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Extended Hydrodynamics Using the Discontinuous-Galerkin Hancock Method

Extended Hydrodynamics Using the Discontinuous-Galerkin Hancock Method
Author: Willem Kaufmann
Publisher:
Total Pages:
Release: 2021
Genre:
ISBN:
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Moment methods derived from the kinetic theory of gases can be used for the prediction of continuum and non-equilibrium flows and offer numerical advantages over other methods, such as the Navier-Stokes model. Models developed in this fashion are described by first-order hyperbolic partial differential equations (PDEs) with stiff local relaxation source terms. The application of discontinuous-Galerkin (DG) methods for the solution of such models has many benefits. Of particular interest is the third-order accurate, coupled space-time discontinuous-Galerkin Hancock (DGH) method. This scheme is accurate, as well as highly efficient on large-scale distributed-memory computers. The current study outlines a general implementation of the DGH method used for the parallel solution of moment methods in one, two, and three dimensions on modern distributed clusters. An algorithm for adaptive mesh refinement (AMR) was developed alongside the implementation of the scheme, and is used to achieve even higher accuracy and efficiency. Many different first-order hyperbolic and hyperbolic-relaxation PDEs are solved to demonstrate the robustness of the scheme. First, a linear convection-relaxation equation is solved to verify the order of accuracy of the scheme in three dimensions. Next, some classical compressible Euler problems are solved in one, two, and three dimensions to demonstrate the scheme's ability to capture discontinuities and strong shocks, as well as the efficacy of the implemented AMR. A special case, Ringleb's flow, is also solved in two-dimensions to verify the order of accuracy of the scheme for non-linear PDEs on curved meshes. Following this, the shallow water equations are solved in two dimensions. Afterwards, the ten-moment (Gaussian) closure is applied to two-dimensional Stokes flow past a cylinder, showing the abilities of both the closure and scheme to accurately compute classical viscous solutions. Finally, the one-dimensional fourteen-moment closure is solved.

Modeling Shallow Water Flows Using the Discontinuous Galerkin Method

Modeling Shallow Water Flows Using the Discontinuous Galerkin Method
Author: Abdul A. Khan
Publisher: CRC Press
Total Pages: 218
Release: 2014-03-03
Genre: Science
ISBN: 1482226014
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Replacing the Traditional Physical Model Approach Computational models offer promise in improving the modeling of shallow water flows. As new techniques are considered, the process continues to change and evolve. Modeling Shallow Water Flows Using the Discontinuous Galerkin Method examines a technique that focuses on hyperbolic conservation laws and includes one-dimensional and two-dimensional shallow water flows and pollutant transports. Combines the Advantages of Finite Volume and Finite Element Methods This book explores the discontinuous Galerkin (DG) method, also known as the discontinuous finite element method, in depth. It introduces the DG method and its application to shallow water flows, as well as background information for implementing and applying this method for natural rivers. It considers dam-break problems, shock wave problems, and flows in different regimes (subcritical, supercritical, and transcritical). Readily Adaptable to the Real World While the DG method has been widely used in the fields of science and engineering, its use for hydraulics has so far been limited to simple cases. The book compares numerical results with laboratory experiments and field data, and includes a set of tests that can be used for a wide range of applications. Provides step-by-step implementation details Presents the different forms in which the shallow water flow equations can be written Places emphasis on the details and modifications required to apply the scheme to real-world flow problems This text enables readers to readily understand and develop an efficient computer simulation model that can be used to model flow, contaminant transport, and other aspects in rivers and coastal environments. It is an ideal resource for practicing environmental engineers and researchers in the area of computational hydraulics and fluid dynamics, and graduate students in computational hydraulics.

The Discontinuous Galerkin Method Applied on the Equations of Ideal Relativistic Hydrodynamics

The Discontinuous Galerkin Method Applied on the Equations of Ideal Relativistic Hydrodynamics
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Release: 2002
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To solve numerically the problems of ideal relativistic hydrodynamics we have developed a high-order accurate and time-explicite 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.

