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Simulation numérique de la propagation d'une décharge dans un plasma sur maillage non stucturés adaptés dynamiquement / Numerical simulation of streamer propagation on unstructured dynamically adapted gridsKarel, Jan 02 December 2014 (has links)
L'objectif de cette thèse est la simulation numérique de la propagation d'une décharge électrique dans un champ électrique à haute tension. Un modèle minimal est utilisé pour la description de la physique. Le modèle consiste en un modèle d'équations de convectiondiffusionréaction de particules électrique couplé à l'équation de Poisson pour le potentiel électrique. Nous simulons la propagation d'une décharge en 3D, qui présente des ramifications causées par des perturbations locales dans le champ électrique. Nous avons mis en oeuvre une méthode basée sur l'adaptation dynamique de maillages pour la simulation numérique. Les propriétés de la méthode sont testées d'abord sur un simple problème analogue en 2D. Cette approche a été suffisante pour le développement de la méthode, même si en 2D le problème est d'un type différent (décharge plane), et cela a permis une transition simple au vrai problème 3D. / The aim of this thesis is a numerical simulation of a streamer propagation (electric discharge in a high voltage electric field). The minimal model is used for the streamer description. The model consists of a system of convectiondiffusionreaction equations for electric particles coupled with Poisson’s equation for an electric potential. We simulate a general streamer motion in 3D which is presented by streamer branching. It is caused by local disturbances in the electric field. We have developed a method based on a dynamically adaptation of grids for the simulation. The properties of the method are tested on simpler problems in 2D (less time consuming). This approach is sufficient for the development of the method even if it is different type of problem (planar discharge) and it allows a simple transition to 3D. / Tato dizertační práce se zabývá numerickou simulací propagace streameru (elektrický výbojve vysokonapět'ovém elektrickém poli). Pro popis streameru je použit minimální model, který se skládá ze soustavy transportních rovnic pro elektricky nabité částice spárovaných s Poissonovou rovnicí pro elektrický potenciál. V práci simulujeme obecný pohyb streameru ve 3D. Tento obecný pohyb je prezentován rozvětvením streameru, kterého se dosáhne pomocí lokálních poruch v elektrickem poli. Pro numerickou simulaci streameru jsme vyvinuli meto du založenou na dynamické adaptaci síte, jejíž vlastnosti byly otestováný na jednodušších problémech ve 2D (menší časová náročnost). I když jde o jiný typ problému (rovinný výboj), pro vývoj metody je dostatečný a umožňuje snadný přechod do 3D.

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Solution Adaptive Isotropic And Anisotropic Mesh Refinement Using General ElementsSenguttuvan, Vinoad 07 May 2005 (has links)
Two refinement techniques to generate solution adaptive meshes have been developed. Both techniques utilize arbitrary polyhedra (general elements) to constrain the propagation of refinement. A facebased approach that produces isotropic refinement and a combined element and edgebased approach that produces anisotropic refinement are presented. Refinement is triggered through sensors that use a shock detection algorithm or error estimation based on the smoothness of the reconstructed solution variables. The basic algorithms as well as specific implementation issues are presented. The advantages and disadvantages of the different methods are discussed and illustrated through a set of synthetic and realistic test cases. It is shown that general elements can be employed effectively in solution adaptive meshes generated using refinement.

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Mesh adaptation through rrefinement using a truss network analogyJones, Bevan W S 15 August 2016 (has links)
This project investigates the use of a truss network, a structural mechanics model, as a metaphor for adapting a computational fluid dynamics (CFD) mesh. The objective of such adaptation is to increase computational effi ciency by reducing the numerical error. To drive the adaptation, or to give the scheme an understanding of accuracy, computational errors are translated into forces at mesh vertices via a socalled monitor function. The ballvertex truss network method is employed as it offers robustness and is applicable to problems in both two and three dimensions. In support of establishing a stateoftheart adaptive meshing tool, boundary vertices are allowed to slide along geometric boundaries in an automated manner. This is achieved via feature identification followed by the construction of 3rd order bezier surface patches over boundary faces. To investigate the ability of the scheme, three numerical test cases were investigated. The first comprised an analytical case, with the aim of qualitatively assessing the ability to cluster vertices according to gradient. The developed scheme proved successful in doing this. Next, compressible transonic flow cases were considered in 2D and 3D. In both cases, the computed coefficient of lift and moment were investigated on the unrefined and refined meshes and then compared for error reduction. Improvements in accuracy of at least 60% were guaranteed, even on coarse meshes. This is viewed as a marked achievement in the sphere of robust and industrially viable rrefinement schemes.

