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Showing 1 to 20 of 41 for “"discontinuous galerkin finite element"”.
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A Spacetime Discontinuous Galerkin Finite-Element Method for Elastodynamic Analysis
We use the new spacetime discontinuous Galerkin finite element model to investigate a series of elastodynamic problems in both one and two spatial dimensions. The first study focuses on the problems that exhibit discontinuities or shocks. The new method delivers high accurate results. The second …
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Adaptive unstructured spacetime meshing for four-dimensional spacetime discontinuous Galerkin finite element methods
We describe the spacetime discontinuous Galerkin method, a new type of finite-element method which promises dramatic improvement in solution speed for hyperbolic problems. These methods require the generation of spacetime meshes that satisfy a special causality constraint. This work focuses on the …
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Efficient matrix-free implementation and automated verification of hybridizable discontinuous Galerkin finite element methods
… robust implementation methods for hybridizable discontinuous Galerkin (HDG) schemes for fluid and ocean dynamics. In the first part, we compare choices in weak formulations and their numerical consequences. We address details in making the leap from the mathematical formulation to the …
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Hypersonic heat transfer and anisotropic visualization with a higher order discontinuous Galerkin finite element method
… aerodynamics methods. In particular, the discontinuous Galerkin (DG) finite element method has O(hP+l) design accuracy and allows for subcell resolution of shocks. This work furthers the DG finite element method in two ways. First, it demonstrates the results of DG when used to predict …
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Stable algorithms for generalized thermoelasticity based on operator-splitting and time-discontinuous Galerkin finite element methods
… based on operator-splitting and the time-discontinuous Galerkin finite element method for the non-classical, linear thermoelastic model. The coupled problem is split into two contractive sub-problems, namely, the mechanical phase and thermal phase, on the basis of an entropy controlling …
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A high-order, adaptive, discontinuous Galerkin finite element method for the Reynolds-Averaged Navier-Stokes equations
This thesis presents high-order, discontinuous Galerkin (DG) discretizations of the Reynolds-Averaged Navier-Stokes (RANS) equations and an output-based error estimation and mesh adaptation algorithm for these discretizations. In particular, DG discretizations of the RANS equations with the …
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An a posteriori error control framework for adaptive precision optimization using discontinuous Galerkin finite element method
Introduction: Aerodynamic design optimization has seen significant development over the past decade. Adjoint-based shape design for elliptic systems was first proposed by Pironneau and applied to transonic flow by Jameson . A review of the aerodynamic shape optimization literature and a large list …
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Shock capturing with PDE-based artificial viscosity for an adaptive, higher-order discontinuous Galerkin finite element method
… viscosity can be combined with a higher-order discontinuous Galerkin finite element discretization to resolve a shock layer within a single cell. However, when a nonsmooth artificial viscosity model is employed with an otherwise higher-order approximation, element-to-element variations induce …
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On the Formulation of a Hybrid Discontinuous Galerkin Finite Element Method (DG-FEM) for Multi-layered Shell Structures
A high-order hybrid discontinuous Galerkin finite element method (DG-FEM) is developed for multi-layered curved panels having large deformation and finite strain. The kinematics of the multi-layered shells is presented at first. The Jacobian matrix and its determinant are also calculated. The weak …
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Immersed Discontinuous Galerkin Methods for Acoustic Wave Propagation in Inhomogeneous Media
We present immersed discontinuous Galerkin finite element methods for one and two dimensional acoustic wave propagation problems in inhomogeneous media where elements are allowed to be cut by the material interface. The proposed methods use the standard discontinuous Galerkin finite element …
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A dynamic multiscale viscosity algorithm for shock capturing in Runge Kutta Discontinuous Galerkin methods
… order to improve the performance of higher-order Discontinuous Galerkin finite element solvers, a shock capturing procedure has been developed for hyperbolic equations. The Dynamic Multiscale Viscosity method, originally presented by Oberai and Wanderer [8, 9] in a Fourier Galerkin context, is …
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An output-based adaptive and high-order method for a rotor in hover
A high-order discontinuous Galerkin finite element discretization and output-based adaptation scheme for the compressible Euler equations are presented and applied to an isolated rotor in hover. A simplex cut-cell mesh generation technique is used to support robust and autonomous creation of …
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Optimization and validation of discontinuous Galerkin Code for the 3D Navier-Stokes equations
… linear solve, the components of a high-order, Discontinuous Galerkin Finite Element Method (DGFEM) for the Navier-Stokes equations in 3D are presented. Emphasis is given to residual and Jacobian assembly, since these are rarely discussed in the literature; in particular, this thesis focuses on …
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A high-order discontinuous Galerkin multigrid solver for aerodynamic applications
… presented from the development of a high-order discontinuous Galerkin finite element solver using p-multigrid with line Jacobi smoothing. The line smoothing algorithm is presented for unstructured meshes, and p-multigrid is outlined for the nonlinear Euler equations of gas dynamics. Analysis of …
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Error analysis of higher order time-domain finite element methods for the one-dimensional Maxwell's equations
A well known nodal discontinuous Galerkin finite element method has been extended for higher order temporal accuracy using several schemes. While common in computational fluid dynamics, less research has been conducted with these methods for computational electromagnetics. A stabilized finite …
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A Perfectly Matched Layer Method for the Navier-Stokes equations
… equations, and is implemented with a high-order discontinuous Galerkin finite element method (DGFEM). The weaknesses and strengths of the method are investigated, and its performance is assessed when applied to complex flows; in particular, a viscous cavity flow is investigated. Stabilizing …
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A-Posteriori bounds on linear functionals of coercive 2nd order PDEs using discontinuous Galerkin methods
… previous approaches, we base our method on the Discontinuous Galerkin finite element method. For equations such as the convection-diffusion equation, the convection term is handled by the standard DG method for hyperbolic problems while the diffusion operator is discretized by the LDG scheme. …
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Spacetime Meshing for Discontinuous Galerkin Methods
… solution of nonlinear phenomena using spacetime discontinuous Galerkin finite element methods. Given a triangulated d-dimensional Euclidean space domain M (a simplicial complex) corresponding to time t = 0 and initial conditions of the underlying hyperbolic spacetime PDE, we construct an …
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A space-time adaptive method for flows in oil reservoirs
… algorithm for metric-based mesh optimization. A discontinuous Galerkin finite element discretization is used to solve on simplex meshes with arbitrary anisotropy, and thereby obtain solutions of higher order accuracy in both space and time. The adaptive framework has been applied to single-phase …
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Multigrid solution for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
A high-order discontinuous Galerkin finite element discretization and p-multigrid solution procedure for the compressible Navier-Stokes equations are presented. The discretization has an element-compact stencil such that only elements sharing a face are coupled, regardless of the solution space. …
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