Download or read book On the Derivation of the Discontinuous Galerkin Method for Hyperbolic Conservation Laws written by Sebastian Noelle and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Priori Error Estimates for an Hp version of the Discontinuous Galerkin Method for Hyperbolic Conservation Laws written by Kim S. Bey and published by . This book was released on 1993 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An HP adaptive discontinuous Galerkin method for hyperbolic conservation laws written by Kim S. Bey and published by . This book was released on 1994 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Methods for Conservation Laws written by Jan S. Hesthaven and published by SIAM. This book was released on 2018-01-30 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material will be available online at publication.

Download or read book A Priori Error Estimates for an Hp Version of the Discontinuous Galerkin Method for Hyperbolic Conservation Laws written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-28 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: A priori error estimates are derived for hp-versions of the finite element method for discontinuous Galerkin approximations of a model class of linear, scalar, first-order hyperbolic conservation laws. These estimates are derived in a mesh dependent norm in which the coefficients depend upon both the local mesh size h(sub K) and a number p(sub k) which can be identified with the spectral order of the local approximations over each element. Bey, Kim S. and Oden, J. Tinsley Langley Research Center RTOP 505-43-31...

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.

Download or read book Discontinuous Galerkin Methods for Hyperbolic Conservation Laws written by Justin Hadi and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: New numerical methods are developed for single phase compressible gas flow and two phase gas/liquid flow in the framework of the discontinuous Galerkin finite element method (DGFEM) and applied to Riemann problems. A residual based diffusion scheme inspired by the streamline upwind Petrov-Galerkin method (SUPG) of Brookes and Hughes [15] is applied to the Euler equations of gas dynamics and the single pressure incompressible liquid/compressible gas flow system of Toumi and Kumbaro [137]. A Roe [119] based approximate Riemann solver is applied. To minimise unstable overshoots, diffusivity is added in the direction of the gradient of the solution as opposed to the direction of the streamlines in SUPG for the continuous finite element method (CFEM). The methods are tested on Cartesian meshes with scalar advection problems, the computationally challenging Sod shock tube and Lax Riemann problems, explosion problems in gas dynamics and the water faucet test and explosion problems in two phase flow. An extension to two dimensions and comparisons to existing methods are made. A framework for the well posedness of two phase flow equations is posited and virtual mass terms are added to the two phase flow equations of Toumi and Kumbaro to ensure hyperbolicity. A viscous path based Roe solver for DGFEM is applied mirroring the method of Toumi and Kumbaro in a framework for discontinuous solutions.

Download or read book Compact Higher order Numerical Methods for Hyperbolic Conservation Laws written by Robert Byron Lowrie and published by . This book was released on 1996 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Moving Mesh Discontinuous Galerkin Method for Hyperbolic Conservation Laws written by Ruo Li and published by . This book was released on 2004 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discontinuous Galerkin Methods for Hyperbolic Conservation Laws written by Justin Hadi and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Runge Kutta Discontinuous Galerkin Methods for Convection dominated Problems written by Bernardo Cockburn and published by . This book was released on 2000 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Solutions of Multidimensional Hyperbolic Systems of Conservation Laws by Discontinuous Galerkin Methods and a Derivation of the Moore Greitzer Equation Using Homogenization written by Songming Hou and published by . This book was released on 2002 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hp version discontinuous Galerkin methods for hyperbolic conservation laws written by Kim S. Bey and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Spacetime Discontinuous Galerkin Method for Hyperbolic Conservation Laws written by Jayandran Palaniappan and published by . This book was released on 2007 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic SDG approximation is a simple Bubnov-Galerkin projection that is not prone to global patterns of spurious oscillations. However, it does require stabilization to eliminate local overshoot and undershoot in the immediate vicinity of shocks and other discontinuous solution features. We address this requirement with a diffusion operator whose intensity is controlled by a shock indicator that measures the relative strength of the high-frequency components of the SDG approximation. Results demonstrating the performance of the SDG method, the h-adaptive refinement scheme, and the diffusion operator for applications of the inviscid Euler equations in one and two spatial dimensions are presented.

Download or read book Stabilized Discontinuous Galerkin Methods for Solving Hyperbolic Conservation Laws on Grids with Embedded Objects written by Florian Streitbürger and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Convergence of the Discontinuous Galerkin Finite Element Method for Hyperbolic Conservation Laws written by Jerome Jaffre and published by . This book was released on 1993 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On Formulations of Discontinuous Galerkin and Related Methods for Conservation Laws written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-05-22 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: A formulation for the discontinuous Galerkin (DG) method that leads to solutions using the differential form of the equation (as opposed to the standard integral form) is presented. The formulation includes (a) a derivative calculation that involves only data within each cell with no data interaction among cells, and (b) for each cell, corrections to this derivative that deal with the jumps in fluxes at the cell boundaries and allow data across cells to interact. The derivative with no interaction is obtained by a projection, but for nodal-type methods, evaluating this derivative by interpolation at the nodal points is more economical. The corrections are derived using the approximate (Dirac) delta functions. The formulation results in a family of schemes: different approximate delta functions give rise to different methods. It is shown that the current formulation is essentially equivalent to the flux reconstruction (FR) formulation. Due to the use of approximate delta functions, an energy stability proof simpler than that of Vincent, Castonguay, and Jameson (2011) for a family of schemes is derived. Accuracy and stability of resulting schemes are discussed via Fourier analyses. Similar to FR, the current formulation provides a unifying framework for high-order methods by recovering the DG, spectral difference (SD), and spectral volume (SV) schemes. It also yields stable, accurate, and economical methods. Huynh, H. T. Glenn Research Center COMPUTATIONAL FLUID DYNAMICS; CONSERVATION LAWS; DIFFERENTIAL EQUATIONS; DERIVATION; DELTA FUNCTION; GALERKIN METHOD; FOURIER ANALYSIS; FLUX DENSITY; NUMERICAL ANALYSIS; SPECTRAL METHODS; NAVIER-STOKES EQUATION; UNSTRUCTURED GRIDS (MATHEMATICS); STABILITY; COSTS; PROVING