Solvers for the CFD-code X-stream
Jarno Verkaik
Site of the project:
TNO Technisch Physische Dienst
Stieltjesweg 1 (Post box 155)
2600 AD Delft
start of the project: October 2002
In February 2003 the
Interim
Thesis has been appeared.
The Master project has been finished in August 2003
( Masters Thesis).
For working address etc. we refer to our
alumnipage.
Summary of the master project:
At the Department of Process Physics at TNO TPD transport phenomena are
investigated. For the glass industry a large CFD simulation package
called X-stream is developed to simulate flows in glass furnaces. The
involving equations are the incompressible Navier-Stokes equations, the
energy equation, and other equations arising from additional physical
models related to the process of glass melting. These equations are
discretised with the Finite Volume Method on a colocated grid.
Within X-stream a domain decomposition (DD) approach is used. A DD
algorithm (or multi-block algorithm) is an iterative method in which
the spatial domain is decomposed into subdomains (blocks) for which the
equation is solved. In X-stream an additive Schwarz DD method with
minimal overlap is used with inaccurate subdomain solution. Different
equations on different subdomains can be solved and local grid
refinement
is possible at subdomain level. The DD algorithm in X-stream can be run
in
parallel.
Solving the incompressible Navier-Stokes equations is time consuming
because
they are nonlinear. In X-stream the Semi-Implicit Method for
Pressure-Linked
Equations (SIMPLE) is used to solve the nonlinear system of equations.
SIMPLE
is an iterative method where the system in each iteration is split up
into
linear systems for the various unknowns. With a DD approach these
systems
contain couplings between the subdomains. In each SIMPLE iteration the
systems for the velocities and the pressure are solved with the Schwarz
method. This we will refer to as Schwarz in the SIMPLE method.
There is not much experience with the DD algorithm in X-stream. The aim
of
the Master's project is to improve the DD algorithm used for solving
the
incompressible Navier-Stokes equations. It can be observed that more
iterations are needed when the pressure is solved with the Schwarz
method
for an increasing number of subdomains. This is due to the elliptic
nature
of discretised equations for the pressure. To overcome this problem,
and
to make the DD algorithm scalable, a deflation coarse grid correction
will
be applied. Besides this, another aim in the project is to accelerate
Schwarz in the SIMPLE method. This method can be seen as nested basic
iterative methods which lend themselves well for Krylov subspace or
multigrid
acceleration. Acceleration will be focussed on the Schwarz method for
the
pressure and the SIMPLE method because they are most time-consuming.
This
will be done with the GCR Krylov subspace method. Also parallellization
aspects will be considered in the Master's project.
Contact information:
Kees
Vuik
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