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Author : Sebastian Noelle
Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.:/5 (17 download)
Download or read book High order finite volume schemes for the two-dimensional compressible Euler equations written by Sebastian Noelle and published by . This book was released on 1997 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Institute for Computer Applications in Science and Engineering
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (317 download)
Download or read book On Positivity Preserving Finite Volume Schemes for Compressible Euler Equations written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1993 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Emmanuel Franck
Publisher : Springer Nature
ISBN 13 : 3031408608
Total Pages : 296 pages
Book Rating : 4.0/5 (314 download)
Download or read book Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems written by Emmanuel Franck and published by Springer Nature. This book was released on 2023-10-12 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the second part of the proceedings of the 10th International Conference on Finite Volumes for Complex Applications, FVCA, held in Strasbourg, France, during October 30 to November 3, 2023. The Finite Volume method, and several of its variants, is a spatial discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods are also built to preserve some properties of the continuous equations, including maximum principles, dissipativity, monotone decay of the free energy, asymptotic stability, or stationary solutions. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. In recent years, the efficient implementation of these methods in numerical software packages, more specifically to be used in supercomputers, has drawn some attention. The first volume contains all invited papers, as well as the contributed papers focusing on finite volume schemes for elliptic and parabolic problems. They include structure-preserving schemes, convergence proofs, and error estimates for problems governed by elliptic and parabolic partial differential equations. This volume is focused on finite volume methods for hyperbolic and related problems, such as methods compatible with the low Mach number limit or able to exactly preserve steady solutions, the development and analysis of high order methods, or the discretization of kinetic equations.
Author : Ivan Padilla Montero
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (112 download)
Download or read book Study of Unstructured Finite Volume Methods for the Solution of the Euler Equations written by Ivan Padilla Montero and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work deals with the numerical solution of inviscid compressible flows by means of the Euler equations. It focuses on the description of an unstructured finite volume method for these equations and its numerical application to solve external, two-dimensional steady problems. On first place, the standard formulation of the Euler equations is presented, reviewing the most important properties that characterize their mathematical behavior. The hyperbolic nature of the system is discussed, emphasizing the fundamental importance of taking into account the propagation of information in the flow field in order to obtain physically meaningful solutions, which also leads to a description of how the boundary conditions should be treated to avoid undesirable behaviors. To complete this presentation, a dimensionless form of the equations is derived, which provides substantial advantages to the numerical solution. The attention is then focused on the unstructured finite volume formulation, which is based on a central approximation of the fluxes at the volume interfaces. According to the need of properly accounting for the propagation of characteristic variables, the requirement to add artificial dissipation terms to the central discretization is justified. Then, two classical forms of artificial dissipation are defined, namely, the first-order upwind scheme and the Jameson-Schmidt-Turkel high-order model, detailing how to adapt the formulation of the dissipation terms to an unstructured mesh. Eventually, the time integration of the spatially discretized equations is assessed. With the objective of performing a practical implementation of the theoretical concepts studied, the development of a numerical solver is presented next, briefly describing the program structure and characteristics. After that, five different test cases are solved with the purpose of validating the code, consisting on two transonic flows around a NACA0012 airfoil and three supersonic examples, respectively around a NACA0012 airfoil, a double wedge airfoil and circular cylinder. The results obtained for each case are then analyzed and compared against reference solutions, showing an overall satisfactory performance of the solver developed.
Download or read book TWO-DIMENSIONAL FINITE VOLUME WEIGHTED ESSENTIALLY NON-OSCILLATORY EULER SCHEMES WITH DIFFERENT FLUX ALGORITHMS. written by and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this thesis is to implement Finite Volume Weighted Essentially Non-Oscillatory (FV-WENO) scheme to solution of one and two-dimensional discretised Euler equations with different flux algorithms. The effects of the different fluxes on the solution have been tested and discussed. Beside, the effect of the grid on these fluxes has been investigated. Weighted Essentially Non-Oscillatory (WENO) schemes are high order accurate schemes designed for problems with piecewise smooth solutions that involve discontinuities. WENO schemes have been successfully used in applications, especially for problems containing both shocks and complicated smooth solution structures. Fluxes are used as building blocks in FV-WENO scheme. The efficiency of the scheme is dependent on the fluxes used in scheme The applications tested in this thesis are the 1-D Shock Tube Problem, Double Mach Reflection, Supersonic Channel Flow, and supersonic Staggered Wedge Cascade. The numerical solutions for 1-D Shock Tube Problem and the supersonic channel flow are compared with the analytical solutions. The results for the Double Mach Reflection and the supersonic staggered cascade are compared with results from literature.
