Development of a laminar Navier-Stokes solver for incompressible flows using structured grids

Akın, Ayhan
A method to solve the Navier-Stokes equations for incompressible viscous flows is proposed. This method is SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm to iteratively solve the two-dimensional laminar steady momentum equations and based upon finite volume method on staggered grids. Numerical tests are performed on several cases of the flow in the lid-driven cavity, as well as of the flow after a backward-facing step with SIMPLE and SIMPLER (SIMPLE Revised) methods. Finally, results are compared qualitatively and quantitatively with numerical and experimental results available in the literature for different Reynolds numbers to validate the methods.


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A recently introduced potential integral equations for stable analysis of low-frequency problems involving dense discretizations with respect to wavelength are solved by using the fast multipole method (FMM). Two different implementations of FMM based on multipoles and an approximate diagonalization employing scaled plane waves are developed and used for rigorous solutions of low-frequency problems. Numerical results on canonical problems demonstrate excellent stability and solution capabilities of both imp...
Citation Formats
A. Akın, “Development of a laminar Navier-Stokes solver for incompressible flows using structured grids,” M.S. - Master of Science, Middle East Technical University, 2006.