Efficient High-order Accurate Unstructured Finite-volume Algorithms for Viscous and Inviscid Compressible Flows PDF Download
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Languages : en
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High-order accurate methods have the potential to dramatically reduce the computational time needed for aerodynamics simulations. This thesis studies the discretization and efficient convergence to steady state of the high-order accurate finite-volume method applied to the simplified problem of inviscid and laminar viscous two-dimensional flow equations. Each of the three manuscript chapters addresses a specific problem or limitation previously experienced with these schemes. The first manuscript addresses the absence of a method to maintain monotonicity of the solution at discontinuities while maintaining high-order accuracy in smooth regions. To resolve this, a slope limiter is carefully developed which meets these requirements while also maintaining the good convergence properties and computational efficiency of the least-squares reconstruction scheme. The second manuscript addresses the relatively poor convergence properties of Newton-GMRES methods applied to high-order accurate schemes. The globalization of the Newton method is improved through the use of an adaptive local timestep and of a line search algorithm. The poor convergence of the linear solver is improved through the efficient assembly of the exact flux Jacobian for use in preconditioning and to eliminate the additional residual evaluations needed by a matrix-free method. The third manuscript extends the discretization method to the viscous fluxes and boundary conditions. The discretization is demonstrated to achieve the expected order of accuracy. The fourth-order scheme is also shown to be more computationally efficient than the second-order scheme at achieving grid-converged values of drag for two-dimensional laminar flow over an airfoil.
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Languages : en
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Book Description
High-order accurate methods have the potential to dramatically reduce the computational time needed for aerodynamics simulations. This thesis studies the discretization and efficient convergence to steady state of the high-order accurate finite-volume method applied to the simplified problem of inviscid and laminar viscous two-dimensional flow equations. Each of the three manuscript chapters addresses a specific problem or limitation previously experienced with these schemes. The first manuscript addresses the absence of a method to maintain monotonicity of the solution at discontinuities while maintaining high-order accuracy in smooth regions. To resolve this, a slope limiter is carefully developed which meets these requirements while also maintaining the good convergence properties and computational efficiency of the least-squares reconstruction scheme. The second manuscript addresses the relatively poor convergence properties of Newton-GMRES methods applied to high-order accurate schemes. The globalization of the Newton method is improved through the use of an adaptive local timestep and of a line search algorithm. The poor convergence of the linear solver is improved through the efficient assembly of the exact flux Jacobian for use in preconditioning and to eliminate the additional residual evaluations needed by a matrix-free method. The third manuscript extends the discretization method to the viscous fluxes and boundary conditions. The discretization is demonstrated to achieve the expected order of accuracy. The fourth-order scheme is also shown to be more computationally efficient than the second-order scheme at achieving grid-converged values of drag for two-dimensional laminar flow over an airfoil.
Author: Herman Deconinck
Publisher: Springer
ISBN: 9783662500903
Category :
Languages : en
Pages : 916
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Book Description
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
Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
ISBN: 9781793951823
Category : Science
Languages : en
Pages : 28
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A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods. Loh, Ching Y. and Jorgenson, Philip C. E. Glenn Research Center NAS3-0372; WBS 561581.02.08.03.18.02
Author: Wanai Li
Publisher: Springer
ISBN: 3662434326
Category : Technology & Engineering
Languages : en
Pages : 158
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Book Description
This thesis focuses on the development of high-order finite volume methods and discontinuous Galerkin methods, and presents possible solutions to a number of important and common problems encountered in high-order methods, such as the shock-capturing strategy and curved boundary treatment, then applies these methods to solve compressible flows.
Author: Xueshang Feng
Publisher: Springer
ISBN: 9811390819
Category : Science
Languages : en
Pages : 772
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Book Description
The book covers intimately all the topics necessary for the development of a robust magnetohydrodynamic (MHD) code within the framework of the cell-centered finite volume method (FVM) and its applications in space weather study. First, it presents a brief review of existing MHD models in studying solar corona and the heliosphere. Then it introduces the cell-centered FVM in three-dimensional computational domain. Finally, the book presents some applications of FVM to the MHD codes on spherical coordinates in various research fields of space weather, focusing on the development of the 3D Solar-InterPlanetary space-time Conservation Element and Solution Element (SIP-CESE) MHD model and its applications to space weather studies in various aspects. The book is written for senior undergraduates, graduate students, lecturers, engineers and researchers in solar-terrestrial physics, space weather theory, modeling, and prediction, computational fluid dynamics, and MHD simulations. It helps readers to fully understand and implement a robust and versatile MHD code based on the cell-centered FVM.
Author: Z. J. Wang
Publisher: World Scientific
ISBN: 9814313181
Category : Science
Languages : en
Pages : 471
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Book Description
This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, residual distribution, finite volume, differential quadrature, spectral volume, spectral difference, PNPM, and correction procedure via reconstruction methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an understanding of the state of the art and remaining challenges in high-order CFD methods.
