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Compact High Order Schemes For The Euler Equations
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Book Synopsis Compact High Order Schemes for the Euler Equations by : Saul Abarbanel
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.
Book Synopsis A Comparison of High Order Control Volume Schemes for Solving the Euler Equations by : Vivekananda Vedanayagam S. Chetty
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:
Book Synopsis Compact Finite Difference Schemes for the Euler and Navier-Stokes Equations by :
Download or read book Compact Finite Difference Schemes for the Euler and Navier-Stokes Equations written by and published by . This book was released on 1982 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis High order finite volume schemes for the two-dimensional compressible Euler equations by : Sebastian Noelle
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:
Book Synopsis A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations by : Margot Gerritsen
Download or read book A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations written by Margot Gerritsen and published by . This book was released on 1996 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We derive a high-order finite difference scheme for the Euler equations that satisfies a semi-discrete energy estimate, and present an efficient strategy for the treatment of discontinuities that leads to sharp shock resolution. The formulation of the semi-discrete energy estimate is based on a symmetrization of the Euler equations that preserves the homogeneity of the flux vector, a canonical splitting of the flux derivative vector, and the use of difference operators that satisfy a discrete analogue to the integration by parts procedure used in the continuous energy estimate. Around discontinuities or sharp gradients, refined grids are created on which the discrete equations are solved after adding a newly constructed artificial viscosity. The positioning of the sub-grids and computation of the viscosity are aided by a detection algorithm which is based on a multi-scale wavelet analysis of the pressure grid function. The wavelet theory provides easy to implement mathematical criteria to detect discontinuities, sharp gradients and spurious oscillations quickly and efficiently."
Book Synopsis One-dimension High-order Compact Method for Solving Euler's Equation by : Mahmod Abd Hakim Mohamad
Download or read book One-dimension High-order Compact Method for Solving Euler's Equation written by Mahmod Abd Hakim Mohamad and published by . This book was released on 2010 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the field of computational fluid dynamics, many numerical algorithms have been developed to simulate inviscid, compressible flows problems. Among those most famous and relevant are based on flux vector splitting and Godunov-type schemes. Previously, this system was developed through computational studies by Mawlood (2004). However the new test cases for compressible flows, the shock tube problems namely the receding flow and shock waves were not investigated before by Mawlood (2004). Thus, the objective of this study is to develop a high-order compact (HOC) finite difference solver for one-dimensional Euler equation. Before developing the solver, a detailed investigation was conducted to assess the performance of the basic third-order compact central discretization schemes. Spatial discretization of the Euler equation is based on flux-vector splitting. From this observation, discretization of the convective flux terms of the Euler equation is based on a hybrid flux-vector splitting, known as the advection upstream splitting method (AUSM) scheme which combines the accuracy of flux-difference splitting and the robustness of flux-vector splitting. The AUSM scheme is based on the third-order compact scheme to the approximate finite difference equation was completely analyzed consequently. In one-dimensional problem for the first order schemes, an explicit method is adopted by using time integration method. In addition to that, development and modification of source code for the one-dimensional flow is validated with four test cases namely, unsteady shock tube, quasi-one-dimensional supersonic-subsonic nozzle flow, receding flow and shock waves in shock tubes. From these results, it was also carried out to ensure that the definition of Riemann problem can be identified. Further analysis had also been done in comparing the characteristic of AUSM scheme against experimental results, obtained from previous works and also comparative analysis with computational results generated by van Leer, KFVS and AUSMPW schemes. Furthermore, there is a remarkable improvement with the extension of the AUSM scheme from first-order to third-order accuracy in terms of shocks, contact discontinuities and rarefaction waves.
Book Synopsis High-order Schemes for Navier-Stokes Equations by : Datta V. Gaitonde
Download or read book High-order Schemes for Navier-Stokes Equations written by Datta V. Gaitonde and published by . This book was released on 1998 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: A spectrum of higher-order schemes is developed to solve the Navier-Stokes equations in finite-difference formulations. Pade type formulas of up to sixth order with a five-point stencil are developed for the difference scheme. Viscous terms are treated by successive applications of the first derivative operator. However, formulas are also derived for use in a mid-point interpolation-differentiation strategy. For numerical stability, up to tenth-order filtering schemes are developed. The spectral properties of the differentiation and filtering schemes are examined and guidelines are provided to choose proper filter coefficients. Special high-order formulas are obtained for differentiation and filtering in the vicinity of boundaries. The coefficients required for systematic implementation of Neumann-type boundary conditions are also presented. A brief description is provided of the manner in which the FDL3DI code is enhanced by coupling the approximately-factored procedure with these compact-difference based algorithms and by incorporating an explicit fourth-order Runge-Kutta scheme.
