Euler equation with finite volume method without division

tkk88 · June 25, 2014, 16:33

Hello,

I want to simulate the flow of a fluid using the euler equations and the finite volume method. Since the aim is to do this on hardware I don't want to use a division in the algorithm. Now I'm wondering if there's a algorithm which doesnt need a division in it.

At the moment my state variables are a combination with rho, like speed times rho or energy times rho, but for the calculation I need the e.g. speed^2 times rho.

Can anybody help?

Thanks

mprinkey · July 29, 2014, 02:43

You can rewrite the Euler equations in primitive variables instead of conserved variables and that will allow you to compute almost all quantities without division, but I think that you will always need rho^-1 or something similar no matter how you manipulate the equations. The momentum equation includes the pressure and that term is scaled by the inverse of density.

Another option may be to model the Euler equations with Lattice Boltzmann. You may be able to find an LB update can be done without division. Note that you'll need to do some significant post processing (that may involve division) to turn the LB results into rho, U, and e.

Note across the board, Euler equations are difficult to solve due to their admission of genuinely discontinuous solutions--there is no viscosity to damp things out. The solvers in the text books are there for a reason--they work. Deviating from that well traveled path may result in nothing but a huge waste of time. Make sure that you read up extensively so you are aware of the possible pitfalls (like negative density, etc) and some of the tricks (like flux evaluations and artificial dissipation, etc).

Good luck.

June 25, 2014, 16:33	Euler equation with finite volume method without division	#1
tkk88 New Member Dennis Brauch Join Date: Jun 2014 Posts: 2 Rep Power: 0	Hello, I want to simulate the flow of a fluid using the euler equations and the finite volume method. Since the aim is to do this on hardware I don't want to use a division in the algorithm. Now I'm wondering if there's a algorithm which doesnt need a division in it. At the moment my state variables are a combination with rho, like speed times rho or energy times rho, but for the calculation I need the e.g. speed^2 times rho. Can anybody help? Thanks

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July 29, 2014, 02:43		#2
mprinkey Senior Member Michael Prinkey Join Date: Mar 2009 Location: Pittsburgh PA Posts: 363 Rep Power: 25	You can rewrite the Euler equations in primitive variables instead of conserved variables and that will allow you to compute almost all quantities without division, but I think that you will always need rho^-1 or something similar no matter how you manipulate the equations. The momentum equation includes the pressure and that term is scaled by the inverse of density. Another option may be to model the Euler equations with Lattice Boltzmann. You may be able to find an LB update can be done without division. Note that you'll need to do some significant post processing (that may involve division) to turn the LB results into rho, U, and e. Note across the board, Euler equations are difficult to solve due to their admission of genuinely discontinuous solutions--there is no viscosity to damp things out. The solvers in the text books are there for a reason--they work. Deviating from that well traveled path may result in nothing but a huge waste of time. Make sure that you read up extensively so you are aware of the possible pitfalls (like negative density, etc) and some of the tricks (like flux evaluations and artificial dissipation, etc). Good luck.