On Essentially Non-Oscillatory Schemes on Unstructured Meshes

On Essentially Non-Oscillatory Schemes on Unstructured Meshes
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
Total Pages: 42
Release: 2018-07-09
Genre:
ISBN: 9781722450847

A few years ago, the class of Essentially Non-Oscillatory Schemes for the numerical simulation of hyperbolic equations and systems was constructed. Since then, some extensions have been made to multidimensional simulations of compressible flows, mainly in the context of very regular structured meshes. In this paper, we first recall and improve the results of an earlier paper about non-oscillatory reconstruction on unstructured meshes, emphasizing the effective calculation of the reconstruction. Then we describe a class of numerical schemes on unstructured meshes and give some applications for its third order version. This demonstrates that a higher order of accuracy is indeed obtained, even on very irregular meshes. Abgrall, R. Unspecified Center NAS1-19480; RTOP 505-90-52-01...

Weighted Essentially Non-oscillatory Schemes on Triangular Meshes

Weighted Essentially Non-oscillatory Schemes on Triangular Meshes
Author: Changqing Hu
Publisher:
Total Pages: 36
Release: 1998
Genre:
ISBN:

In this paper we construct high order weighted essentially non-oscillatory (WENO) schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. We present third order schemes using a combination of linear polynomials, and fourth order schemes using a combination of quadratic polynomials. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations.

High-Order Methods for Computational Physics

High-Order Methods for Computational Physics
Author: Timothy J. Barth
Publisher: Springer Science & Business Media
Total Pages: 594
Release: 2013-03-09
Genre: Mathematics
ISBN: 366203882X

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.

Handbook of Numerical Methods for Hyperbolic Problems

Handbook of Numerical Methods for Hyperbolic Problems
Author: Remi Abgrall
Publisher: Elsevier
Total Pages: 668
Release: 2016-11-17
Genre: Mathematics
ISBN: 0444637958

Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. 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 readily understand their relative advantages and limitations. - Provides detailed, cutting-edge background explanations of existing algorithms and their analysis - Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis - Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications - Written by leading subject experts in each field who provide breadth and depth of content coverage

Lecture Notes on Numerical Methods for Hyperbolic Equations

Lecture Notes on Numerical Methods for Hyperbolic Equations
Author: Elena Vázquez-Cendón
Publisher: CRC Press
Total Pages: 144
Release: 2011-05-23
Genre: Mathematics
ISBN: 0203590627

This volume contains the lecture notes of the Short Course on Numerical Methods for Hyperbolic Equations (Faculty of Mathematics, University of Santiago de Compostela, Spain, 2-4 July 2011). The course was organized in recognition of Prof. Eleuterio Toro‘s contribution to education and training on numerical methods for partial differential equation

Computational Fluid Dynamics

Computational Fluid Dynamics
Author: Jiri Blazek
Publisher: Butterworth-Heinemann
Total Pages: 466
Release: 2015-04-23
Genre: Science
ISBN: 0128011726

Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics. By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques. This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization. An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques. - Will provide you with the knowledge required to develop and understand modern flow simulation codes - Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics - Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws

Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws
Author: Rainer Ansorge
Publisher: Springer Science & Business Media
Total Pages: 325
Release: 2012-09-14
Genre: Technology & Engineering
ISBN: 3642332218

In January 2012 an Oberwolfach workshop took place on the topic of recent developments in the numerics of partial differential equations. Focus was laid on methods of high order and on applications in Computational Fluid Dynamics. The book covers most of the talks presented at this workshop.

Godunov Methods

Godunov Methods
Author: E.F. Toro
Publisher: Springer Science & Business Media
Total Pages: 1050
Release: 2012-12-06
Genre: Computers
ISBN: 1461506638

This edited review book on Godunov methods contains 97 articles, all of which were presented at the international conference on Godunov Methods: Theory and Applications, held at Oxford in October 1999, to commemo rate the 70th birthday of the Russian mathematician Sergei K. Godunov. The meeting enjoyed the participation of 140 scientists from 20 countries; one of the participants commented: everyone is here, meaning that virtu ally everybody who had made a significant contribution to the general area of numerical methods for hyperbolic conservation laws, along the lines first proposed by Godunov in the fifties, was present at the meeting. Sadly, there were important absentees, who due to personal circumstance could not at tend this very exciting gathering. The central theme o{ the meeting, and of this book, was numerical methods for hyperbolic conservation laws fol lowing Godunov's key ideas contained in his celebrated paper of 1959. But Godunov's contributions to science are not restricted to Godunov's method.

Progress in Analysis

Progress in Analysis
Author: Heinrich G. W. Begehr
Publisher: World Scientific
Total Pages: 1557
Release: 2003
Genre: Mathematics
ISBN: 981238572X

The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.