Implementation and Validation of Semi-Implicit WENO Schemes Using Openfoam®
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Conservative High Order Semi-Lagrangian Finite Difference WENO Methods for Advection in Incompressible Flow Jing-Mei Qiu1 and Ch
Conservative high order semi-Lagrangian finite difference WENO methods for advection in incompressible flow Jing-Mei Qiu1 and Chi-Wang Shu 2 Abstract In this paper, we propose a semi-Lagrangian finite difference formulation for approximat- ing conservative form of advection equations with general variable coefficients. Compared with the traditional semi-Lagrangian finite difference schemes [4, 21], which approximate the advective form of the equation via direct characteristics tracing, the scheme proposed in this paper approximates the conservative form of the equation. This essential difference makes the proposed scheme naturally conservative for equations with general variable coef- ficients. The proposed conservative semi-Lagrangian finite difference framework is coupled with high order essentially non-oscillatory (ENO) or weighted ENO (WENO) reconstructions to achieve high order accuracy in smooth parts of the solution and to capture sharp inter- faces without introducing spurious oscillations. The scheme is extended to high dimensional problems by Strang splitting. The performance of the proposed schemes is demonstrated by linear advection, rigid body rotation and swirling deformation. As the information is propa- gating along characteristics, the proposed scheme does not have CFL time step restriction of the Eulerian method, allowing for a more efficient numerical realization for many application problems. Keywords: advection in incompressible flow; conservative scheme; semi-Lagrangian meth- ods; WENO reconstruction. 1Department of Mathematical and Computer Science, Colorado School of Mines, Golden, 80401. E-mail: [email protected]. Research supported by NSF grant number 0914852 and Air Force Office of Scientific Research grant number FA9550-09-1-0344. 2Division of Applied Mathematics, Brown University, Providence, 02912. -
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. -
PROGRAM and ABSTRACTS
LASERENANUM E´ R I C A II Octavo Encuentro de Analisis´ Numerico´ de Ecuaciones Diferenciales Parciales Departamento de Matem´aticas,Universidad de La Serena La Serena, Chile, Enero 14 - 16, 2015 PROGRAM and ABSTRACTS Contents 1 Introduction 2 2 Wednesday, January 14 3 3 Thursday, January 15 4 4 Friday, January 16 5 5 Abstracts 6 1 1 Introduction The Octavo Encuentro de An´alisisNum´ericode Ecuaciones Diferenciales Parciales has been organized in sequential talks of 45 and 30 minutes length (40 and 25 minutes of presentation, respectively, and 5 minutes for questions and comments). All the talks will be given at Salon´ Multiuso, CETECFI (3th floor), Facultad de Ingenier´ıa, Universi- dad de la Serena. In the following pages we describe the corresponding program. In case of a multi-authored contribution, the speaker is underlined. The organizers acknowledge financial support by: • CONICYT-Chile through Project Anillo ACT 1118 ANANUM, • Departamento de Matem´aticas, Universidad de La Serena, • Centro de Modelamiento Matem´atico(CMM), Universidad de Chile, and • Centro de Investigaci´onen Ingenier´ıaMatem´atica(CI2MA), Universidad de Concepci´on. In addition, we express our recognition and gratitude to all speakers for making La Serena Num´ericaII possible. Organizing Committee Raimund B¨urger Gabriel N. Gatica Ricardo Oyarz´ua H´ectorTorres La Serena, January 2015 2 2 Wednesday, January 14 8.30-9.15 REGISTRATION 9.15-9.30 WELCOME SPEECH [Chairman: N. HEUER] 9.30-10.15 Alexandre Ern, Martin Vohral´ık: Polynomial-degree-robust a posteri- ori estimates in a unified setting. 10.15-10.45 Dante Kalise: High-order semi-Lagrangian schemes for static Hamilton- Jacobi-Bellman equations. -
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 . -
AN13 and CT13 Abstracts
AN13 and CT13 Abstracts Abstracts are printed as submitted by the authors. Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference web: www.siam.org/meetings/ Membership and Customer Service: 800-447-7426 (US & Canada) or +1-215-382-9800 (worldwide) 2 2013 SIAM Annual Meeting • SIAM Conference on Control & Its Applications Table of Contents Annual Meeting (AN13) Abstracts ...............................................3 Control & Its Applications (CT13) .............................................127 SIAM Presents Since 2008, SIAM has recorded many Invited Lectures, Prize Lectures, and selected Minisymposia from various conferences. These are available by visiting SIAM Presents (http://www.siam.org/meetings/presents.php). 