Author :National Aeronautics and Space Adm Nasa Publisher :Independently Published ISBN 13 :9781729052969 Total Pages :36 pages Book Rating :4.0/5 (529 download)
Book Synopsis A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations by : National Aeronautics and Space Adm Nasa
Download or read book A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations written by National Aeronautics and Space Adm Nasa and published by Independently Published. This book was released on 2018-10-21 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a high-order finite difference scheme for the Euler equations that satisfies a semi-discrete energy estimate, and present an efficient strategy for the treatment of discontinuities that leads to sharp shock resolution. The formulation of the semi-discrete energy estimate is based on a symmetrization of the Euler equations that preserves the homogeneity of the flux vector, a canonical splitting of the flux derivative vector, and the use of difference operators that satisfy a discrete analogue to the integration by parts procedure used in the continuous energy estimate. Around discontinuities or sharp gradients, refined grids are created on which the discrete equations are solved after adding a newly constructed artificial viscosity. The positioning of the sub-grids and computation of the viscosity are aided by a detection algorithm which is based on a multi-scale wavelet analysis of the pressure grid function. The wavelet theory provides easy to implement mathematical criteria to detect discontinuities, sharp gradients and spurious oscillations quickly and efficiently. Gerritsen, Margot and Olsson, Pelle Ames Research Center NAS2-13721; NSF ASC-93-18166...
Book Synopsis Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations by :
Download or read book Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations written by and published by . This book was released on 1998 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Efficient Implementation of High-Order Accurate Numerical Methods on Unstructured Grids by : Wanai Li
Download or read book Efficient Implementation of High-Order Accurate Numerical Methods on Unstructured Grids written by Wanai Li and published by Springer. This book was released on 2014-05-23 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Explicit and Implicit Compact High-resolution Shock-capturing Methods for Multidimensional Euler Equations 1: Formulation by :
Download or read book Explicit and Implicit Compact High-resolution Shock-capturing Methods for Multidimensional Euler Equations 1: Formulation written by and published by . This book was released on 1995 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis High Order Nonlinear Numerical Schemes for Evolutionary PDEs by : Rémi Abgrall
Download or read book High Order Nonlinear Numerical Schemes for Evolutionary PDEs written by Rémi Abgrall and published by Springer. This book was released on 2014-05-19 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.
Book Synopsis An Introduction to the Study of Stellar Structure by : Subrahmanyan Chandrasekhar
Download or read book An Introduction to the Study of Stellar Structure written by Subrahmanyan Chandrasekhar and published by Courier Corporation. This book was released on 1957-01-01 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rigorous examination of relationship between loss of energy, mass, and radius of stars in a steady state. Unabridged, corrected republication of original (1939) edition. "The material is throughout presented with enviable crispness and clarity of expression. The work will undoubtedly become an indispensable handbook for future researchers in the field." — Nature.
Book Synopsis On High Resolution Finite Difference Schemes for the Euler Equations by : Nicholas Clarke
Download or read book On High Resolution Finite Difference Schemes for the Euler Equations written by Nicholas Clarke and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis High Accuracy Non-centered Compact Difference Schemes for Fluid Dynamics Applications by : A. I. Tolstykh
Download or read book High Accuracy Non-centered Compact Difference Schemes for Fluid Dynamics Applications written by A. I. Tolstykh and published by World Scientific. This book was released on 1994 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book which describes completely the nontraditional difference schemes which combine the ideas of Pad-type approximation and upwind differencing. These possess some favorable properties and can be used to solve various problems in fluid dynamics and related disciplines. They were proposed by the author in the seventies and are extensively used in Russia. However, they seem to be relatively unknown outside the country. In this book, the author presents the theory of the schemes, to provide some sophisticated algorithms for different computational fluid dynamics problems, to supply readers with useful information which would permit them to construct a rich variety of algorithms of this type and to illustrate the applications of these methods to the numerical simulation of various fluid dynamics phenomena, ranging from supersonic viscous flows to some atmosphere and ocean processes. This book is an essential guide for anyone keenly interested in this field.
Book Synopsis Uniform High Order Spectral Methods for One and Two Dimensional Euler Equations by : Institute for Computer Applications in Science and Engineering
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:
Book Synopsis On Positivity Preserving Finite Volume Schemes for Compressible Euler Equations by : Institute for Computer Applications in Science and Engineering
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:
