L2Roe: A low-dissipation version of Roe's approximate Riemann solver for low Mach numbers

Research output: Contribution to journalArticle


A modification of the Roe scheme called L2Roe for low dissipation low Mach Roe is presented. It reduces the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is achieved by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime. Furthermore, the analysis allows a comparison with two other schemes that employ different scaling of discrete velocity jumps, namely, LMRoe and a method of Thornber et al. To this end, we present for the first time an asymptotic analysis of the last method. Numerical tests on cases ranging from low Mach number (M∞=0.001) to hypersonic (M∞=5) viscous flows are used to illustrate the differences between the methods and to show the correct behavior of L2Roe. No conflict is observed between the reduced numerical dissipation and the accuracy or stability of the scheme in any of the investigated test cases.


  • Kai Osswald
  • Alexander Siegmund
  • Philipp Birken
  • Volker Hannemann
  • Andreas Meister
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computational Mathematics


  • Riemann solvers, finite volume methods, low mach, asymptotic analysis, numerical dissipation
Original languageEnglish
JournalInternational Journal for Numerical Methods in Fluids
Early online date2015 Sep 24
Publication statusPublished - 2015
Publication categoryResearch

Bibliographic note

The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)