Author : Norbert Kroll
Publisher :
ISBN 13 :
Total Pages : 150 pages
Book Rating : 4.E/5 ( download)
Download or read book Solution of Two-dimensional Euler Equations written by Norbert Kroll and published by . This book was released on 1987 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Saul Abarbanel
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (317 download)
Download or read book Compact High Order Schemes for the Euler Equations written by Saul Abarbanel and published by . This book was released on 1988 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: An implicit approximate factorization (AF) algorithm is constructed which has the following characteristics. In 2-D: The scheme is unconditionally stable, has a 3 x 3 stencil and at steady state has a fourth order spatial accuracy. The temporal evolution is time accurate either to 1st or 2nd order through choice of parameter. In 3-D: The scheme has almost the same properties as in 2-D except that it is now only conditionally stable, with the stability condition (the CFL number) being dependent on the cell aspect ratios, Delta y/Delta x and Delta z/Delta x. The stencil is still compact and fourth order accuracy at steady state is maintained. Numerical experiments on a 2-D shock-reflection problem show the expected improvement over lower order schemes, not only in accuracy (measured by the L2 error) but also in the dispersion. It is also shown how the same technique is immediately extendable to Runge Kutta type schemes resulting in improved stability in addition to the enhanced accuracy. Keywords: Euler equations; Compact schemes; High order accuracy; Dispersion.
Author : Institute for Computer Applications in Science and Engineering
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (317 download)
Download or read book Uniform High Order Spectral Methods for One and Two Dimensional Euler Equations written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1991 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bernardo Cockburn
Publisher : Springer Science & Business Media
ISBN 13 : 3642597211
Total Pages : 468 pages
Book Rating : 4.6/5 (425 download)
Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
Author : Yi Zhu
Publisher :
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.:/5 (53 download)
Download or read book Multidimensional Upwind Finite-volume Schemes for the Euler Equations and Finite-difference Schemes for the Maxwell's Equations written by Yi Zhu and published by . This book was released on 1993 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Randall J. LeVeque
Publisher : Cambridge University Press
ISBN 13 : 1139434187
Total Pages : 582 pages
Book Rating : 4.1/5 (394 download)
Download or read book Finite Volume Methods for Hyperbolic Problems written by Randall J. LeVeque and published by Cambridge University Press. This book was released on 2002-08-26 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Author : Clément Cancès
Publisher : Springer
ISBN 13 : 3319573977
Total Pages : 457 pages
Book Rating : 4.3/5 (195 download)
Download or read book Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects written by Clément Cancès and published by Springer. This book was released on 2017-05-23 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier–Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asy mptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is a valuable resource for researchers, PhD and master’s level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.
Author : Raphaèle Herbin
Publisher : Elsevier Science & Technology
ISBN 13 :
Total Pages : 860 pages
Book Rating : 4.3/5 (91 download)
Download or read book Finite Volumes for Complex Applications III written by Raphaèle Herbin and published by Elsevier Science & Technology. This book was released on 2002 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific computing, which involves the analysis of complex systems in real applications with numerical simulations, is becoming an important field of research in itself, in relation to theoretical investigations and physical experiments. In many cases, the underlying mathematical models consist of large systems of partial differential equations, which have to be solved with high accuracy and efficiency. Among the successful methods, in particular for discretizations on unstructured grids, are the Finite Volume schemes. This publication contains the contributions presented at the third Symposium on Finite Volumes for Complex Applications, held in Porquerolles in June 2002. After a critical review of the submitted papers, 96 papers by authors from more than 20 countries are presented in this volume. The subject of these papers ranges from theoretical and numerical results such as theoretical foundation and validation, adaptivity in space and time, higher order discretization and parallelization, to physical,applications, such as multiphase flow and flows through porous media, magnetohydrodynamics, reacting and turbulent flows, elastic structures, granular avalanches, and image processing.
Author : Timothy J. Barth
Publisher : Springer Science & Business Media
ISBN 13 : 366203882X
Total Pages : 594 pages
Book Rating : 4.6/5 (62 download)
Download or read book High-Order Methods for Computational Physics written by Timothy J. Barth and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal lenges facing the field of computational fluid dynamics. In structural me chanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com putation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order ac curacy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence sug gests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Cen ter. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18,1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25,1998 at the NASA Ames Research Center in the United States.
Author : F. Moukalled
Publisher : Springer
ISBN 13 : 3319168746
Total Pages : 799 pages
Book Rating : 4.3/5 (191 download)
Download or read book The Finite Volume Method in Computational Fluid Dynamics written by F. Moukalled and published by Springer. This book was released on 2015-08-13 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.
Author : Remi Abgrall
Publisher : Elsevier
ISBN 13 : 044463911X
Total Pages : 612 pages
Book Rating : 4.4/5 (446 download)
Download or read book Handbook of Numerical Methods for Hyperbolic Problems written by Remi Abgrall and published by Elsevier. This book was released on 2017-01-16 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations. Provides detailed, cutting-edge background explanations of existing algorithms and their analysis Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage
Author : Vivekananda Vedanayagam S. Chetty
Publisher :
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.:/5 (73 download)
Download or read book A Comparison of High Order Control Volume Schemes for Solving the Euler Equations written by Vivekananda Vedanayagam S. Chetty and published by . This book was released on 2006 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