2013 SIAM Annual Meeting • SIAM Conference on Control & Its Applications 3 AN13 Abstracts 4 AN13 Abstracts IC1 system including cars, buses, pedestrians, ants and molecu- Social Networks as Information Filters lar motors, which are considered as ”self-driven particles”. We recently call this interdisciplinary research on jamming Social networks, especially online social networks, are of self-driven particles as ”jamology”. This is based on driven by information sharing. But just how much informa- mathematical physics, and and includes engineering appli- tion sharing is influenced by social networks? A large-scale cations as well. In the talk, starting from the backgroud experiment measured the effect of the social network on the of this research, simple mathematical models, such as the quantity and diversity of information being shared within asymmetric simple exclusion process and the Burgers equa- Facebook. While strong ties were found to be individu- tion, are introduced as basis of all kinds of traffic flow. -
AN17-CT17-GD17 Abstracts
AN17-CT17-GD17 Abstracts Abstracts are printed as submitted by the authors. SIAM 2017 Events Mobile App Scan the QR code with any QR reader and download the TripBuilder EventMobile™ app to your iPhone, iPad, iTouch or Android mobile device. You can also visit www.tripbuildermedia.com/apps/siamevents Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference Web: www.siam.org/meetings/ Membership and Customer Service: (800) 447-7426 (USA & Canada) or +1-215-382-9800 (worldwide) www.siam.org/meetings/ 2 2017 SIAM Annual Meeting Table of Contents AN17 Annual Meeting Abstracts ................................................3 CT17 Abstracts .........................................................................130 GD17 Abstracts .........................................................................183 SIAM Presents Since 2008, SIAM has recorded many Invited Lectures, Prize Lectures, and selected Minisymposia from various conferences. These are available by visiting SIAM Presents (http://www.siam.org/meetings/presents.php). 2017 SIAM Annual Meeting AN17 Abstracts 4 AN17 Abstracts IP1 for mapping services this is obtained from mobile phones, Genetic Consequences of Range Expansion Under while for ambulance fleets it is obtained from automatic ve- Climate Change hicle location devices. We demonstrate greatly improved accuracy relative to a system used in Bing Maps, and show Range expansion is a crucial population response to cli- the impact of our methods for improving ambulance fleet mate change. Genetic consequences are coupled to ecolog- management decisions. ical dynamics that, in turn, are driven by shifting climate conditions. We model a population with a reactiondiffu- Dawn Woodard sion system, coupled to a heterogeneous environment that Uber, USA shifts with time due to climate change. -
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. -
4 AN10 Abstracts
4 AN10 Abstracts IC1 IC4 On Dispersive Equations and Their Importance in Kinematics and Numerical Algebraic Geometry Mathematics Kinematics underlies applications ranging from the design Dispersive equations, like the Schr¨odinger equation for ex- and control of mechanical devices, especially robots, to the ample, have been used to model several wave phenom- biomechanical modelling of human motion. The major- ena with the distinct property that if no boundary con- ity of kinematic problems can be formulated as systems ditions are imposed then in time the wave spreads out of polynomial equations to be solved and so fall within spatially. In the last fifteen years this field has seen an the domain of algebraic geometry. While symbolic meth- incredible amount of new and sophisticated results proved ods from computer algebra have a role to play, numerical with the aid of mathematics coming from different fields: methods such as polynomial continuation that make strong Fourier analysis, differential and symplectic geometry, an- use of algebraic-geometric properties offer advantages in alytic number theory, and now also probability and a bit of efficiency and parallelizability. Although these methods, dynamical systems. In this talk it is my intention to present collectively called Numerical Algebraic Geometry, are ap- few simple, but still representative examples in which one plicable wherever polynomials arise, e.g., chemistry, biol- can see how these different kinds of mathematics are used ogy, statistics, and economics, this talk will concentrate on in this context. applications in mechanical engineering. A brief review of the main algorithms of the field will indicate their broad Gigliola Staffilani applicability. -
High Order ADER Schemes and GLM Curl Cleaning for a First Order Hyperbolic Formulation of Compressible Flow with Surface Tension
