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1	Performance Comparison Between FEM and DG with Application in Electromagnetics Möller, Oscar January 2016 (has links) Military aircraft have strict requirements to show a low radar signature within different aspect angels and frequency bands. The Finite Difference method and Finite Element method are used by Saab to determine the radar signature from different objects, but the methods suffer from a few limitations. In this master thesis, the Discontinuous Galerkin Finite Element method is implemented to compute the radar signature. The method is implemented in Matlab and is used to discretize Maxwell's Equations in one dimension. The implementation includes dispersive media and absorbing boundary conditions. Performance comparisons between the Finite Element method and the Discontinuous Galerkin Finite Element method are carried out. The results show that the Finite Element method perform better in one dimension, however the results also suggests that the Discontinuous Galerkin Finite Element method will perform better in higher dimensions. DGFEM FEM Other Computer and Information Science Annan data- och informationsvetenskap
2	Efficient Calculations of Two-Dimensional Radar Cross-Section Using DGFEM Persson, Daniel January 2020 (has links) A two-dimensional discontinuous Galerkin finite element method algorithm in the time domain was developed for calculation of the radar cross-section of an arbitrary object. The algorithm was formed using local nodal basis functions in each element and coupling them via numerical upwind flux. Both transverse electric and transverse magnetic polarization, as well as three different dispersive material models, were handled. The computational domain was effectively truncated with low reflections using the uniaxial perfectly matched layer method. Two different time stepping methods were used, low-storage explicit Runge-Kutta and Leap-Frog, to allow for flexibility in the time step and application of a stabilization method. The algorithm was verified with geometries, which have analytical expressions, and an existing validated code. The algorithm was also compared to an existing algorithm, which utilized the continuous finite element method with implicit time stepping, and showed outstanding performance regarding computation time and memory allocation. Since the developed algorithm had explicit time stepping could no general conclusions favoring any of the methods beyond these specific algorithms be made. The results still encouraged continued development of the DGFEM algorithm, where the expansion into three dimensions and optimizations could be explored further. numerical methods DGFEM discontinuous Galerkin finite element method Engineering and Technology Teknik och teknologier
3	Modélisation et Simulation des Ecoulements Compressibles par la Méthode des Eléments Finis Galerkin Discontinus / Modeling and Simulation of Compressible Flows with Galerkin Finite Elements Methods Gokpi, Kossivi 28 February 2013 (has links) L’objectif de ce travail de thèse est de proposer la Méthodes des éléments finis de Galerkin discontinus (DGFEM) à la discrétisation des équations compressibles de Navier-Stokes. Plusieurs challenges font l’objet de ce travail. Le premier aspect a consisté à montrer l’ordre de convergence optimal de la méthode DGFEM en utilisant les polynômes d’interpolation d’ordre élevé. Le deuxième aspect concerne l’implémentation de méthodes de ‘‘shock-catpuring’’ comme les limiteurs de pentes et les méthodes de viscosité artificielle pour supprimer les oscillations numériques engendrées par l’ordre élevé (lorsque des polynômes d’interpolation de degré p>0 sont utilisés) dans les écoulements transsoniques et supersoniques. Ensuite nous avons implémenté des estimateurs d’erreur a posteriori et des procédures d ’adaptation de maillages qui permettent d’augmenter la précision de la solution et la vitesse de convergence afin d’obtenir un gain de temps considérable. Finalement, nous avons montré la capacité de la méthode DG à donner des résultats corrects à faibles nombres de Mach. Lorsque le nombre de Mach est petit pour les écoulements compressibles à la limite de l’incompressible, la solution souffre généralement de convergence et de précision. Pour pallier ce problème généralement on procède au préconditionnement qui modifie les équations d’Euler. Dans notre cas, les équations ne sont pas modifiées. Dans ce travail, nous montrons la précision et la robustesse de méthode DG proposée avec un schéma