOV \\[0mm]
Institute for Mathematical Modeling, Russian Ac.Sci., \\
4-A Miusskaya Square, Moscow 125047, Russia
}
\end{center}
\vspace{\baselineskip}

An efficient computational technique was developed to study
thermal-hydraulics in complicated 2D or 3D geometries.
Global analysis of convective heat and mass transfer in single-phase flows
is performed in the whole problem domain in the conjugate formulation.

Peculiarities of the geometry are described in the framework of the model of
an anisotropic porous medium, i.e. are treated via
distributed volume porosity, directional surface permeabilities,
distributed flow resistances and heat sources/sinks.

Convective flows are governed by the Navier-Stokes equations for a fluid with
variable properties. The 2D/3D time-dependent conservation equations of mass,
momentum and energy with complicated source terms are solved as
an initial/boundary value problem. Effective eddy viscosity and
thermal conductivity can be employed to model turbulent flow regimes.

In the developed mathematical model there is employed the generalized form
of the governing equations that allows to describe thermal and hydrodynamic
phenomena both in solidus and in liquidus in a unified form.
This fact makes possible to construct homogeneous numerical algorithms
for solving conjugate convection/diffusion problems in domains
of complex internal structure.

To solve the above mathematical model, an efficient numerical algorithm
has been developed. Its primary peculiarities are the following: \\
%%%\begin{itemize}
%%%\item
-- discrete approximations are constructed using finite-difference methods
and the MAC-type staggered grid; \\
%%%\item
-- fictitious region method is used to handle irregular complex computational
domains; \\
%%%\item
-- the Douglas-Rachford operator-splitting technique
is employed to construct implicit scheme for the time-dependent equations
of hydrodynamics; \\
%%%\item
-- the fully implicit scheme is utilized for the unsteady heat equation; \\
%%%\item
-- second-order approximations are used for convective terms; \\
%%%\item
-- derived grid elliptic equations are solved at every time-level
using linear iterative solvers based on preconditioned conjugate gradients
methods for symmetric and non-symmetric matrices.
%%%\end{itemize}

A fast reactor with the integral equipment arrangement
with the sodium coolant of BN-800 type has been studied
numerically using the designed computational tools.
Normal operating regimes have been considered in the 2D axisymmetrical
formulation whereas transient processes arising at off-normal regimes were
investigated in the 3D formulation.

It should be noted that the developed code can be employed
not only for design and safety analysis of nuclear reactors
but for prediction of complex heat and flow phenomena in various
technical installations or their particular components
such as steam generators, containment {\it etc}.

This research was supported by Russian Foundation of Fundamental Researches
under grant No.~97-01-00390.

\end{document}