Iterative solvers for the CFD-code X-stream
Eline Jonkers

Site of the project:
TNO Science and Industry
Stieltjesweg 1 (Post box 155)
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

Back to the home page or the Master students page of Kees Vuik