Publication: Velocity-Pressure Coupling in Finite Difference Formulations of the Navier-Stokes Equations

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Title Velocity-Pressure Coupling in Finite Difference Formulations of the Navier-Stokes Equations
Authors/Editors* B Zogheib
Where published* Dept of Mathematics and Statistics, U of Windsor
How published* Thesis
Year* 2006
Keywords CFD, finite difference method, incompressible flow
A new numerical algorithm for solving the two-dimensional, steady, incompressible, laminar, viscous flow equations on a staggered grid is presented in this thesis. The proposed methodology is finite difference based, but essentially takes advantage of the best features of two well-established numerical formulations, the finite difference and finite volume methods. Some weaknesses of the finite difference approach are removed by exploiting the strengths of the finite volume method. In particular, the issue of velocity-pressure coupling is dealt with in the proposed finite difference formulation by developing a new pressure correction equation in a manner similar to the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) approach commonly used in finite volume formulations. However, since this is purely a finite difference formulation, numerical approximation of fluxes is not required. Results obtained from the present method are based on the first-order upwind differencing scheme for the convective terms, but the methodology can easily be modified to accommodate higher order differencing schemes. Comparison with exact solutions for flow in a straight duct is made. The new formulation is also validated against experimental and other numerical data for well-known benchmark problems, namely the lid-driven cavity and backward-facing step flows. For curvilinear domains, the proposed method is validated against numerical results for a complex channel flow and compared to experimental results for the flow over a scour hole. For further validation, some of the results from the present method are compared to results obtained by FLUENT.
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