Adaptive Finite Element Solution Algorithm for the Euler Equations

  • Editors
  • Richard A. Shapiro

Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 32)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Richard A. Shapiro
    Pages 1-4
  3. Richard A. Shapiro
    Pages 5-10
  4. Richard A. Shapiro
    Pages 11-21
  5. Richard A. Shapiro
    Pages 22-41
  6. Richard A. Shapiro
    Pages 42-75
  7. Richard A. Shapiro
    Pages 76-102
  8. Richard A. Shapiro
    Pages 103-119
  9. Richard A. Shapiro
    Pages 120-137
  10. Richard A. Shapiro
    Pages 138-143
  11. Richard A. Shapiro
    Pages 144-151
  12. Richard A. Shapiro
    Pages 152-153
  13. Back Matter
    Pages 154-167

About this book

Introduction

This monograph is the result of my PhD thesis work in Computational Fluid Dynamics at the Massachusettes Institute of Technology under the supervision of Professor Earll Murman. A new finite element al­ gorithm is presented for solving the steady Euler equations describing the flow of an inviscid, compressible, ideal gas. This algorithm uses a finite element spatial discretization coupled with a Runge-Kutta time integration to relax to steady state. It is shown that other algorithms, such as finite difference and finite volume methods, can be derived using finite element principles. A higher-order biquadratic approximation is introduced. Several test problems are computed to verify the algorithms. Adaptive gridding in two and three dimensions using quadrilateral and hexahedral elements is developed and verified. Adaptation is shown to provide CPU savings of a factor of 2 to 16, and biquadratic elements are shown to provide potential savings of a factor of 2 to 6. An analysis of the dispersive properties of several discretization methods for the Euler equations is presented, and results allowing the prediction of dispersive errors are obtained. The adaptive algorithm is applied to the solution of several flows in scramjet inlets in two and three dimensions, demonstrat­ ing some of the varied physics associated with these flows. Some issues in the design and implementation of adaptive finite element algorithms on vector and parallel computers are discussed.

Keywords

Dissipation computational fluid dynamics computer dynamics fluid dynamics physics

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-322-87879-3
  • Copyright Information Springer Fachmedien 1991
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-528-07632-0
  • Online ISBN 978-3-322-87879-3
  • Series Print ISSN 1612-2909
  • Series Online ISSN 1860-0824
  • About this book
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