The numerical simulation of two-dimensional fluid flow with strong shocks

Paul Woodward, Phillip Colella

Research output: Contribution to journalReview articlepeer-review

2267 Scopus citations


Results of an extensive comparison of numerical methods for simulating hydrodynamics are presented and discussed. This study focuses on the simulation of fluid flows with strong shocks in two dimensions. By "strong shocks," we here refer to shocks in which there is substantial entropy production. For the case of shocks in air, we therefore refer to Mach numbers of three and greater. For flows containing such strong shocks we find that a careful treatment of flow discontinuities is of greatest importance in obtaining accurate numerical results. Three approaches to treating discontinuities in the flow are discussed-artificial viscosity, blending of low- and high-order-accurate fluxes, and the use of nonlinear solutions to Riemann's problem. The advantages and disadvantages of each approach are discussed and illustrated by computed results for three test problems. In this comparison we have focused our attention entirely upon the performance of schemes for differencing the hydrodynamic equations. We have regarded the nature of the grid upon which such differencing schemes are applied as an independent issue outside the scope of this work. Therefore we have restricted our study to the case of uniform, square computational zones in Cartesian coordinates. For simplicity we have further restricted our attention to two-dimensional difference schemes which are built out of symmetrized products of one-dimensional difference operators.

Original languageEnglish (US)
Pages (from-to)115-173
Number of pages59
JournalJournal of Computational Physics
Issue number1
StatePublished - Apr 1984
Externally publishedYes

Bibliographical note

Funding Information:
During the course of this work we have benetitted from stimulating discussions with many people. We would particularly like to acknowledge the enlightening discussions we have had with Drs. S. Zalesak and B. van Leer. This work was performed in part under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory and by the Lawrence Berkeley Laboratory under Contract W-7405ENG-48. Partial support was also provided by the Office of Basic Energy Sciences of the U.S. Department of Energy.


Dive into the research topics of 'The numerical simulation of two-dimensional fluid flow with strong shocks'. Together they form a unique fingerprint.

Cite this