You certainly can substitute the equation of state directly and eliminate density if this is the only CFD you will ever do.
General purpose solvers will use various approaches because they want their code to solve many different types of problems, i.e. they want the same code to be easily switchable from incompressible idea gas to classical ideal gas with just the push of a button. |
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Do you have some specific reason for that formulation? For small temperature variation, the Bousinnesq model works fine. Otherwise have a look to the low Mach formulations. |
The code available to me uses the Boussinesq model, but the temperature range I encounter in my scenario is very large. From what I understand, Boussinesq assumes the density variation due to temperature is small, and thus approximately linear. This is not the case for me.
I chose to use the incompressible ideal gas model instead, as the pressure variation in my problem is very small. |
I am confused why you are asking how to numerically solve something if you already have a working code. What even is the question? I can't validate the performance of your code for you.
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Apart from the versatility of being able to switch between models, what are other benefits with applying the EOS separately from the NSEs? Is the implementation in the main solving loop more straightforward? Also, are there any additional modelling errors as opposed to substituting the EOS directly? Thanks, |
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The current code I have is purely incompressible, density is constant. I am not sure if I can include density as a field straight away, especially during the step which solves for pressure as a Poisson equation. I am still looking into this. |
What you have is constrained coupled system of equations. You have your transport equations plus the EOS (the constraint).
When you hard-code the constraint into the transport equation you also force the errors/correctors to be forcibly propagated. When these correctors are large, they can cause the problem to diverge. A similar issue also occurs in the pressure-velocity coupling problem when you solve a Poisson problem for pressure. Not propagating them can mean you need more sweeps to converge (until the correctors are propagated throughout the domain). There is always a tradeoff between stability and convergence rate. Hence, there are endless permutations of solvers available. For example, sometimes you start cranking and end up with a negative temperature, now you have a negative density and you're screwed. |
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I will have to look further into this. Thanks for your advice |
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I never said anything about inviscid.
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My scenario is boundary layer flow over a flat surface, with temperature dependent heat release. I am not simulating combustion with species transport. |
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