The marker and cell method is an efficient co-volume technique suitable for the solution of incompressible flows using a Cartesian mesh. For flows around complex geometries the use of an unstructured mesh is desirable. For geometric flexibility an unstructured mesh implementation is desirable. A co-volume technique requires a dual orthogonal mesh, in the triangular case the Delaunay-Voronoi dual provides the means for determining this dual orthogonal mesh in an unstructured mesh framework. Certain mesh criteria must be placed on the Delaunay-Voronoi to ensure it meets the dual orthogonal requirements. The two dimensional extension of the marker and cell method to an unstructured framework is presented. The requirements of the mesh are defined and methods in their production are discussed. Initially an explicit time stepping scheme is implemented which allows efficient simulation of incompressible fluid flow problems. Limitations of the explicit time stepping scheme that were discovered, mean that high Reynolds number flows that require the use of stretched meshes cannot produce solutions in a reasonable time period. A semi-implicit time stepping routine removes this limitation allowing these types of flows to be successfully modelled. To validate the solvers accuracy and demonstrate its performance, a number of test cases are presented. These include the lid driven cavity, flow over a backward facing step, inviscid flow around a circular cylinder, unsteady flow around a circular cylinder, flow around an SD7003 aerofoil, flow around a NACA0012 aerofoil and flow around a multi element aerofoil. The investigation although revealing a high dependence on the quality of the mesh still demonstrates that accurate results can be obtained efficiently. The efficiency is demonstrated by comparison to the in-house 2D incompressible finite volume solver for flow around a circular cylinder. For this case the unstructured MAC method produced a solution four times faster than the finite volume code.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:678280 |
| Date | January 2013 |
| Creators | Pelley, Rachel Elizabeth |
| Publisher | Swansea University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://cronfa.swan.ac.uk/Record/cronfa42256 |
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