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{\bf
A FIXED GRID TECHNIQUE FOR CONVECTION-DIFFUSION
PHASE CHANGE PROBLEMS
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{\bf
A.E.~Aksenova$^1$, V.V.~Chudanov$^1$,
A.G.~Churbanov$^2$ and P.N.~Vabishchevich$^2$
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$^1$Nuclear Safety Institute, Russian Academy of Sciences \\
52 B.~Tul'skaya, Moscow 113191, Russia \\
E-mail: pbl@ibrae.msk.su, \quad Fax: (095) 230 20 29
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$^2$Institute for Mathematical Modeling, Russian Academy of Sciences \\
4 Miusskaya Square, Moscow 125047, Russia \\
E-mail: sergepol@kiam.ru, \quad Fax: (095) 972 07 23
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Nowadays a great attention is given to the development of efficient
numerical algorithms for solving heat and mass transfer problems
with liquid/solid phase changes. Mathematical modeling of these
phenomena meets many problems concerned with numerical treatment of the
latent heat evolution which takes place at the moving liquid/solid
interface during a phase change process.
Over the years, different computational techniques have been developed
to resolve these problems.
In this work a new fixed grid
approach to predict 2D convection/diffusion phase change problems is
developed and verified for pure substances. This algorithm employs
the temperature-based formulation of the energy equation
where the latent heat of fusion is incorporated via an apparent
heat capacity.
To handle a free convection flow in a varying in time fluid domain,
a new efficient numerical method has been developed. This method for
solving the incompressible unsteady Navier-Stokes equations in the
Boussinesq approximation is based on the primitive variables
formulation for fluid flow problems. This new technique is a generalization
of the early developed by the present authors method to
computation domains of an arbitrary complicated shape. At the heart of this
extension is the fictitious domain method which provides
a correct theoretical basis for using fixed grid techniques in problems
of mathematical physics. The new linearized scheme is unconditionally stable
(in linear sense), i.e. the time-step is practically independent
on the spatial grid. The only restriction does exist due to nonlinearity
of convection and heat transfer problems. The skew-symmetric
second-order approximations are employed for the convective terms.
As a test problem there is predicted here the 2D melting of pure gallium
under the influence of free convection in a rectangular cavity.
A comparison with experimental and
computational results has been performed and indicated
a good enough agreement.
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