Discretely nonreflecting boundary conditions for linear hyperbolic systems

Clarence W. Rowley, Tim Colonius

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


Many compressible flow and aeroacoustic computations rely on accurate nonreflecting or radiation boundary conditions. When the equations and boundary conditions are discretized using a finite-difference scheme, the dispersive nature of the discretized equations can lead to spurious numerical reflections not seen in the continuous boundary value problem. Here we construct discretely nonreflecting boundary conditions, which account for the particular finite-difference scheme used, and are designed to minimize these spurious numerical reflections. Stable boundary conditions that are local and nonreflecting to arbitrarily high order of accuracy are obtained, and test cases are presented for the linearized Euler equations. For the cases presented, reflections for a pressure pulse leaving the boundary are reduced by up to two orders of magnitude over typical ad hoc closures, and for a vorticity pulse, reflections are reduced by up to four orders of magnitude.

Original languageEnglish (US)
Pages (from-to)500-538
Number of pages39
JournalJournal of Computational Physics
Issue number2
StatePublished - Jan 20 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Artificial boundary conditions
  • Euler equations
  • Finite difference
  • High-order-accurate methods
  • Nonreflecting boundary conditions


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