Mohamed S. Ebeida
PhD Candidate
Dept. of Mechanical and Aeronautical Engineering
University of California - Davis

                                        
Research: Simulations

Simulation Projects


     Simulation of unsteady flows using Galerkin finite element and dynamic remeshing:

    (all simulations are done using the primitive variables u, v, and p)

     

    • Incompressible flow over a NACA 0012 airfoil at Re 800 and alpha = 20:

    Vorticity Contours + Adaptive grid 



    Adaptive grid - modified every time step

     

    • Incompressible flow over two vertical cylinders at Re = 200

     


    Vorticity Contours + Adaptive grid

     



     Incompressible Flow Solver at High Re based on GFEM
    • A turbulent flow over a flat plate was simulated using Galerkin Finite Element, k-omega model and the mesh generation algorithm mentioned above. The following results were obtained using only 12995 grid points, Re = 105. 

       


    unstructured grid used in the simualtion - A zoom in near the leading edge of the flat plate


     

       Solution of a convection-diffusion partial differential equation using Galerkin finite elements and fast iterative solvers: 

      • A linear convection diffusion pde was discretized using GFEM and unstructured grid. The resulting non-Hermitian system was then solved using fast iterative solvers such as MG, GMRES and TFQMR. SLOR was used for smoothing the error in MG. It was also used as a preconditioner in GMRES and TFQMR. The problem domain, one of the utilized meshes, solution at various Re as well as the convergence rates of the differnet solvers are presented in the following figures:

               

      Problem Domain - Solutions at Re = 102, 103, 104



      MG Convergence

        


      GMRES Convergence

        

      TFQMR Convergence










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