# Is it possible to solve multi-component Euler equations with finite-difference WENO m

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 December 18, 2017, 07:56 Is it possible to solve multi-component Euler equations with finite-difference WENO m #1 Member   Oleg Sutyrin Join Date: Feb 2016 Location: Russia Posts: 41 Rep Power: 7 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?

December 18, 2017, 08:01
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 5,803
Rep Power: 62
Quote:
 Originally Posted by OlegSutyrin 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?

My opinion is that the Euler equations can produce non-regular solutions and the FD discretization works on the differential form of the equations that is not suitable on singularities. Conversely, the FV discretization adopts the integral form and differentiation of the fluxes is no longer required.

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