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Hooman December 15, 2011 12:22

Near compressible fluid - denstiy-based solver
My problem involves the numerical analysis of a fluid (liquid) with low compressibility. I have varied the density through out my formulations. From how my equations were formed (with the variable density) I naturally used a denistiy-based solver. However I have just realized that for near compressible flows (low Mach number) a pressure-based solver is more efficient. I have found a few references as well. However my problem is also isothermal. I was wondering if anyone knew of any references where an isothermal near compressible flow is being solved using a density-based solver. Also if you knew any example of situations where this might occur, please let me know.

swetkyz December 15, 2011 12:56


If your fluid is only slightly compressible, a pressure based solver will still be applicable. You may also be able to solve the flow as incompressible since your fluid is a liquid and it is at a low speed.

Hooman December 15, 2011 16:08

yeah I know that. I was wondering if you knew of any isothermal examples?

Martin Hegedus December 16, 2011 23:37

Wouldn't the equation of state for the liquid state that if you have constant density and temperature, then the pressure would also be constant?

Hooman December 17, 2011 11:59

I'm using a density-based method, so the density varies.

Martin Hegedus December 17, 2011 14:48

Hi Hooman

Just to be clear, your flow is low speed isothermal. I'm not sure of the equation of state of your liquid, but I'm going to assume that it has the same form as the ideal gas law, i.e. p=k*rho*T. If this is the case, then p/p_inf=rho/rho_inf. As the Mach number decreases, and your pressure and density flucuations decrease, your system becomes stiff. This is a bigger issue with the right hand side than, I believe, how one solves it. Yes, solving a low Mach number problem may take more time. That's an issue with the solver. Unfortunately, the answer you converge on could be bad. That's an issue with the right hand side. Two things you can do. First, use Mach number preconditioning. Or, if your range of Mach numbers is small, increase your Mach number slightly. A Mach number of 0.001 and 0.01 or even 0.1 should produce similar answers, as long as the max Mach number in the field remains below 0.3 to 0.4.

I'm not aware of any isothermal examples. This is not to say they don't exist. It's just not my area of experience.

Hooman December 17, 2011 15:16

Thanks very much Martin.

Martin Hegedus December 17, 2011 21:04

Oh, when I said things would be similar, I meant cp and V/V_inf. Sorry. To get your true pressure, you'll need to take the cp value and multiply it by your true velocity, not the scaled up velocity resulting from the scaled up Mach number. To get your true density you'll need to use your equation of state. Of course I don't know your exact problem, so be careful with this idea of scaling up Mach number.

vicarious December 19, 2011 04:03

Dear Hooman,
if you are solving a low Mach number flow ( approximately lower than 0.3) you better consider incompressible and use pressure based solver, becuase the density based is not a high speed solver and one of the important issue caused by density based is the convergency, it means that your residuals may not drop and oscillate constantly.
I hope this would help. and by the way where are you from?
best regards.

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