Numerical Examination of Flux Correction for Solving the Navier-Stokes Equations on Unstructured Meshes PDF Download
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Author: Dalon G. Work
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This work examines the feasibility of a novel high-order numerical method, which has been termed Flux Correction. It has been given this name because it \corrects" the flux terms of an established numerical method, cancelling various error terms in the fluxes and making the method higher-order. In this work, this change is made to a traditionally second-order finite volume Galerkin method. To accomplish this, higher-order gradients of solution variables, as well as gradients of the fluxes are introduced to the method. Gradients are computed using lagrange interpolations in a fashion reminiscent of Finite Element techniques. For the Euler Equations, Flux Correction is compared against Flux Reconstruction, a derivative of the high-order Discontinuous Galerkin and Spectral Dierence methods, both of which are currently popular areas of research in high-order numerical methods. Flux Correction is found to compare favorably in terms of accuracy, and exceeds expectations for convergence rates. For the full Navier-Stokes Equations, the effect of curved elements on Flux Correction are examined. Flux Correction is found to react negatively to curved elements due to the gradient procedure's poor handling of high-aspect ratio elements.
Author: Dalon G. Work
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This work examines the feasibility of a novel high-order numerical method, which has been termed Flux Correction. It has been given this name because it \corrects" the flux terms of an established numerical method, cancelling various error terms in the fluxes and making the method higher-order. In this work, this change is made to a traditionally second-order finite volume Galerkin method. To accomplish this, higher-order gradients of solution variables, as well as gradients of the fluxes are introduced to the method. Gradients are computed using lagrange interpolations in a fashion reminiscent of Finite Element techniques. For the Euler Equations, Flux Correction is compared against Flux Reconstruction, a derivative of the high-order Discontinuous Galerkin and Spectral Dierence methods, both of which are currently popular areas of research in high-order numerical methods. Flux Correction is found to compare favorably in terms of accuracy, and exceeds expectations for convergence rates. For the full Navier-Stokes Equations, the effect of curved elements on Flux Correction are examined. Flux Correction is found to react negatively to curved elements due to the gradient procedure's poor handling of high-aspect ratio elements.
Author: Dmitri Kuzmin
Publisher: Springer Science & Business Media
ISBN: 3540272062
Category : Science
Languages : en
Pages : 312
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Book Description
Addressing students and researchers as well as CFD practitioners, this book describes the state of the art in the development of high-resolution schemes based on the Flux-Corrected Transport (FCT) paradigm. Intended for readers who have a solid background in computational fluid dynamics, the book begins with historical notes by J.P. Boris and D.L. Book. Review articles that follow describe recent advances in the design of FCT algorithms as well as various algorithmic aspects. The topics addressed in the book and its main highlights include: the derivation and analysis of classical FCT schemes, with special emphasis on the underlying physical and mathematical constraints; flux limiting for hyperbolic systems; generalization of FCT to implicit time-stepping and finite element discretizations on unstructured meshes and its role as a subgrid scale model for Monotonically Integrated Large Eddy Simulation (MILES) of turbulent flows. The proposed enhancements of the FCT methodology also comprise the prelimiting and 'failsafe' adjustment of antidiffusive fluxes, the use of characteristic variables, and iterative flux correction. The cause and cure of detrimental clipping/terracing effects are discussed. Many numerical examples are presented for academic test problems and large-scale applications alike.
Author: Institute for Computer Applications in Science and Engineering
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
Multigrid methods are good candidates for the resolution of the system arising in Numerical Fluid Dynamics. However, the question is to know if those algorithms which are efficient for the Poisson equation on structured meshes will still apply well to the Euler and Navier-Stokes equations on unstructured meshes. The study of elliptic problems leads us to define the conditions where a Full Multigrid-strategy has O(N) complexity. The aim of this paper is to build a comparison between the elliptic theory and practical CFD problems. First, as an introduction, we will recall some basic definitions and theorems applied to a model problem. The goal of this section is to point out the different properties that we need to produce an FMG algorithm with O(N) complexity. Then, we will show how we can apply this theory to the fluid dynamics equations such as Euler and Navier-Stokes equations. At last, we present some results which are 2nd-order accurate and some explanations about the behaviour of the FMG process ... Unstructured, Multigrid, Non-linear, Euler/Navier-Stokes, Steady equations, FMG, O(N) Complexity.
