Single-component Euler equations are solved with finite-difference WENO methods very well. Now I'm trying to apply them to gas mixtures (with aim to reacting mixtures).

While searching for extension to multi-component equations, I find very little on finite-difference WENO methods for them, mostly there are finite-volume formulations. One paper even containts the phrase: "... Care must then be taken when solving the resulting governing equations. They must be cast in a finite-volume framework and discretized with a non-oscillatory spatial and temporal method, with the primitive state variables, rather than the conservative ones, spatially reconstructed".

Is it impossible to achieve all needed equilibriums (mass, momentum, energy) across interfaces in finite-difference formulation? If it is possible, are there any widely accepted FD WENO methods for gas mixtures?

  • $\begingroup$ Can you state the equations you want to solve? $\endgroup$ Commented Dec 18, 2017 at 14:15
  • $\begingroup$ Note that the motivation behind the methods in that paper is for a non-oscillatory, shock capturing scheme which is discretely conservative. If those properties don't matter in your problem space, you can probably do what you want. $\endgroup$
    – origimbo
    Commented Dec 18, 2017 at 15:22

1 Answer 1


Check this out: Wang, W., Shu, C.W., Yee, H.C., Kotov, D.V. and Sjögreen, B., 2015. High order finite difference methods with subcell resolution for stiff multispecies discontinuity capturing. Communications in Computational Physics, 17(2), pp.317-336.

  • $\begingroup$ Why this reference suggested? What does it provide? $\endgroup$
    – nicoguaro
    Commented Dec 29, 2017 at 20:56
  • $\begingroup$ Methodology for FD WENO5-LLF for solving advection and Euler equations with multiple species and multiple reactions. However, the paper is mostly focused on the subcell resolution approach (solve the correct propagation speed of discontinuities with coarse meshes but without resolving the detonation peak and reaction zone). $\endgroup$
    – Eduardo
    Commented Dec 30, 2017 at 19:33
  • $\begingroup$ Add those details to your answer then 😉 $\endgroup$
    – nicoguaro
    Commented Dec 30, 2017 at 19:41

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