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  • 1
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    Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry (1996)
    In:  CASI
    Details
    Publication Date: 2004-12-03
    Description: A highly accurate and efficient numerical method is developed for modeling 3-D reacting flows with detailed chemistry. A contravariant velocity-based governing system is developed for general curvilinear coordinates to maintain simplicity of the continuity equation and compactness of the discretization stencil. A fully-implicit backward Euler technique and a third-order monotone upwind-biased scheme on a staggered grid are used for the respective temporal and spatial terms. An efficient semi-coarsening multigrid method based on line-distributive relaxation is used as the flow solver. The species equations are solved in a fully coupled way and the chemical reaction source terms are treated implicitly. Example results are shown for a 3-D gas turbine combustor with strong swirling inflows.
    Keywords: Numerical Analysis
    Type: Seventh Copper Mountain Conference on Multigrid Methods; 809-824; NASA-CP-3339-Pt-2
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  • 2
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    First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients (1996)
    In:  CASI
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    Publication Date: 2004-12-03
    Description: The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.
    Keywords: Numerical Analysis
    Type: Seventh Copper Mountain Conference on Multigrid Methods; 535-550; NASA-CP-3339
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  • 3
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    First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity (1996)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.
    Keywords: Numerical Analysis
    Type: Seventh Copper Mountain Conference on Multigrid Methods; Part 1; 133-145; NASA-CP-3339
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  • 4
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    First-Order System Least Squares for Velocity-Vorticity-Pressure Form of the Stokes Equations, with Application to Linear Elasticity (1996)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: In this paper, we study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in d = 2 or 3 dimensions. The least squares functional is defined in terms of the sum of the L(exp 2)- and H(exp -1)-norms of the residual equations, which is weighted appropriately by by the Reynolds number. Our approach for establishing ellipticity of the functional does not use ADN theory, but is founded more on basic principles. We also analyze the case where the H(exp -1)-norm in the functional is replaced by a discrete functional to make the computation feasible. We show that the resulting algebraic equations can be uniformly preconditioned by well-known techniques.
    Keywords: Numerical Analysis
    Type: Seventh Copper Mountain Conference on Multigrid Methods; Part 1; 123-132; NASA-CP-3339
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  • 5
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    First-Order System Least-Squares for the Navier-Stokes Equations (1996)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: This paper develops a least-squares approach to the solution of the incompressible Navier-Stokes equations in primitive variables. As with our earlier work on Stokes equations, we recast the Navier-Stokes equations as a first-order system by introducing a velocity flux variable and associated curl and trace equations. We show that the resulting system is well-posed, and that an associated least-squares principle yields optimal discretization error estimates in the H(sup 1) norm in each variable (including the velocity flux) and optimal multigrid convergence estimates for the resulting algebraic system.
    Keywords: Numerical Analysis
    Type: Seventh Copper Mountain Conference on Multigrid Methods; Part 1; 41-55; NASA-CP-3339
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  • 6
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    Algorithms for Ocean Bottom Albedo Determination from In-Water Natural Light Measurements (1999)
    In:  CASI
    Details
    Publication Date: 2019-07-10
    Description: A method for determining ocean bottom optical albedo, R-sub b, from in-water upward and downward irradiance measurements at a shallow site is presented, tested, and compared with a more familiar approach that requires additional measurements at a nearby deep-water site. Also presented are two new algorithms for the estimation of R-sub b from measurements of the downward irradiance and vertically upward radiance.
    Keywords: Numerical Analysis
    Type: SE-1999-03-00011-SSC
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  • 7
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    Seventh Copper Mountain Conference on Multigrid Methods (1996)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: The Seventh Copper Mountain Conference on Multigrid Methods was held on 2-7 Apr. 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection shows its rapid trend to further diversity and depth.
    Keywords: Numerical Analysis
    Type: NASA-CP-3339 , NAS 1.55:3339 , L-17593A , Apr 02, 1995 - Apr 07, 1995; Copper Mountain, CO; United States
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  • 8
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    Seventh Copper Mountain Conference on Multigrid Methods (1996)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: The Seventh Copper Mountain Conference on Multigrid Methods was held on April 2-7, 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The vibrancy and diversity in this field are amply expressed in these important papers, and the collection clearly shows the continuing rapid growth of the use of multigrid acceleration techniques.
    Keywords: Numerical Analysis
    Type: NASA-CP-3339-Pt-2 , NAS 1.55:3339-Pt-2 , L-17593B-Pt-2 , Apr 02, 1995 - Apr 07, 1995; Copper Mountain, CO; United States
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