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  • 2000-2004  (3)
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  • 1
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    Textbook Multigrid Efficiency for the Steady Euler Equations (2004)
    In:  CASI
    Details
    Publication Date: 2018-06-05
    Description: A fast multigrid solver for the steady incompressible Euler equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Solvers for both unstructured triangular grids and structured quadrilateral grids have been written. Computations for channel flow and flow over a nonlifting airfoil have computed. Using Gauss-Seidel relaxation ordered in the flow direction, textbook multigrid convergence rates of nearly one order-of-magnitude residual reduction per multigrid cycle are achieved, independent of the grid spacing. This approach also may be applied to the compressible Euler equations and the incompressible Navier-Stokes equations.
    Keywords: Fluid Mechanics and Thermodynamics
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 2
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    Towards Optimal Multigrid Efficiency for the Navier-Stokes Equations (2001)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: A fast multigrid solver for the steady incompressible Navier-Stokes equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Numerical solutions are shown for flow over a flat plate and a Karman-Trefftz airfoil. Using collective Gauss-Seidel line relaxation in both the vertical and horizontal directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of a Runge-Kutta based multigrid method.
    Keywords: Fluid Mechanics and Thermodynamics
    Type: AIAA Paper 2001-2574 , 15th Computational Fluid Dynamics Conference; Jun 11, 2001 - Jun 14, 2001; Anaheim, CA; United States
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 3
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    Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations (2004)
    In:  CASI
    Details
    Publication Date: 2019-07-10
    Description: A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.
    Keywords: Aerodynamics
    Type: NASA/TM-2004-213026 , L-18375
    Format: application/pdf
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