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 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 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 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 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 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 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 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 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 Stable and Convergent Discontinuous Galerkin Methods for Hyperbolic and Viscous Systems of Conservation Laws written by Mohammad Zakerzadeh 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 Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws written by Philipp Öffner and published by Springer Nature. This book was released on 2023-09-17 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on stability and approximation results concerning recent numerical methods for the numerical solution of hyperbolic conservation laws. The work begins with a detailed and thorough introduction of hyperbolic conservation/balance laws and their numerical treatment. In the main part, recent results in such context are presented focusing on the investigation of approximation properties of discontinuous Galerkin and flux reconstruction methods, the construction of (entropy) stable numerical methods and the extension of existing (entropy) stability results for both semidiscrete and fully discrete schemes, and development of new high-order methods.
Download or read book Nodal Discontinuous Galerkin Methods written by Jan S. Hesthaven and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Efficiency Improvements for Discontinuous Galerkin Finite Element Discretizations of Hyperbolic Conservation Laws written by Benjamin A. Yeager and published by . This book was released on 2014 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discontinuous Galerkin (DG) finite element methods, paired in a method-of-lines approach with an appropriate time stepper, are an increasingly common choice for the numerical solution of hyperbolic conservation laws. They have a number of favorable properties for large-scale modelling of conservative systems, including a high degree of parallelizability, accurate shock capturing, and local conservation; however, they also tend to be computationally expensive in comparison to other common solution techniques. In this work, the computational cost of DG schemes is reduced through the development of new, efficient time steppers and numerical integration rules. New Runge--Kutta, linear multistep, and two-step Runge--Kutta methods are developed that allow for larger stable time steps and higher order accuracy without an overly restrictive time step constraint. New numerical integration rules are constructed specifically for DG spatial discretizations using quadrilateral, triangular, and hexahedral elements, minimizing the total number of function evaluations needed to integrate the DG polynomial approximation over each element. The new methods are then applied to a numerical test case to demonstrate the reduction in computational cost that they afford over existing methods.
Download or read book Aspects on Discontinuous Galerkin Solutions of Hyperbolic Conservation Laws written by Jianguo Xin and published by . This book was released on 2005 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Element Based Galerkin Methods on Tensor Product Bases written by Francis X. Giraldo and published by Springer Nature. This book was released on 2020-10-30 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations.
Download or read book Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws written by Ralf Hartmann and published by . This book was released on 2001 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
