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Discontinuous Galerkin Finite Element Method (discontinuous + galerkin_finite_element_method)
Selected AbstractsOn the computation of steady-state compressible flows using a discontinuous Galerkin methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008Hong 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 problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Radek 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 materialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005Ravi 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] Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9-10 2006Koen 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] | ||||||||||