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Galerkin Finite Element Method (galerkin + finite_element_method)

Distribution by Scientific Domains
Engineering100%

Kinds of Galerkin Finite Element Method

  • discontinuous galerkin finite element method
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    Selected Abstracts

    Stabilized finite element formulation of buoyancy driven incompressible flows

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2002
    S. Aliabadi
    Abstract Streamline-upwind/Petrov,Galerkin finite element method is developed for buoyancy-driven incom-pressible flows with heat and mass transfer. The stabilized finite element formulations are implemented in parallel using message passing interface libraries. To measure the accuracy of the method, we solve a 2D numerical example of natural convection flows at moderate to high Rayleigh numbers. The 3D applications include the dispersion of smoke from a chimney and within a stadium. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    On the computation of steady-state compressible flows using a discontinuous Galerkin method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008
    Hong Luo
    Abstract Computation of compressible steady-state flows using a high-order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics-based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low-storage p -multigrid method is used for solving the governing compressible Euler equations to obtain steady-state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady-state flows. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006
    Radek Tezaur
    Abstract Recently, a discontinuous Galerkin finite element method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution in two dimensions of Helmholtz problems in the mid-frequency regime. In this paper, this method is extended to three dimensions and several new elements are proposed. Computational results obtained for several wave guide and acoustic scattering model problems demonstrate one to two orders of magnitude solution time improvement over the higher-order Galerkin method. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Modelling and process optimization for functionally graded materials

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005
    Ravi S. Bellur-Ramaswamy
    Abstract We optimize continuous quench process parameters to produce functionally graded aluminium alloy extrudates. To perform this task, an optimization problem is defined and solved using a standard non-linear programming algorithm. Ingredients of this algorithm include (1) the process parameters to be optimized, (2) a cost function: the weighted average of the precipitate number density distribution, (3) constraint functions to limit the temperature gradient (and hence distortion and residual stress) and exit temperature, and (4) their sensitivities with respect to the process parameters. The cost and constraint functions are dependent on the temperature and precipitate size which are obtained by balancing energy to determine the temperature distribution and by using a reaction-rate theory to determine the precipitate particle sizes and their distributions. Both the temperature and the precipitate models are solved via the discontinuous Galerkin finite element method. The energy balance incorporates non-linear boundary conditions and material properties. The temperature field is then used in the reaction rate model which has as many as 105 degrees-of-freedom per finite element node. After computing the temperature and precipitate size distributions we must compute their sensitivities. This seemingly intractable computational task is resolved thanks to the discontinuous Galerkin finite element formulation and the direct differentiation sensitivity method. A three-dimension example is provided to demonstrate the algorithm. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    New stabilized finite element method for time-dependent incompressible flow problems

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2010
    *Article first published online: 20 FEB 200, Yueqiang Shang
    Abstract A new stabilized finite element method is considered for the time-dependent Stokes problem, based on the lowest-order P1,P0 and Q1,P0 elements that do not satisfy the discrete inf,sup condition. The new stabilized method is characterized by the features that it does not require approximation of the pressure derivatives, specification of mesh-dependent parameters and edge-based data structures, always leads to symmetric linear systems and hence can be applied to existing codes with a little additional effort. The stability of the method is derived under some regularity assumptions. Error estimates for the approximate velocity and pressure are obtained by applying the technique of the Galerkin finite element method. Some numerical results are also given, which show that the new stabilized method is highly efficient for the time-dependent Stokes problem. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equations

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9-10 2006
    Koen Hillewaert
    Abstract We study the efficient use of the discontinuous Galerkin finite element method for the computation of steady solutions of the Euler equations. In particular, we look into a few methods to enhance computational efficiency. In this context we discuss the applicability of two algorithmical simplifications that decrease the computation time associated to quadrature. A simplified version of the quadrature free implementation applicable to general equations of state, and a simplified curved boundary treatment are investigated. We as well investigate two efficient iteration techniques, namely the classical Newton,Krylov method used in computational fluid dynamics codes, and a variant of the multigrid method which uses interpolation orders rather than coarser tesselations to define the auxiliary coarser levels. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    A level set characteristic Galerkin finite element method for free surface flows

