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Showing 1 to 20 of 65 for “"Discontinuous Galerkin method"”.
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Towards Coupled Nonhydrostatic-Hydrostatic Hybridizable Discontinuous Galerkin Method
… NHS solver developed using the hybridizable discontinuous Galerkin (HDG) finite element methodology by taking advantage of the local and global HDG solvers for combining HS with NHS solvers. The multi-dynamics is derived, and the first version is implemented in the HDG framework to quantify …
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A Spacetime Discontinuous Galerkin Method for Hyperbolic Conservation Laws
The basic SDG approximation is a simple Bubnov-Galerkin projection that is not prone to global patterns of spurious oscillations. However, it does require stabilization to eliminate local overshoot and undershoot in the immediate vicinity of shocks and other discontinuous solution features. We …
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Analysis of a Spacetime Discontinuous Galerkin Method for Elastodynamics
We prove error estimates for the case of both element-wise and patch-wise causal partitions.
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Development of discontinuous Galerkin method for nonlocal linear elasticity
… of continuity of the solution of higher order. Discontinuous Galerkin methods are particularly attractive toward this end, as they provide a means to naturally enforce higher interelement continuity in a weak manner without the need of modifying the finite element interpolation. In this work, a …
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Runge-Kutta Discontinuous Galerkin method for the Boltzmann equation
… we investigate the ability of the Runge-Kutta Discontinuous Galerkin (RKDG) method to provide accurate and efficient solutions of the Boltzmann equation. Solutions of the Boltzmann equation are desirable in connection to small scale science and technology because when characteristic flow length …
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Studies of Coherent Synchrotron Radiation with the Discontinuous Galerkin Method
In this thesis, we present methods for integrating Maxwell's equations in Frenet-Serret coordinates in several settings using discontinuous Galerkin (DG) finite element method codes in 1D, 2D, and 3D. We apply these routines to the study of coherent synchrotron radiation, an important topic in …
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An adaptive space-time discontinuous Galerkin method for reservoir flows
… autonomy and reliability prevents most numerical methods from being used to their full potential in engineering analysis. This thesis presents work towards the development of an efficient and robust numerical framework for solving reservoir flow problems in a fully-automated manner. In particular, …
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Numerical Simulations of Viscoelastic Flows Using the Discontinuous Galerkin Method
In this work, we develop a method for solving viscoelastic fluid flows using the Navier-Stokes equations coupled with the Oldroyd-B model. We solve the Navier-Stokes equations in skew-symmetric form using the mixed finite element method, and we solve the Oldroyd-B model using the discontinuous …
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Development of Discontinuous Galerkin Method for 1-D Inviscid Burgers Equation
… objective of this research work is to apply the discontinuous Galerkin method to a classical partial differential equation to investigate the properties of the numerical solution and compare the numerical solution to the analytical solution by using discontinuous Galerkin method. This scheme is …
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Implementation and experiments with the discontinuous Galerkin method for Maxwell's equations
… and implementation of, and improvements to, the discontinuous Galerkin method (DGM) for solving Maxwell’s equations. Each step leading to the development of a computer code for this method is explained in detail, and samples codes are included in the Appendix. This work also shows numerical …
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A hybridized discontinuous galerkin method for fully implicit petroleum reservoir simulation
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms
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A time-spectral hybridizable discontinuous Galerkin method for periodic flow problems
… by the low-order Finite Volume and time-marching methods they typically employ. These methods introduce significant numerical dissipation in the simulated flow, and can require hundreds of timesteps to describe a periodic flow with only a few harmonic modes. However, recent developments in …
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DGM-FD: A Finite Difference Scheme Based on the Discontinuous Galerkin Method
… dispersion errors influence the accuracy of a method, efficiency can be assessed by convergence rates and effective adaptability to different mesh structures. Finite difference and finite element methods are commonly used numerical schemes in CAA. Finite difference methods have the advantages …
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The Discontinuous Galerkin Method applied on the equations of ideal relativistic hydrodynamics
… code. For the spatial discretisation we use the Discontinuous Galerkin Method (DGM). Numerical we studied the propagation of relativistic jets and the accretion onto black holes in two dimensions.
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Asynchronous parallel solver for hyperbolic problems via the Spacetime Discontinuous Galerkin method
This thesis presents a parallel Space Time Discontinuous Galerkin (SDG) finite element method which makes use of the method's unstructured mesh generation and localized solution technique to achieve a high level of parallel scalability. Our SDG method is different from most traditional adaptive …
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Analysis of a Spacetime Discontinuous Galerkin Method for Systems of Conservation Laws
… dissertation is analysis of a causal spacetime discontinuous Galerkin (CSDG) method for one-dimensional hyperbolic systems of conservation laws. The CSDG method is based on causal spacetime discretizations, and the Galerkin basis herewith consists of piecewise constant functions. The method can …
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A stabilized discontinuous Galerkin method for variational embedding of physics-based data
… Equations (PDEs) is employed in this work. This method accommodates non-matching meshes across the interfaces between the subdomain boundaries and allows for sharp changes in mechanical material properties. Interface coupling operators that emanate via embedding of Discontinuous Galerkin ideas in …
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Simulations of a passively actuated oscillating airfoil using a discontinuous Galerkin method
… The simulations are performed using a high-order Discontinuous Galerkin finite element solver for the compressible Navier Stokes equations. A brief investigation of a simple problem in which pitch and heave of a foil are prescribed highlights the necessity to use an inexpensive lower fidelity …
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