Author: Yun Zheng
Publisher:
ISBN:
Category :
Languages : en
Pages :
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New 2D and 3D unstructured-grid based flow solvers have been developed for simulating steady compressible flows for aerodynamic applications. The codes employ the full compressible Euler/Navier-Stokes equations. The Spalart-Al Imaras one equation turbulence model is used to model turbulence effects of flows. The spatial discretisation has been obtained using a cell-centred finite volume scheme on unstructured-grids, consisting of triangles in 2D and of tetrahedral and prismatic elements in 3D. The temporal discretisation has been obtained with an explicit multistage Runge-Kutta scheme. An "inflation" mesh generation technique is introduced to effectively reduce the difficulty in generating highly stretched 2D/3D viscous grids in regions near solid surfaces. The explicit flow method is accelerated by the use of a multigrid method with consideration of the high grid aspect ratio in viscous flow simulations. A solution mesh adaptation technique is incorporated to improve the overall accuracy of the 2D inviscid and viscous flow solutions. The 3D flow solvers are parallelised in a MIMD fashion aimed at a PC cluster system to reduce the computing time for aerodynamic applications. The numerical methods are first applied to several 2D inviscid flow cases, including subsonic flow in a bump channel, transonic flow around a NACA0012 airfoil and transonic flow around the RAE 2822 airfoil to validate the numerical algorithms. The rest of the 2D case studies concentrate on viscous flow simulations including laminar/turbulent flow over a flat plate, transonic turbulent flow over the RAE 2822 airfoil, and low speed turbulent flows in a turbine cascade with massive separations. The results are compared to experimental data to assess the accuracy of the method. The over resolved problem with mesh adaptation on viscous flow simulations is addressed with a two phase mesh reconstruction procedure. The solution convergence rate with the aspect ratio adaptive multigrid method and the direct connectivity based multigrid is assessed in several viscous turbulent flow simulations. Several 3D test cases are presented to validate the numerical algorithms for solving Euler/Navier-Stokes equations. Inviscid flow around the M6 wing airfoil is simulated on the tetrahedron based 3D flow solver with an upwind scheme and spatial second order finite volume method. The efficiency of the multigrid for inviscid flow simulations is examined. The efficiency of the parallelised 3D flow solver and the PC cluster system is assessed with simulations of the same case with different partitioning schemes. The present parallelised 3D flow solvers on the PC cluster system show satisfactory parallel computing performance. Turbulent flows over a flat plate are simulated with the tetrahedron based and prismatic based flow solver to validate the viscous term treatment. Next, simulation of turbulent flow over the M6 wing is carried out with the parallelised 3D flow solvers to demonstrate the overall accuracy of the algorithms and the efficiency of the multigrid method. The results show very good agreement with experimental data. A highly stretched and well-formed computational grid near the solid wall and wake regions is generated with the "inflation" method. The aspect ratio adaptive multigrid displayed a good acceleration rate. Finally, low speed flow around the NREL Phase 11 Wind turbine is simulated and the results are compared to the experimental data.
Author: Miloslav Feistauer
Publisher: Oxford University Press, USA
ISBN: 9780198505884
Category : Computers
Languages : en
Pages : 560
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Book Description
This book is concerned with mathematical and numerical methods for compressible flow. It aims to provide the reader with a sufficiently detailed and extensive, mathematically precise, but comprehensible guide, through a wide spectrum of mathematical and computational methods used in Computational Fluid Dynamics (CFD) for the numerical simulation of compressible flow. Up-to-date techniques applied in the numerical solution of inviscid as well as viscous compressible flow on unstructured meshes are explained, thus allowing the simulation of complex three-dimensional technically relevant problems. Among some of the methods addressed are finite volume methods using approximate Riemann solvers, finite element techniques, such as the streamline diffusion and the discontinuous Galerkin methods, and combined finite volume - finite element schemes. The book gives a complex insight into the numerics of compressible flow, covering the development of numerical schemes and their theoretical mathematical analysis, their verification on test problems and use in solving practical engineering problems. The book will be helpful to specialists coming into contact with CFD - pure and applied mathematicians, aerodynamists, engineers, physicists and natural scientists. It will also be suitable for advanced undergraduate, graduate and postgraduate students of mathematics and technical sciences.
Author: Sachin Premasuthan
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Despite the advance in CFD over the past few decades, the field of high-order methods for unstructured grids has not yet reached the level of maturity required to solve real flow problems on complicated geometries. The present thesis work makes an effort towards the realization of a flow solver that is high-order accurate but also efficient, robust and geometrically flexible at the same time. The approach to high-order spatial discretization is based on the Spectral Difference (SD) method for unstructured quadrilateral meshes. High-order (quadratic and cubic) representation is used for curved boundary surfaces. Due to their slow convergence rates with standard explicit time-stepping schemes, the use of high order schemes becomes viable only when there is some kind of convergence acceleration technique used. Towards this end, the multi-order (p-multigrid) method and Implicit time-stepping are implemented, and significant convergence acceleration is achieved for both steady and unsteady flow problems. Another significant challenge with using high-order methods is their inability to handle flow discontinuities. An artificial viscosity based approach is designed and implemented to enable computation of flows with shocks. Adaptive mesh and order refinement have great potential in reducing the computational effort required to reach a specified level of accuracy, particularly in the context of high-order formulations. The capability for adaptive mesh and order refinement is enabled using mortar elements to handle non-conforming solution approximations at the cell interfaces. The flow solver is tested, validated and applied to a variety of flow problems. The current work also demonstrates the effectiveness of computational tools such as convergence acceleration, shock-capturing and adaptive refinement, for enhancing the efficiency and robustness of high order flow computations.
Author: Suvanjan Bhattacharyya
Publisher: Springer Nature
ISBN: 9811962707
Category : Science
Languages : en
Pages : 628
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Book Description
This book presents the select proceedings of the 48th National Conference on Fluid Mechanics and Fluid Power (FMFP 2021) held at BITS Pilani in December 2021. It covers the topics such as fluid mechanics, measurement techniques in fluid flows, computational fluid dynamics, instability, transition and turbulence, fluidâstructure interaction, multiphase flows, micro- and nanoscale transport, bio-fluid mechanics, aerodynamics, turbomachinery, propulsion and power. The book will be useful for researchers and professionals interested in the broad field of mechanics.
