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Discontinuous Galerkin Finite Element Method for The
DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR THE NONLINEAR HYPERBOLIC PROBLEMS WITH ENTROPY-BASED ARTIFICIAL VISCOSITY STABILIZATION A Dissertation by VALENTIN NIKOLAEVICH ZINGAN Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of Doctor of Philosophy May 2012 Major Subject: Nuclear Engineering DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR THE NONLINEAR HYPERBOLIC PROBLEMS WITH ENTROPY-BASED ARTIFICIAL VISCOSITY STABILIZATION A Dissertation by VALENTIN NIKOLAEVICH ZINGAN Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Approved by: Co-Chairs of Committee, Jim E. Morel Jean-Luc Guermond Committee Members, Marvin L. Adams Jean C. Ragusa Pavel V. Tsvetkov Head of Department, Yassin A. Hassan May 2012 Major Subject: Nuclear Engineering iii ABSTRACT Discontinuous Galerkin Finite Element Method for the Nonlinear Hyperbolic Problems with Entropy-Based Artificial Viscosity Stabilization. (May 2012 ) Valentin Nikolaevich Zingan, B.S.N.E., Moscow State Engineering Physics Institute (MEPhI); M.S.N.E., Moscow State Engineering Physics Institute (MEPhI) Co-Chairs of Committee: Dr. Jim E. Morel Dr. Jean-Luc Guermond This work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabi- lization built on an entropy-based artificial viscosity approximation. The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux. -
Numerical Solution for Two-Dimensional Flow Under Sluice Gates Using the Natural Element Method
1550 Numerical solution for two-dimensional flow under sluice gates using the natural element method Farhang Daneshmand, S.A. Samad Javanmard, Tahereh Liaghat, Mohammad Mohsen Moshksar, and Jan F. Adamowski Abstract: Fluid loads on a variety of hydraulic structures and the free surface profile of the flow are important for design purposes. This is a difficult task because the governing equations have nonlinear boundary conditions. The main objective of this paper is to develop a procedure based on the natural element method (NEM) for computation of free surface pro- files, velocity and pressure distributions, and flow rates for a two-dimensional gravity fluid flow under sluice gates. Natu- ral element method is a numerical technique in the field of computational mechanics and can be considered as a meshless method. In this analysis, the fluid was assumed to be inviscid and incompressible. The results obtained in the paper were confirmed via a hydraulic model test. Calculation results indicate a good agreement with previous flow solutions for the water surface profiles and pressure distributions throughout the flow domain and on the gate. Key words: free surface flow, meshless methods, meshfree methods, natural element method, sluice gate, hydraulic struc- tures. Re´sume´ : Les charges de fluides sur les structures hydrauliques et le profil de la surface libre de l’e´coulement sont impor- tants aux fins de conception. Cette conception est une taˆche difficile puisque les e´quations principales pre´sentent des conditions limites non line´aires. Cet article a comme objectif principal de de´velopper une proce´dure base´e sur la me´thode des e´le´ments naturels (NEM) pour calculer les profils de la surface libre, les distributions de vitesse et de pression ainsi que les de´bits pour un e´coulement gravitaire bidimensionnel sous les panneaux de vannes. -
UC Santa Cruz UC Santa Cruz Electronic Theses and Dissertations
UC Santa Cruz UC Santa Cruz Electronic Theses and Dissertations Title High-Order Methods for Computational Fluid Dynamics Using Gaussian Processes Permalink https://escholarship.org/uc/item/7j45v9cx Author Reyes, Adam Canady Publication Date 2019 License https://creativecommons.org/licenses/by/4.0/ 4.0 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA SANTA CRUZ HIGH-ORDER METHODS FOR COMPUTATIONAL FLUID DYNAMICS USING GAUSSIAN PROCESSES A dissertation submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in PHYSICS by Adam Reyes June 2019 The Dissertation of Adam Reyes is approved: Professor Dongwook Lee, Chair Professor Petros Tzeferacos Professor Onuttom Narayan Lori Kletzer Vice Provost and Dean of Graduate Studies Copyright © by Adam Reyes 2019 Table of Contents List of Figures v List of Tables xi Abstract xii Dedication xiv Acknowledgments xv 1 Introduction 1 1.1 Overview of this dissertation . .3 2 Discretizing Hyperbolic Conservation Laws 4 2.1 Hyperbolic Conservation Laws . .5 2.1.1 Nonlinear Systems . .6 2.2 Time Integration . .8 2.2.1 Runge-Kutta Methods . .9 2.2.2 Predictor-Corrector Methods . 