** Iterative solvers for the CFD-code X-stream **

Eline Jonkers

Site of the project:

TNO Science and Industry

Stieltjesweg 1 (Post box 155)

2600 AD Delft

start of the project: April 2005

In August 2005 the Interim Thesis and a presentation has been given.

The Master project has been finished in February 2006
by the completion of the
Masters Thesis and a final
presentation has been given.
For working address etc. we refer to our
alumnipage.

**Summary of the master project:**

At the Department of Process Modeling and Control at TNO
Science and
Industry 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.

Glass furnace

Within X-stream a domain decomposition (DD) approach is used. A DD
algorithm is an iterative method in which the spatial domain is
decomposed into subdomains 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.

Model of a glass furnace

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.

The goal of the Master's project research is to get experience with
the
algorithm used in X-stream for solving the incompressible
Navier-Stokes
equations and to improve it. Deflation will be studied and reviewed,
there are cases for which deflation does not work properly in
X-stream.
Also GCR-SIMPLE (SIMPLE accelerated by the GCR Krylov subspace method)
will be implemented.

## Contact information:
Kees
Vuik

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