Two-Dimensional Riemann Solver for Euler Equations of Gas Dynamics

M. Brio, A. R. Zakharian, G. M. Webb

Research output: Contribution to journalArticlepeer-review

90 Scopus citations


We construct a Riemann solver based on two-dimensional linear wave contributions to the numerical flux that generalizes the one-dimensional method due to Roe (1981, J. Comput. Phys. 43, 157). The solver is based on a multistate Riemann problem and is suitable for arbitrary triangular grids or any other finite volume tessellations of the plane. We present numerical examples illustrating the performance of the method using both first- and second-order-accurate numerical solutions. The numerical flux contributions are due to one-dimensional waves and multidimensional waves originating from the corners of the computational cell. Under appropriate CFL restrictions, the contributions of one-dimensional waves dominate the flux, which explains good performance of dimensionally split solvers in practice. The multidimensional flux corrections increase the accuracy and stability, allowing a larger time step. The improvements are more pronounced on a coarse mesh and for large CFL numbers. For the second-order method, the improvements can be comparable to the improvements resulting from a less diffusive limiter.

Original languageEnglish (US)
Pages (from-to)177-195
Number of pages19
JournalJournal of Computational Physics
Issue number1
StatePublished - Feb 10 2001


  • Conservation laws
  • Godunov-type schemes
  • Two-dimensional Riemann problem

ASJC Scopus subject areas

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


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