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  • 1
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    A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis in fluids (1991)
    In:  Other Sources
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    Publication Date: 2019-07-12
    Description: A solution procedure for solving nonlinear time-marching problems is presented. The nonsymmetric systems of equations arising from a Newton-type linearization of these time-marching problems are solved using an iterative strategy based on the generalized minimal residual (GMRES) algorithm. Matrix-free techniques leading to reduction in storage are presented. Incorporation of a linesearch algorithm in the Newton-GMRES scheme is discussed. An automatic time-increment control strategy is developed to increase the stability of the time-marching process. High-speed flow computations demonstrate the effectiveness of these algorithms.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Computer Methods in Applied Mechanics and Engineering (ISSN 0045-7825); 87; 3-Feb; 281-304
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  • 2
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    Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations (1987)
    In:  Other Sources
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    Publication Date: 2019-07-12
    Description: The current status of streamline-upwind/Petrov-Galerkin (SUPG) methods for the analysis of flow problems is surveyed in an analytical review. Problem areas addressed include classical Galerkin, upwind, artificial-diffusion, SUPG, discontinuous Galerkin, space-time FEM, and discontinuity-capturing approaches to the scalar advection-diffusion equation; incompressible flows; advective-diffusive systems; and the compressible Euler and Navier-Stokes equations. Graphs and diagrams are provided, and the good stability properties of state-of-the-art SUPG methods are pointed out.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: International Journal for Numerical Methods in Fluids (ISSN 0271-2091); 7; 1261-127
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  • 3
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    A new family of stable elements for the Stokes problem based on a mixed Galerkin/least-squares finite element formulation (1989)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: International Conference on Finite Element Methods in Flow Problems; Apr 03, 1989 - Apr 07, 1989; Huntsville, AL; United States
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  • 4
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    The Stokes problem with various well-posed boundary conditions - Symmetric formulations that converge for all velocity/pressure spaces (1989)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: Symmetric finite-element formulations are presented for the primitive-variables form of the Stokes equations. These formulations are convergent for any combination of pressure and velocity interpolations. Various boundary conditions, such as pressure, are accommodated.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: International Conference on Finite Element Methods in Flow Problems; Apr 03, 1989 - Apr 07, 1989; Huntsville, AL; United States
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  • 5
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    Galerkin/least-squares procedures in computational fluid dynamics (1989)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: The application of Galerkin/least-squares methodology to computational fluid dynamics is reviewed. Applications to advective-diffusive systems of equations and incompressible and compressible Euler and Navier-Stokes equations are described. Space-time finite-element methodology for time-dependent problems is emphasized and the status and role of so-called 'discontinuity-capturing operators' is reviewed.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: International Conference on Finite Element Methods in Flow Problems; Apr 03, 1989 - Apr 07, 1989; Huntsville, AL; United States
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