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ResidualBased Isotropic and Anisotropic Mesh Adaptation for Computational Fluid DynamicsBaserinia, Amir Reza January 2008 (has links)
The accuracy of a fluid flow simulation depends not only on the numerical method used for discretizing the governing equations, but also on the distribution and topology of the mesh elements. Mesh adaptation is a technique for automatically modifying the mesh in order to improve the simulation accuracy in an attempt to reduce the manual work required for mesh generation. The conventional approach to mesh adaptation is based on a featurebased criterion that identifies the distinctive features in the flow field such as shock waves and boundary layers. Although this approach has proved to be simple and effective in many CFD applications, its implementation may require a lot of trial and error for determining the appropriate criterion in certain applications. An alternative approach to mesh adaptation is the residualbased approach in which the discretization error of the fluid flow quantities across the mesh faces is used to construct an adaptation criterion. Although this approach provides a general framework for developing robust mesh adaptation criteria, its incorporation leads to significant computational overhead.
The main objective of the thesis is to present a methodology for developing an appropriate mesh adaptation criterion for fluid flow problems that offers the simplicity of a featurebased criterion and the robustness of a residualbased criterion. This methodology is demonstrated in the context of a secondorder accurate cellcentred finite volume method for simulating laminar steady incompressible flows of constant property fluids. In this methodology, the error of mass and momentum flows across the faces of each control volume are estimated with a Taylor series analysis. Then these face flow errors are used to construct the desired adaptation criteria for triangular isotropic meshes and quadrilateral anisotropic meshes. The adaptation results for the liddriven cavity flow show that the solution error on the resulting adapted meshes is 80 to 90 percent lower than that of a uniform mesh with the same number of control volumes.
The advantage of the proposed mesh adaptation method is the capability to produce meshes that lead to more accurate solutions compared to those of the conventional methods with approximately the same amount of computational effort.

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ResidualBased Isotropic and Anisotropic Mesh Adaptation for Computational Fluid DynamicsBaserinia, Amir Reza January 2008 (has links)
The accuracy of a fluid flow simulation depends not only on the numerical method used for discretizing the governing equations, but also on the distribution and topology of the mesh elements. Mesh adaptation is a technique for automatically modifying the mesh in order to improve the simulation accuracy in an attempt to reduce the manual work required for mesh generation. The conventional approach to mesh adaptation is based on a featurebased criterion that identifies the distinctive features in the flow field such as shock waves and boundary layers. Although this approach has proved to be simple and effective in many CFD applications, its implementation may require a lot of trial and error for determining the appropriate criterion in certain applications. An alternative approach to mesh adaptation is the residualbased approach in which the discretization error of the fluid flow quantities across the mesh faces is used to construct an adaptation criterion. Although this approach provides a general framework for developing robust mesh adaptation criteria, its incorporation leads to significant computational overhead.
The main objective of the thesis is to present a methodology for developing an appropriate mesh adaptation criterion for fluid flow problems that offers the simplicity of a featurebased criterion and the robustness of a residualbased criterion. This methodology is demonstrated in the context of a secondorder accurate cellcentred finite volume method for simulating laminar steady incompressible flows of constant property fluids. In this methodology, the error of mass and momentum flows across the faces of each control volume are estimated with a Taylor series analysis. Then these face flow errors are used to construct the desired adaptation criteria for triangular isotropic meshes and quadrilateral anisotropic meshes. The adaptation results for the liddriven cavity flow show that the solution error on the resulting adapted meshes is 80 to 90 percent lower than that of a uniform mesh with the same number of control volumes.
The advantage of the proposed mesh adaptation method is the capability to produce meshes that lead to more accurate solutions compared to those of the conventional methods with approximately the same amount of computational effort.