Computational Fluid Dynamics 2006

Computational Fluid Dynamics 2006
Author: Herman Deconinck
Publisher: Springer
Total Pages: 916
Release: 2016-04-01
Genre:
ISBN: 9783662500903
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ThisbookcontainstheproceedingsoftheFourthInternationalConference onComputationalFluidDynamics(ICCFD4), heldinGent, Belgiumfrom July10through16,2006. TheICCFDconferenceseriesisanoutcomeofthe mergeroftwoimportantstreamsofconferencesinComputationalFluid- namics: InternationalConferenceonNumericalMethodsinFluidDynamics, ICNMFD(since1996)andInternationalSymposiumonComputationalFluid Dynamics, ISCFD(since1985). In1998itwasdecidedtojointhetwoand ICCFD emerged as a biannual meeting, held in Kyoto in 2000, Sydney in 2002, Toronto in 2004 and Gent in 2006. Thus, the ICCFD series became theleadinginternationalconferenceseriesforscientists, mathematiciansand engineersinterestedinthecomputationof?uid?ow. The4theditionoftheconferencehasattracted200participantsfromall overtheworld;270abstractswerereceived, ofwhich135wereselectedina carefulpeerreviewprocessbytheexecutivecommittee(C. H. Bruneau, J. -J. Chattot, D. Kwak, N. Satofuka, D. W. Zingg, E. DickandH. Deconinck)for oralpresentationandafurther21forposterpresentation. Thepaperscontainedintheseproceedingsprovideanexcellentsnapshot of the ?eld of Computational Fluid Dynamics as of 2006. Invited keynote lecturesbyrenownedresearchersareincluded, withcontributionsinthe?eld ofdiscretizationschemes, high-endcomputingandengineeringchallenges, and two-phase?ow. Thesekeynotecontributionsarecomplementedby137regular papersonthemostdiverseaspectsofCFD: -Innovativealgorithmdevelopmentfor?owsimulation, optimisationandc- trol: higher-ordermethods(DG, FV, FEandRDmethods), iterativemethods andmultigrid, solutionadaptivemeshtechniques, errorestimationandc- trol, parallelalgorithms. -Innovativemodelingof?owphysicsintheareaofcompressibleandinc- pressible ?ows: hypersonic and reacting ?ows, two-phase ?ows, turbulence (LES, DES, DNS, andtransition), vortexdynamics, boundarylayerstability, multi-scalephysics, magnetohydrodynamics. Preface VII -advancedapplicationsusingtheabovementionedinnovativetechnology, and multidisciplinaryapplicationsincludingaero-elasticityandaero-acoustics. ThanksareduetooursponsorsNASA, theFWOResearchFoundation FlandersandtheEuropeanUnionthroughtheEUA4XMarieCurieproject. Inparticular, thegenerousgrantfromNASAisakeyfactorinthesuccessof thisconferenceseriesandthepublicationoftheseProceedings. Wealsowouldliketothankthesta?andPhDstudentsofthevonKarman InstituteandtheDepartmentof?ow, heatandcombustionmechanicsofthe University of Gent, for the help they provided toward the success of this conference. Sint-Genesius-Rode, Belgium HermanDeconinck vonKarmanInstituteforFluidDynamics Ghent, Belgium ErikDick GhentUniversity September2006 ConferenceChair Contents PartIInvitedSpeakers Twonewtechniquesforgeneratingexactlyincompressible approximatevelocities BernardoCockburn. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 RoleofHigh-EndComputinginMeetingNASA'sScience andEngineeringChallenges RupakBiswas, EugeneL. Tu, WilliamR. VanDalsem. . . . . . . . . . . . . . . . 14 RecentAdvancesofMulti-phaseFlowComputationwiththe AdaptiveSoroban-gridCubicInterpolatedPropagation(CIP) Method TakashiYabe, YouichiOgata, KenjiTakizawa. . . . . . . . . . . . . . . . . . . . . . . 29 PartIISchemes OntheComputationofSteady-StateCompressibleFlows UsingaDGMethod HongLuo, JosephD. Baum, RainaldL]ohner. . . . . . . . . . . . . . . . . . . . . . . . 47 Space-TimeDiscontinuousGalerkinMethodforLarge AmplitudeNonlinearWaterWaves YanXu, JaapJ. W. vanderVegt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 AdiscontinuousGalerkinmethodwi

Elements of Continuum Mechanics and Conservation Laws

Elements of Continuum Mechanics and Conservation Laws
Author: S.K. Godunov
Publisher: Springer Science & Business Media
Total Pages: 263
Release: 2013-03-09
Genre: Computers
ISBN: 1475751176
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Elements of Continuum Mechanics and Conservation Laws presents a systematization of different models in mathematical physics, a study of the structure of conservation laws, thermodynamical identities, and connection with criteria for well-posedness of the corresponding mathematical problems. The theory presented in this book stems from research carried out by the authors concerning the formulations of differential equations describing explosive deformations of metals. In such processes, elasticity equations are used in some zones, whereas hydrodynamics equations are stated in other zones. Plastic deformations appear in transition zones, which leads to residual stresses. The suggested model contains some relaxation terms which simulate these plastic deformations. Certain laws of thermodynamics are used in order to describe and study differential equations simulating the physical processes. This leads to the special formulation of differential equations using generalized thermodynamical potentials.

Riemann Solvers and Numerical Methods for Fluid Dynamics

Riemann Solvers and Numerical Methods for Fluid Dynamics
Author: Eleuterio F. Toro
Publisher: Springer Science & Business Media
Total Pages: 635
Release: 2013-04-17
Genre: Technology & Engineering
ISBN: 366203915X
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High resolution upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows.