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Title: Numerical solutions of the Navier-Stokes equations on generalised grids
Author: Beaven, F.
Awarding Body: University College of Swansea
Current Institution: Swansea University
Date of Award: 1995
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This thesis presents a numerical procedure for the solution of compressible laminar viscous flow in two and three dimensions. The scheme is based on the finite volume method due to Jameson for the solution of the compressible Euler equations on triangular meshes. The method has been extended for the solution of flows on generalised structured and unstructured grids. Three flow solvers have been written, a 2-D cell centre code, a 2-D cell vertex code and a 3-D cell centre code. Particular attention has been paid to the discretization of the viscous fluxes and the artificial dissipation terms. A contour integral method is used for the calculation of variable gradients. A number of different stencils for such a calculation are presented and discussed. A finite volume type discretization, due to Natakusumah, has been implemented in the 2-D cell centre code and has been extended to 3-D. A finite element type discretization, due to Jameson, has been implemented in the cell vertex code. Two methods are presented for the calculation of artificial dissipation. An edge differencing method due to Jameson, with additional scaling terms for application to viscous solutions, is presented and is shown to work well provided the mesh is smoothly varying. An alternative contour integral method is shown to produce superior results on unsmooth meshes. Finally, some examples are presented which demonstrate the flexibility of the methods discussed, in particular is the ability to obtain accurate solutions on a large variety of grid types.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available