Title page for ETD etd-07052007-103047


Document Type Master's Dissertation
Author Pattinson, John
Email s20131942@tuks.co.za
URN etd-07052007-103047
Document Title A cut-cell, agglomerated-multigrid accelerated, Cartesian mesh method for compressible and incompressible flow
Degree MEng (Mechanical Engineering)
Department Mechanical and Aeronautical Engineering
Supervisor
Advisor Name Title
Prof A G Malan
Prof J P Meyer
Keywords
  • cut-cell non-conforming Cartesian meshes
  • inviscid
Date 2007-04-20
Availability unrestricted
Abstract
This work details a multigrid-accelerated cut-cell Cartesian mesh methodology for the solution of a single partial differential equation set that describes incompressible as well as compressible flow. The latter includes sub-, trans- and supersonic flows. Cut-cell technology is developed which furnishes body-fitted meshes with an overlapping Cartesian mesh as starting point, and in a manner which is insensitive to surface definition inconsistencies. An edge-based vertex-centred finite volume method is employed for the purpose of spatial discretisation. Further, an alternative dual-mesh construction strategy is developed and the standard discretisation scheme suitably enhanced. Incompressibility is dealt with via a locally preconditioned artificial compressibility algorithm, and stabilisation is in all cases achieved with scalar-valued artificial dissipation. In transonic flows, shocks are captured via pressure switch-activated upwinding. The solution process is accelerated by the use of a full approximation scheme (FAS) multigrid method where coarse meshes are generated automatically via a volume agglomeration methodology. The developed modelling technology is validated by application to the solution of a number of benchmark problems. The standard discretisation as well as the alternative method are found to be equivalent in terms of both accuracy and computational cost. Finally, the multigrid implementation is shown to achieve decreases in CPU time of between a factor two to one order of magnitude. In the context of cut-cell Cartesian meshes, the above work has resulted in the following novel contributions: the development of an alternative vertex-centred discretisation method; the use of volume agglomerated multigrid solution technology and the use of a single equation set for both incompressible and compressible flows.
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