Author: Dmitri Kuzmin
Publisher: Springer
ISBN: 9789400797291
Category : Science
Languages : en
Pages : 0
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Book Description
Addressing students and researchers as well as Computational Fluid Dynamics practitioners, this book is the most comprehensive review of high-resolution schemes based on the principle of Flux-Corrected Transport (FCT). The foreword by J.P. Boris and historical note by D.L. Book describe the development of the classical FCT methodology for convection-dominated transport problems, while the design philosophy behind modern FCT schemes is explained by S.T. Zalesak. The subsequent chapters present various improvements and generalizations proposed over the past three decades. In this new edition, recent results are integrated into existing chapters in order to describe significant advances since the publication of the first edition. Also, 3 new chapters were added in order to cover the following topics: algebraic flux correction for finite elements, iterative and linearized FCT schemes, TVD-like flux limiters, acceleration of explicit and implicit solvers, mesh adaptation, failsafe limiting for systems of conservation laws, flux-corrected interpolation (remapping), positivity preservation in RANS turbulence models, and the use of FCT as an implicit subgrid scale model for large eddy simulations.
Author: Jan S. Hesthaven
Publisher: Springer Science & Business Media
ISBN: 0387720650
Category : Mathematics
Languages : en
Pages : 507
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Book Description
This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781720572145
Category :
Languages : en
Pages : 30
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Book Description
The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.Jothiprasad, Giridhar and Mavriplis, Dimitri J. and Caughey, David A. and Bushnell, Dennis M. (Technical Monitor)Langley Research CenterALGORITHMS; NAVIER-STOKES EQUATION; UNSTRUCTURED GRIDS (MATHEMATICS); MEASURE AND INTEGRATION; RUNGE-KUTTA METHOD; AGGLOMERATION; CONVERGENCE; LINEAR SYSTEMS; NONLINEAR SYSTEMS
Author: Bruce A. Finlayson
Publisher: Bruce Alan Finlayson
ISBN: 9780963176509
Category : Mathematics
Languages : en
Pages : 605
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Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781723558153
Category :
Languages : en
Pages : 286
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Book Description
A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required. Jiang, Yi-Tsann and Usab, William J., Jr. Unspecified Center NASA-CR-193241, NAS 1.26:193241 NAG3-1127...
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 704
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Author: Miloslav Feistauer
Publisher: Springer Science & Business Media
ISBN: 3642187757
Category : Mathematics
Languages : en
Pages : 873
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Book Description
These proceedings collect the major part of the lectures given at ENU MATH2003, the European Conference on Numerical Mathematics and Ad vanced Applications, held in Prague, Czech Republic, from 18 August to 22 August, 2003. The importance of numerical and computational mathematics and sci entific computing is permanently growing. There is an increasing number of different research areas, where numerical simulation is necessary. Let us men tion fluid dynamics, continuum mechanics, electromagnetism, phase transi tion, cosmology, medicine, economics, finance, etc. The success of applications of numerical methods is conditioned by changing its basic instruments and looking for new appropriate techniques adapted to new problems as well as new computer architectures. The ENUMATH conferences were established in order to provide a fo rum for discussion of current topics of numerical mathematics. They seek to convene leading experts and young scientists with special emphasis on con tributions from Europe. Recent results and new trends are discussed in the analysis of numerical algorithms as well as in their applications to challenging scientific and industrial problems. The first ENUMATH conference was organized in Paris in 1995, then the series continued by the conferences in Heidelberg 1997, Jyvaskyla 1999 and Ischia Porto 2001. It was a great pleasure and honour for the Czech numerical community that it was decided at Ischia Porto to organize the ENUMATH2003 in Prague. It was the first time when this conference crossed the former Iron Courtain and was organized in a postsocialist country.