10 2.3 Finite Volume Methods . 11 2.3.1 The Riemann Problem . 12 2.3.2 High-Order FVM . 14 2.4 Finite Difference Methods . 16 2.5 Conclusion . 20 3 High-Order Interpolation/Reconstruction for FDM and FVM 22 3.1 Total Variation Diminishing Methods . 24 3.2 Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Methods . 27 3.2.1 WENO . 30 iii 4 Gaussian Processes for CFD 34 4.1 Gaussian Processes . -
Program Booklet
DD23 International Conference on Domain Decomposition Methods 23rd International Conference on Domain Decomposition Methods http://dd23.kaist.ac.kr July 6-10, 2015 International Convention Center Jeju (ICC-Jeju) Jeju Island, Korea Sponsors Supporter Maps around the ICC Jeju * Banquet at Cao Cao (Wednesday, July 8th 2015, 19:00 – 20:50) Block Schedule Sunday Monday Tuesday Wednesday Thursday Friday July 05 July 06 July 07 July 08 July 09 July 10 (Day 1) (Day 2) (Day 3) (Day 4) (Day 5) Opening Clark 08:30 - 09:00 Ceremony Dohrmann Panayot (08:30 - 09:15) 09:00 - 09:30 Jysoo Lee Felix Kwok Vassilevski (09:00 - 09:45) (09:00 - 09:45) Nicole Spillane Parallel Sessions VIII (09:00 - 09:45) 09:30 - 10:00 (09:15 - 10:00) (09:00 – 10:40) 10:00 - 10:30 MS12, CT-7 10:30 - 11:00 Parallel Sessions I (10:15 – 11:55) Parallel Sessions III Parallel Sessions V (10:15 – 11:55) (10:15 – 11:55) 11:00 - 11:30 MS3-1, MS4-1, MS5-1, CT-3 MS6, CT-5 Frédéric Nataf CT-1 (11:10 - 11:55) 11:30 - 12:00 12:00 - 12:30 Closing Ceremony 12:30 - 13:00 Lunch Lunch Lunch (11:55 - 14:00) (11:55 - 14:00) (11:55 - 14:00) Lunch 13:00 - 13:30 (12:10 - 14:00) Social 13:30 – 14:00 Program 14:00 - 14:30 Yuri Bazilevs Sang Joon Shin (14:00 - 14:45) Parallel Sessions IV (14:00 - 14:45) (14:00 – 15:40) 14:30 - 15:00 Andrew Wathen MS5-2, MS7-1, Parallel Sessions VI 15:00 - 15:30 (14:45 - 15:30) CT-4 (14:50 – 16:30) 15:30 - 16:00 MS7-2, MS11-1,MS14 16:00 - 16:30 Parallel Sessions II (16:00 – 17:40) 16:30 - 17:00 Lori Badea (16:10 - 16:55) MS3-2, MS4-2, 17:00 - 17:30 CT-2 Parallel SessionsVII Luca F. -
BOOK of ABSTRACTS Conferências 5: Book of Abstracts 15/05/2018, 08:15
4th International Conference on Mechanics of Composites 9-12 July 2018 Universidad Carlos III de Madrid, Spain Chairs: A. J. M. Ferreira (Univ. Porto, Portugal), Carlos Santiuste (Univ. Carlos III, Spain) BOOK OF ABSTRACTS Conferências 5: Book of Abstracts 15/05/2018, 08:15 Book of Abstracts 14470 | NUMERICAL MODELLING OF SOFT ARMOUR PANELS UNDER HIGH-VELOCITY IMPACTS (Composite Structures) Ester Jalón ([email protected]), Department of Continuum Mechanics and Structural Analysis, Universidad Carlos III de Madrid, Spain Marcos Rodriguez , Department of Mechanical Engineering, Universidad Carlos III de Madrid, Spain José Antonio Loya , Department of Continuum Mechanics and Structural Analysis, Universidad Carlos III de Madrid, Spain Carlos Santiuste , Department of Continuum Mechanics and Structural Analysis, Universidad Carlos III de Madrid, Spain Nowadays, the role of personal protection is crucial in order to minimize the morbidity and mortality from ballistic injuries. The aim of these research is to investigate the behavior of UHMWPE fibre under high-velocity impact. There are two different UHMWPE packages: ‘soft’ ballistics packages (SB) and rigid ‘hard’ ballistics packages (SB). UHMWPE UD has not been sufficiently analyzed since new SB layers have been manufactured. This work, compares the impact behavior of different UHMWPE composites using spherical projectiles. Firstly, the parameter affecting the ballistic capacity are determined in order to define an optimal configuration to fulfill the requirements of manufactured. Then, the experimental test are conducted on different single SB sheets under spherical projectiles. Finally, the FEM model is validated with experimental test on multilayer specimens of the different UD materials considered. A FEM model is developed to predict the response of UHMWPE sheets under ballistic impact and calibrated with the previous experimental test. -