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2005
    Ching-Long Lin
    Abstract This paper presents a numerical method for free surface flows that couples the incompressible Navier,Stokes equations with the level set method in the finite element framework. The implicit characteristic-Galerkin approximation together with the fractional four-step algorithm is employed to discretize the governing equations. The schemes for solving the level set evolution and reinitialization equations are verified with several benchmark cases, including stationary circle, rotation of a slotted disk and stretching of a circular fluid element. The results are compared with those calculated from the level set finite volume method of Yue et al. (Int. J. Numer. Methods Fluids 2003; 42:853,884), which employed the third-order essentially non-oscillatory (ENO) schemes for advection of the level set function in a generalized curvilinear coordinate system. The comparison indicates that the characteristic Galerkin approximation of the level set equations yields more accurate solutions. The second-order accuracy of the Navier,Stokes solver is confirmed by simulation of decay vortex. The coupled system of the Navier,Stokes and level set equations then is validated by solitary wave and broken dam problems. The simulation results are in excellent agreement with experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    A Lagrangian level-set approach for the simulation of incompressible two-fluid flows,

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005
    F. S. Sousa
    Abstract A Lagrangian level-set method to solve incompressible two-dimensional two-fluid flows is presented. The Navier,Stokes equations are discretized by a Galerkin finite element method. A projection method is employed to decouple the system of non-linear equations. The interface between fluids is represented by the zero level set of a function , plus additional marker points of the computational mesh. In the standard Eulerian level-set method, this function is advected through the domain by solving a pure advection equation. To reduce mass conservation errors that can arise from this step, our method employs a Lagrangian technique which moves the nodes of the finite element mesh, and consequently, the information stored in each node. The quality of the mesh is controlled by a remeshing procedure, avoiding bad triangles by flipping edges, inserting or removing vertices from the triangulation. Results of numerical simulations are presented, illustrating the improvements in mass conservation and accuracy of this new methodology. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    LS-DYNA and the 8:1 differentially heated cavity

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2002
    Mark A. Christon
    Abstract This paper presents results computed using LS-DYNA's new incompressible flow solver for a differentially heated cavity with an 8:1 aspect ratio at a slightly super-critical Rayleigh number. Three Galerkin-based solution methods are applied to the 8:1 thermal cavity on a sequence of four grids. The solution methods include an explicit time-integration algorithm and two second-order projection methods,one semi-implicit and the other fully implicit. A series of ad hoc modifications to the basic Galerkin finite element method are shown to result in degraded solution quality with the most serious effects introduced by row-sum lumping the mass matrix. The inferior accuracy of a lumped mass matrix relative to a consistent mass matrix is demonstrated with the explicit algorithm which fails to obtain a transient solution on the coarsest grid and exhibits a general trend to under-predict oscillation amplitudes. The best results are obtained with semi-implicit and fully implicit second-order projection methods where the fully implicit method is used in conjunction with a ,smart' time integrator. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Parallelization of a vorticity formulation for the analysis of incompressible viscous fluid flows

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002
    Mary J. Brown
    Abstract A parallel computer implementation of a vorticity formulation for the analysis of incompressible viscous fluid flow problems is presented. The vorticity formulation involves a three-step process, two kinematic steps followed by a kinetic step. The first kinematic step determines vortex sheet strengths along the boundary of the domain from a Galerkin implementation of the generalized Helmholtz decomposition. The vortex sheet strengths are related to the vorticity flux boundary conditions. The second kinematic step determines the interior velocity field from the regular form of the generalized Helmholtz decomposition. The third kinetic step solves the vorticity equation using a Galerkin finite element method with boundary conditions determined in the first step and velocities determined in the second step. The accuracy of the numerical algorithm is demonstrated through the driven-cavity problem and the 2-D cylinder in a free-stream problem, which represent both internal and external flows. Each of the three steps requires a unique parallelization effort, which are evaluated in terms of parallel efficiency. Copyright © 2002 John Wiley & Sons, Ltd. [source]