High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension Simone Chiocchetti∗a, Ilya Peshkova, Sergey Gavrilyukb, Michael Dumbsera aLaboratory of Applied Mathematics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento, Italy bIUSTI UMR 7343-CNRS, D´epartement de M´ecanique, Aix-Marseille Universit´e,5 rue Enrico Fermi, 13453 Marseille, France Abstract In this work, we introduce two novel reformulations of the weakly hyperbolic model for two-phase flow with surface tension, recently forwarded by Schmidmayer et al. In the model, the tracking of phase boundaries is achieved by using a vector interface field, rather than a scalar tracer, so that the surface-force stress tensor can be expressed directly as an algebraic function of the state variables, without requiring the computation of gradients of the scalar tracer. An interesting and important feature of the model is that this interface field obeys a curl involution constraint, that is, the vector field is required to be curl-free at all times. The proposed modifications are intended to restore the strong hyperbolicity of the model, and are closely related to divergence-preserving numerical approaches developed in the field of numerical magnetohydrody- namics (MHD). The first strategy is based on the theory of Symmetric Hyperbolic and Thermodynamically Compatible (SHTC) systems forwarded by Godunov in the 60s and 70s and yields a modified system of governing equations which includes some symmetrisation terms, in analogy to the approach adopted later by Powell et al in the 90s for the ideal MHD equations. -
Final Program
Final Program The SIAM Conference on the Life Sciences is sponsored by the SIAM Activity Group on Life Sciences (SIAG/LS) The SIAM Activity Group on the Life Sciences was established to foster the application of mathematics to the life sciences and research in mathematics that leads to new methods and techniques useful in the life sciences. The life sciences have become quantitative as new technologies facilitate collection and analysis of vast amounts of data ranging from complete genomic sequences of organisms to satellite imagery of forest landscapes on continental scales. Computers enable the study of complex models of biological processes. The activity group brings together researchers who seek to develop and apply mathematical and computational methods in all areas of the life sciences. It provides a forum that cuts across disciplines to catalyze mathematical research relevant to the life sciences and rapid diffusion of advances in mathematical and computational methods. AN16/LS16 Mobile App Scan the QR code with any QR reader and download the TripBulder EventMobileTM app to your iPhone, iPad, iTouch, or Android devices. You can also visit www.tripbuildermedia.com/apps/siam2016events Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215- 386-7999 Conference E-mail: [email protected] Conference Web: www.siam.org/meetings/ Membership and Customer Service: (800) 447-7426 (US & Canada) or +1-215-382-9800 (worldwide) www.siam.org/meetings 2 2016 SIAM Annual Meeting General Information Table of Contents C. David Levermore SIAM Registration Desk University of Maryland, College Park, USA General Information ...............................2 The SIAM registration desk is located on Rachel Levy Exhibitor and Sponsor Information .6 the Concourse Level of the Westin Boston Harvey Mudd College, USA Waterfront. -
Deterministic Numerical Schemes for the Boltzmann Equation
Deterministic Numerical Schemes for the Boltzmann Equation by Akil Narayan and Andreas Klöckner <{anaray,kloeckner}@dam.brown.edu> Abstract This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping schemes to achieve the splitting as well as numerical methods for each part of the operator are reviewed, with an emphasis on clearly exposing the challenges posed by the equation as well as their resolution by various schemes. 1 Introduction The Boltzmann equation is an equation of statistical mechanics describing the evolution of a rarefied gas. In a fluid in continuum mechanics, all particles in a spatial volume element are approximated as • having the same velocity. In a rarefied gas in statistical mechanics, there is enough space that particles in one spatial volume • element may have different velocities. The equation itself is a nonlinear integro-differential equation which decribes the evolution of the density of particles in a monatomic rarefied gas. Let the density function be f( x, v, t) . The quantity f( x, v, t)dx dv represents the number of particles in the phase-space volume element dx dv at time t. Both x and 3 3 + v are three-dimensional independent variables, so the density function is a map f: R R R R 6 × × → 0 R 0, . The theory of kinetics and statistical mechanics gives rise to the laws which the density func- ∪ ∞ tion {f must} obey in the absence of external forces.