A Numerical Formulation and Algorithm for Limit and Shakedown Analysis Of
A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures Heng Peng1, Yinghua Liu1,* and Haofeng Chen2 1Department of Engineering Mechanics, AML, Tsinghua University, Beijing 100084, People’s Republic of China 2Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK *Corresponding author: [email protected] Abstract In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm. Keywords Direct method; Shakedown analysis; Stress compensation method; Large-scale; Elastoplastic structures 1 Introduction In many fields of technology, such as petrochemical, civil, mechanical and space engineering, structures are usually subjected to variable repeated loading. The computation of the load-carrying capability of those structures beyond the elastic limit is an important but 1 difficult task in structural design and integrity assessment. -
Numerical Modeling of Metal Cutting Processes Using the Particle Finite Element Method
Numerical modeling of metal cutting processes using the Particle Finite Element Method by Juan Manuel Rodriguez Prieto Advisors Juan Carlos Cante Terán Xavier Oliver Olivella Barcelona, October 2013 1 Abstract Metal cutting or machining is a process in which a thin layer or metal, the chip, is removed by a wedge-shaped tool from a large body. Metal cutting processes are present in big industries (automotive, aerospace, home appliance, etc.) that manufacture big products, but also high tech industries where small piece but high precision is needed. The importance of machining is such that, it is the most common manufacturing processes for producing parts and obtaining specified geometrical dimensions and surface finish, its cost represent 15% of the value of all manufactured products in all industrialized countries. Cutting is a complex physical phenomena in which friction, adiabatic shear bands, excessive heating, large strains and high rate strains are present. Tool geometry, rake angle and cutting speed play an important role in chip morphology, cutting forces, energy consumption and tool wear. The study of metal cutting is difficult from an experimental point of view, because of the high speed at which it takes place under industrial machining conditions (experiments are difficult to carry out), the small scale of the phenomena which are to be observed, the continuous development of tool and workpiece materials and the continuous development of tool geometries, among others reasons. Simulation of machining processes in which the workpiece material is highly deformed on metal cutting is a major challenge of the finite element method (FEM). The principal problem in using a conventional FE model with langrangian mesh are mesh distortion in the high deformation. -
High-Order Simulation of Polymorphic Crystallization Using Weighted Essentially Nonoscillatory Methods
High-Order Simulation of Polymorphic Crystallization Using Weighted Essentially Nonoscillatory Methods Martin Wijaya Hermanto Dept. of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117576 Richard D. Braatz Dept. of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, IL 61801 Min-Sen Chiu Dept. of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117576 DOI 10.1002/aic.11644 Published online November 21, 2008 in Wiley InterScience (www.interscience.wiley.com). Most pharmaceutical manufacturing processes include a series of crystallization processes to increase purity with the last crystallization used to produce crystals of desired size, shape, and crystal form. The fact that different crystal forms (known as polymorphs) can have vastly different characteristics has motivated efforts to under- stand, simulate, and control polymorphic crystallization processes. This article pro- poses the use of weighted essentially nonoscillatory (WENO) methods for the