en temps implicite de second ordre et des conditions de bords adéquats. / The aim of this thesis is to deal with compressible Navier-Stokes flows discretized by Discontinuous Galerkin Finite Elements Methods. Several aspects has been considered. One is to show the optimal convergence of the DGFEM method when using high order polynomial. Second is to design shock-capturing methods such as slope limiters and artificial viscosity to suppress numerical oscillation occurring when p>0 schemes are used. Third aspect is to design an a posteriori error estimator for adaptive mesh refinement in order to optimize the mesh in the computational domain. And finally, we want to show the accuracy and the robustness of the DG method implemented when we reach very low mach numbers. Usually when simulating compressible flows at very low mach numbers at the limit of incompressible flows, there occurs many kind of problems such as accuracy and convergence of the solution. To be able to run low Mach number problems, there exists solution like preconditioning. This method usually modifies the Euler. Here the Euler equations are not modified and with a robust time scheme and good boundary conditions imposed one can have efficient and accurate results. Ecoulements compressibles Méthodes Eléments Finis Equations d’Euler et Navier-Stokes Ecoulements à Mach élevés et faibles Estimateurs d’erreur Compressible Flows Finite elements Methods Galerkin finite elements Methods (DGFEM) High order finite elements Euler and Navier-Stokes equations High and Low mach Number flows Implicit and explicit methods Error estimators 530
4	High order numerical methods for a unified theory of fluid and solid mechanics Chiocchetti, Simone 10 June 2022 (has links) This dissertation is a contribution to the development of a unified model of continuum mechanics, describing both fluids and elastic solids as a general continua, with a simple material parameter choice being the distinction between inviscid or viscous fluid, or elastic solids or visco-elasto-plastic media. Additional physical effects such as surface tension, rate-dependent material failure and fatigue can be, and have been, included in the same formalism. The model extends a hyperelastic formulation of solid mechanics in Eulerian coordinates to fluid flows by means of stiff algebraic relaxation source terms. The governing equations are then solved by means of high order ADER Discontinuous Galerkin and Finite Volume schemes on fixed Cartesian meshes and on moving unstructured polygonal meshes with adaptive connectivity, the latter constructed and moved by means of a in- house Fortran library for the generation of high quality Delaunay and Voronoi meshes. Further, the thesis introduces a new family of exponential-type and semi- analytical time-integration methods for the stiff source terms governing friction and pressure relaxation in Baer-Nunziato compressible multiphase flows, as well as for relaxation in the unified model of continuum mechanics, associated with viscosity and plasticity, and heat conduction effects. Theoretical consideration about the model are also given, from the solution of weak hyperbolicity issues affecting some special cases of the governing equations, to the computation of accurate eigenvalue estimates, to the discussion of the geometrical structure of the equations and involution constraints of curl type, then enforced both via a GLM curl cleaning method, and by means of special involution-preserving discrete differential operators, implemented in a semi-implicit framework. Concerning applications to real-world problems, this thesis includes simulation ranging from low-Mach viscous two-phase flow, to shockwaves in compressible viscous flow on unstructured moving grids, to diffuse interface crack formation in solids. High order ADER Discontinuous Galerkin DG Finite Volume FV Finite Element FE FEM DGFEM CFD Voronoi Delaunay Unstructured meshe Fortran Fluid mechanic Solid Mechanic Continuum Mechanic Baer Nunziato Surface tension Multiphase flow Compressible flow Navier Stoke Semi-implicit GLM cleaning Partial differential equation Numerical method Stiff source Finite rate stiff relaxation Hyperbolic equation Metodi d'alto ordine ADER Discontinous Galerkin Volumi Finiti Elementi Finiti Meccanica dei fluidi Meccanica dei solidi Meccanica dei continui Fluidi multifase Fluidi comprimibili Metodi semi-impliciti Equazioni alle derivate parziali Metodi numerici Equazioni iperboliche Griglie non strutturate

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