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The simulation of incompressible flow using the artificial compressibility method. / Saeid Reza Sabbagh-Yazdi
Swansea University Author: Saeid Reza, Sabbagh-Yazdi
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In this work an algorithm is developed for simulating incompressible steady flow on two and three-dimensional unstructured meshes. The Navier-Stokes equations are briefly reviewed as the basic governing equation for fluid flow. Using this set of equations, in the limit of incompressible flow, the pr...
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In this work an algorithm is developed for simulating incompressible steady flow on two and three-dimensional unstructured meshes. The Navier-Stokes equations are briefly reviewed as the basic governing equation for fluid flow. Using this set of equations, in the limit of incompressible flow, the problem of imposing the time independent continuity equation on the momentum equations arises. This difficulty can be removed by employing the Artificial Compressibility approach. This approach modifies the continuity equation by adding a pseudo pressure time derivative. This modification makes the set of equations well conditioned for numerical solution. If the set of modified equations is used for the solution of steady state problems, the added pressure derivative tends to zero and the set of equations reduces to the steady state incompressible Navier-Stokes equations. The cell-vertex finite volume method is employed for solving the modified equations on unstructured triangular and tetrahedral meshes. The principles of central difference space discretisation are described and the basic ideas behind adding artificial dissipation term are reviewed. A normalisation procedure for the computation of the artificial dissipation term is adopted. Two different formulations based upon a cell-vertex finite volume method and a Galerkin finite element method for the discretisation of the viscous terms on unstructured triangular meshes are employed in two and three dimensions. A modification to the finite volume formulation is introduced for improving accuracy on unstructured grids. The issues relating to multi-stage time stepping, boundary conditions and some techniques for increasing computational efficiency are described. A general review of several methods for generating regular and irregular unstructured triangular and tetrahedral meshes are presented. The proposed algorithm is validated by solving several inviscid and viscous two-dimensional test cases. Extension of the algorithm to three dimensions are studied by using some further benchmark examples. Some engineering applications are considered to present the ability of the developed flow solver to simulate more complicated real world problems. Finally, some conclusions are drawn and a few guidelines for further research work are suggested.
Civil engineering.;Fluid mechanics.
College of Engineering