numeri- cal simulation of population balance models (PBMs) for crystallization processes, which provide much higher order accuracy than previously considered methods for simulating PBMs, and also excellent accuracy for sharp or discontinuous distributions. Three different WENO methods are shown to provide substantial reductions in numeri- cal diffusion or dispersion compared with the other finite difference and finite volume methods described in the literature for solving PBMs, in an application to the polymorphic crystallization of L-glutamic acid. Ó 2008 American Institute of Chemical Engineers AIChE J, 55: 122–131, 2009 Keywords: pharmaceutical crystallization, polymorphism, hyperbolic partial differential equation, weighted essentially nonoscillatory, high resolution, finite difference Introduction motivated by patent, operability, profitability, regulatory, and 1–3 Most manufacturing processes include a series of crystalli- scientific considerations. -
Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists
P. E. Vincent and A. Jameson Unstructured High-Order Methods Math. Model. Nat. Phenom. Vol. 6, No. 3, 2011, pp.97-140 DOI: 10.1051/mmnp/20116305 Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists P. E. Vincent∗ and A. Jameson Department of Aeronautics and Astronautics, Stanford University, Stanford, California, USA Abstract. Theoretical studies and numerical experiments suggest that unstructured high-order methods can provide solutions to otherwise intractable fluid flow problems within complex ge- ometries. However, it remains the case that existing high-order schemes are generally less robust and more complex to implement than their low-order counterparts. These issues, in conjunction with difficulties generating high-order meshes, have limited the adoption of high-order techniques in both academia (where the use of low-order schemes remains widespread) and industry (where the use of low-order schemes is ubiquitous). In this short review, issues that have hitherto pre- vented the use of high-order methods amongst a non-specialist community are identified, and cur- rent efforts to overcome these issues are discussed. Attention is focused on four areas, namely the generation of unstructured high-order meshes, the development of simple and efficient time integration schemes, the development of robust and accurate shock capturing algorithms, and fi- nally the development of high-order methods that are intuitive and simple to implement. With regards to this final area, particular attention is focused on the recently proposed flux reconstruc- tion approach, which allows various well known high-order schemes (such as nodal discontinuous Galerkin methods and spectral difference methods) to be cast within a single unifying framework. -
Program PMAA14.Indd
Università Facoltà Institute of della di scienze Computational Svizzera informatiche Science italiana ICS PMAA14 8th International Workshop on Parallel Matrix Algorithms and Applications Università della Svizzera italiana, Switzerland pmaa14.ics.usi.ch PMAA14 8th International Workshop on Parallel Matrix Algorithms and Applications Università della Svizzera italiana, Switzerland pmaa14.ics.usi.ch Welcome Dear participants, Welcome to the 8th International Workshop on Parallel Matrix Algorithms and Applications (PMAA14). The workshop Co-chairs are happy to host this international conference here at the Università della Svizzera italiana, in the Italian-speaking part of Switzerland. The Institute of Computational Science (ICS) of the Faculty of Informatics at the Università della Svizzera italiana (USI) is delighted to host the eigth edition of this workshop series. The ICS was founded in 2009 towards realizing the vision of USI to become a new sci- entifi c and educational node for computational science in Switzerland. It has since then grown into a place with strong competences in mathematical modeling, numerical simulation, and high-performance computing. Research areas range from high-performance numerical simulation in science, medicine, and engineering, through computational time series analysis and computational shape analysis, to computational cardiology and the multi-scale simulation of physical and biological systems. The PMAA workshop series aims to be a forum for an exchange of ideas, insights and experiences in different areas of parallel com- puting in which matrix algorithms are employed. The workshop will bring together experts and practitioners from diverse disciplines with a common interest in matrix computation. The PMAA14 programme consists of 27 regular sessions, 4 plenary talks and around 112 presentations. -