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Algorithmes multigrilles adaptatifs et scalables / Adaptative and scalable mesh adaptationBrèthes, Gautier 08 December 2015 (has links)
Dans toutes sortes de milieux industriels comme l'aéronautique, l'industrie spatiale, l'industrie pétrolière et tant d'autres, il est indispensable d'effectuer des calculs numériques pour simuler des phénomènes intervenant dans des systèmes naturels ou artificiels modélisables par la mécanique des milieux continus. Nous nous sommes intéressés à la question scientifique suivante: Comment, pour une simulation donnée et des moyens de calcul donnés, obtenir la plus grande précision de prédiction ? Le but de cette thèse est de faire le lien entre deux techniques de simulation numérique : les méthodes multigrilles et les nouvelles méthodes adaptatives anisotropes récemment développées. On résout une équation aux dérivées partielles elliptique. L'adaptation des maillages au problème donné repose sur une minimisation d'une grandeur donnée suivant la méthode d'adaptation employée: l'erreur d'interpolation pour l'adaptation baséehessiens, une pondération de l'erreur d'approximation pour la méthode goaloriented et la norme de l'erreur d'approximation pour la méthode normoriented. La méthode multigrille permet d'accelérer la convergence sur chaque maillage. Plusieurs cas tests ont été effectués pour s'assurer de l'efficacité des différentes méthodes. / In many industrial activities such as aeronautics, space industry, oil industry and many others, it is essential to carry out numerical computations to simulate phenomena occurring in natural or artificial systems modelisable by mechanical Continuum. This thesis focuses on the following scientific question: how, for a given simulation and computing means given, obtain the highest prediction accuracy? Our contribustion makes the link between two numerical simulation techniques: multigrid methods and new recently developed anisotropic adaptative methods. We solve an elliptic partial differential equation. The adaptation of the mesh to the given problem is based on minimization of a given magnitude following the adaptation method employed: the interpolation error for the Hessianbased adaptation, a weighting of the approximation error for goaloriented method and the norm of the approximation error for the normoriented method. The multigrid method permits to accelerate convergence on each mesh. Several tests cases were carried out to ensure the effectiveness of the different methods.

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Truncation Error Based Mesh Adaptation and its Application to MultiMesh CFDJackson, Charles Wilson, V 18 July 2019 (has links)
One of the largest sources of error in a CFD simulation is the discretization error. One of the least computationally expensive ways of reducing the discretization error in a simulation is by performing mesh adaptation. In this work, the mesh adaptation processes are driven by the truncation error, which is the local source of the discretization error. Because this work is focused on methods for structured grids, radaptation is used as opposed to hadaptation.
A new method for performing the radaptation based on an optimization process is developed and presented here. This optimization process was applied to simple 1D and 2D Euler problems as a method of testing the approach. The mesh optimization approach is compared to the more common equidistribution approach to determine which produces more accurate results as well as the costs associated with each. It is found that the optimization process is able to reduce the truncation error than equidistribution. However, in the 2D cases optimization does not reduce the discretization error sufficiently to warrant the significant costs of the approach. This indicates that the much cheaper equidistribution process provides a costeffective manner to reduce the discretization error in the solution. Further, equidistribution is able to achieve the bulk of the potential reductions in discretization error possible through radaptation.
This work also develops a new framework for reducing the cost of performing truncation error based radaptation. This new framework also addresses some of the issues associated with radaptation. In this framework, adaptation is performed on a coarse mesh where it is faster to perform, creating a mapping function for this mesh, and finally evaluating this mapping at a fine enough mesh to meet the error target. The framework is used for 2D Euler and 2D laminar NavierStokes problems and shown to be the most costeffective way to meet a desired error target.
Finally, the multimesh CFD method is introduced and applied to a wide variety of problems from quasi1D nozzle to 2D laminar and turbulent boundary layers. The multimesh method allows the system of equations to be solved on a system of meshes. With this method, each equation is solved on a mesh that is adapted specifically for it, meaning that more accurate solutions for each equation can be obtained. This work shows that, for certain problems, the multimesh approach is able to achieve more accurate results in less time compared to using a single mesh. / Doctor of Philosophy / Computational fluid dynamics (CFD) describes a method of numerically solving equations that attempt to model the behavior of a fluid. As computers have become cheaper and more powerful and the software has become more capable, CFD has become an integral part of the engineering process. One of the goals of the field is to be able to bring these higher fidelity simulations into the design loop earlier. Ideally, using CFD earlier in the design process would allow design engineers to create new innovative designs with less programmatic risk. Likewise, it is also becoming necessary to use these CFD tools later in the final design process to replace some physical experiments which can be expensive, unsafe, or infeasible to run. Both of these goals require the CFD codes to meet the accuracy requirements for the results as fast as possible. This work discusses several different methods for improving the accuracy of the simulations as well as ways of obtaining these more accurate results for the cheapest cost. In CFD, the governing equations modeling the flow behavior are solved on a computer. As a result, these continuous differential equations must be approximated as a system of discrete equations, so that they can be solved on a computer. These approximations result in discretization error, the difference between the exact solutions to the discrete and continuous equations, which is typically the largest type of numerical error in a CFD solution. The source of the discretization error is the truncation error, which is composed of the terms left out of the approximations made when discretizing the continuous equations. Thus, if the truncation error can be reduced, the discretization error in the solution should also be reduced. In this work, several different ways of reducing this truncation error through mesh adaptation are discussed, including the use of optimization methods. These mesh optimization methods are compared to a more common way of performing adaptation, namely equidistribution. It is determined that equidistribution is able to reduce the discretization error by a similar amount while being significantly faster than mesh optimization. This work also presents a framework for making the adaptation process faster overall by performing the adaptation on a coarse mesh and then refining the mesh enough to meet the error tolerance for the application. This framework was the cheapest method investigated to meet a given error target. This work also introduces a new technique called multimesh CFD, which allows each equation (conservation of mass, momentum, energy, etc.) to be solved on a separate mesh. This allows each equation to be solved on a mesh that is specifically adapted for it, resulting in a more accurate solution. Here, it is shown that, for certain problems, the multimesh technique is able to obtain a solution with lower error than only using a single mesh. This work also shows that these more accurate results can be obtained in less time using multiple meshes than on a single mesh.

