Upwind and High-Resolution Schemes

  • M. Yousuff Hussaini
  • Bram van Leer
  • John Van Rosendale

Table of contents

  1. Front Matter
    Pages I-X
  2. ICASE and the History of High-Resolution Schemes

  3. A Brief Introduction to High-Resolution Schemes

  4. Riemann Solvers and Upwind Schemes

  5. Second-Order TVD Schemes

    1. Front Matter
      Pages 91-93
    2. G. D. van Albada, B. van Leer, W. W. Roberts Jr.
      Pages 95-103
    3. Stanley Osher, Sukumar Chakravarthy
      Pages 104-133
    4. Stanley Osher
      Pages 134-148
    5. R. C. Swanson, Eli Turkel
      Pages 167-181
  6. Essentially Non-oscillatory Schemes

    1. Front Matter
      Pages 183-186
    2. Ami Harten, Stanley Osher
      Pages 187-217
    3. Ami Harten, Bjorn Engquist, Stanley Osher, Sukumar R. Chakravarthy
      Pages 218-290
    4. Ami Harten
      Pages 291-327
    5. Wei Cai, David Gottlieb, Chi-Wang Shu
      Pages 375-396
    6. Wei Cai, David Gottlieb, Ami Harten
      Pages 397-417
  7. Multidimensional Schemes

  8. Back Matter
    Pages 585-588

About this book


One of the major achievements in computational fluid dynamics has been the development of numerical methods for simulating compressible flows. These methods combine higher-order accuracy in smooth regions, with sharp, oscillation-free representation of embedded shocks, and are now known as "high-resolution schemes". This volume collects in one place many of the most significant papers in the development of high-resolution schemes as occurred at ICASE, together with introductions from the editors, written from the modern vantage point. Chapter I covers the early development of approximate Riemann solvers in the context of monotonic schemes. Chapter II continues with papers dealing with second-order total-variation-diminishing (TVD) schemes. Chapter III presents papers which show the historical development of total-variation-bounded (TVB) schemes at ICASE. Finally, Chapter IV collects papers on inherently multidimensional schemes, which preserve the attractive features of their one-dimensional predecessors.


Oscillation compressible flows conservation conservation law dynamics entropy fluid dynamics high-resolution schemes hypersonic flows numerical analysis numerical method paper plasma dynamics solution wave propagation

Editors and affiliations

  • M. Yousuff Hussaini
    • 1
  • Bram van Leer
    • 2
  • John Van Rosendale
    • 3
  1. 1.Program in Computational Science & EngineeringFlorida State UniversityTallahasseeUSA
  2. 2.Department of Aerospace EngineeringUniversity of MichiganAnn ArborUSA
  3. 3.ICASENASA Langley Research CenterHamptonUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-64452-8
  • Online ISBN 978-3-642-60543-7
  • Buy this book on publisher's site