A Stabilized and Coupled Meshfree/Meshbased Method for Fluid-Structure Interaction Problems
Braunschweiger Schriften zur Mechanik Nr. 59-2005 A Stabilized and Coupled Meshfree/Meshbased Method for Fluid-Structure Interaction Problems von Thomas-Peter Fries aus Lubeck¨ Herausgegeben vom Institut fur¨ Angewandte Mechanik der Technischen Universit¨at Braunschweig Schriftleiter: Prof. H. Antes Institut fur¨ Angewandte Mechanik Postfach 3329 38023 Braunschweig ISBN 3-920395-58-1 Vom Fachbereich Bauingenieurwesen der Technischen Universit¨at Carolo-Wilhelmina zu Braunschweig zur Erlangung des Grades eines Doktor-Ingenieurs (Dr.-Ing.) genehmigte Dissertation From the Faculty of Civil Engineering at the Technische Universit¨at Carolo-Wilhelmina zu Braunschweig in Brunswick, Germany, approved dissertation Eingereicht am: 10.05.2005 Mundliche¨ Prufung¨ am: 21.07.2005 Berichterstatter: Prof. H.G. Matthies, Inst. fur¨ Wissenschaftliches Rechnen Prof. M. Krafczyk, Inst. fur¨ Computeranwendungen im Bauingenieurwesen c Copyright 2005 Thomas-Peter Fries, Brunswick, Germany Abstract A method is presented which combines features of meshfree and meshbased methods in order to enable the simulation of complex flow problems involving large deformations of the domain or moving and rotating objects. Conventional meshbased methods like the finite element method have matured as standard tools for the simulation of fluid and structure problems. They offer efficient and reliable approximations, provided that a conforming mesh with sufficient quality can be maintained throughout the simulation. This, however, may not be guaranteed for complex fluid and fluid-structure interaction problems. Meshfree methods on the other hand approximate partial differential equations based on a set of nodes without the need for an additional mesh. Therefore, these methods are frequently used for problems where suitable meshes are prohibitively expensive to construct and maintain. -
The Optimal Transportation Meshfree Method for General Fluid Flows and Strongly Coupled Fluid-Structure Interaction Problems
The Optimal Transportation Meshfree Method for General Fluid Flows and Strongly Coupled Fluid-Structure Interaction Problems Thesis by Feras Habbal In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2009 (Defended May 5, 2009) ii c 2009 Feras Habbal All Rights Reserved iii "The way to get started is to quit talking and begin doing." -Walt Disney iv Acknowledgments There are many people who, over the years, have provided me invaluable support and friendship. At Caltech, I would like to thank my advisor Michael Ortiz as well as Professors Ravichandran and Phillips for their support and guidance. Furthermore, the staff at Caltech has been wonderful in their support and assistance. Also, I would like to genuinely thank my mentor at JPL, Claus Hoff, for his support and guidance. During my time at Caltech, I have had the distinct pleasure of working with a number of individuals who ended up being friends beyond school-related tasks, including the members of the group: Lenny, Julian, Bo, Ben, Luigi, Marcial, Gabriela, Celia, and Daniel, among other. I would like to thank my Caltech DJ friends Bodhi, Juanse, Patrick, Signe, and Joe for the Lazy Sundays sessions. Also, I would like to thank my officemates and friends, Mike and Francesco. Outside of Caltech, I would like to thank the Mammoth crew including Jasmine, Charles, Steve, Chris, Marcie, and Alice for their friendship and lasting memories of powder days on the steeps. Also, I would like to thank Alan for his true friendship and for making me relearn everything I thought I knew.