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Application of rAdaptation Techniques for Discretization Error Improvement in CFDTyson, William Conrad 29 January 2016 (has links)
Computational fluid dynamics (CFD) has proven to be an invaluable tool for both engineering design and analysis. As the performance of engineering devices become more reliant upon the accuracy of CFD simulations, it is necessary to not only quantify and but also to reduce the numerical error present in a solution. Discretization error is often the primary source of numerical error. Discretization error is introduced locally into the solution by truncation error. Truncation error represents the higher order terms in an infinite series which are truncated during the discretization of the continuous governing equations of a model. Discretization error can be reduced through uniform grid refinement but is often impractical for typical engineering problems. Grid adaptation provides an efficient means for improving solution accuracy without the exponential increase in computational time associated with uniform grid refinement. Solution accuracy can be improved through local grid refinement, often referred to as hadaptation, or by node relocation in the computational domain, often referred to as radaptation. The goal of this work is to examine the effectiveness of several radaptation techniques for reducing discretization error. A framework for geometry preservation is presented, and truncation error is used to drive adaptation. Sample problems include both subsonic and supersonic inviscid flows. Discretization error reductions of up to an order of magnitude are achieved on adapted grids. / Master of Science

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A Numerical Study of Droplet Formation and Behavior using Interface Tracking MethodsMenon, Sandeep 01 September 2011 (has links)
An adaptive remeshing algorithm has been developed for multiphase flow simulations using the movingmesh interface tracking (MMIT) technique. The edgeswapping algorithm uses the Delaunay criterion (in 2D) and a dynamic programming technique (in 3D) to maximize the quality of mesh primitives surrounding edges in the mesh, and performs local remeshing to minimize interpolation errors. Edge bisection and contraction operations are also performed to adjust the mesh resolution around important features like fluidinterfaces, driven by a local length scale estimation algorithm that is efficient and easily parallelized. Flowfield interpolation after reconnection is achieved using a conservative, secondorder accurate remapping scheme that can be extended to arbitrary mesh pairs. To minimize the number of mesh reconnection operations, vertices in the mesh are also moved in a manner that optimizes the quality of cells at every time step, using a springanalogy based Laplacian smoother for surface meshes, and an optimizationbased smoothing approach for interior points. To facilitate the simulation of largescale problems, all smoothing and reconnection algorithms in this work have been parallelized for shared and distributedmemory paradigms. This approach allows meshes to undergo very large deformations which are characteristic of multiphase flows, and the method is versatile enough to extend its applicability to a broad range of problems including errordriven mesh refinement, reciprocating machinery, fluidstructure interation, and wing flapping simulations.

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TwoDimensional Anisotropic Cartesian Mesh Adaptation for the Compressible Euler EquationsKeats, William A. January 2004 (has links)
Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This document discusses a novel twodimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible flow. This technique, originally developed for laminar incompressible flow, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this document the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the objectoriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant.

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