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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