On the Use of the HLL-Scheme for the Simulation of the Multi-Species Euler Equations

  • Phillip Berndt
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 78)


The HLL approximate Riemann solver is a reliable, fast and easy to implement tool for the under-resolved computation of inviscid flows. When applied to multi-species flows, it generates pressure oscillations at material interfaces. This is a well-known behaviour of conservative solvers and has been addressed as a problem by several authors before. We show that for this particular solver, the generation of pressure oscillations can be desired and is consistent with the underlying physics.


Mass Fraction Euler Equation Riemann Problem Pressure Oscillation Contact Discontinuity 
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This work was funded by the German Research Foundation (DFG) as part of the collaborative research center (SFB) 1029 “Turbin—Substantial efficiency increase in gas turbines through direct use of coupled unsteady combustion and flow dynamics”. It is part of doctoral studies supervised by Rupert Klein at the Geophysical Fluid Dynamics group at Freie Universität Berlin.


  1. 1.
    Abgrall, R., Karni, S.: Computations of compressible multifluids. J. Comput. Phys. 169, 594–623 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Einfeldt, B.: On godunov-type methods for gas dynamics. SIAM J. Numer. Anal. 25(2), 294–318 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Einfeldt, B.: A intuitionistic approach to the fluid continuum. (2012) Accessed 7 Feb 2014
  4. 4.
    Harten, A., Lax, P., van Leer, B.: On upstream differencing and godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25(1), 35–61 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Larrouturou, B.: How to preserve the mass fractions positivity when computing compressible multi-component flows. J. Comput. Phys. 95, 59–84 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Larrouturou, B., Fezoui, L.: On the equations of multi-component perfect or real gas inviscid flow. Nonlinear Hyperbolic Problems, Lecture Notes in Math. 1402, 69–98 (1989)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Tadmor, E.: Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comput. 43(168), 369–381 (1984)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Freie Universität BerlinDepartment of Mathematics and Computer ScienceBerlinGermany

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