Validity of very fast boussinesq time-explicit CFD solver.

ALVRM · May 5, 2023, 19:33

Hello

First time using this forum. I have been trying to build my own CFD code from scratch and have recently been testing the concept of a very quick time explicit solver for natural convection.

In the near-zero Mach range, the buoyancy force experienced in natural convection problems dominate the total forces experienced on a discretized element. Is it reasonable to completely ignore the convection and diffusion terms for zero-Mach problems? The pressure is solved implicitly in space, and therefore, guarantees a divergence free velocity field, which makes the solution incompressible in its nature.

Does anyone have a resource or white paper on this, where someone has tried to make a quick and dirty estimation of natural convection?

I would like to know the potential errors involved in doing this, and also would like to know the time step constraint required. Currently, I am using the convection term time step constraint, but that seems unnecessary considering I'm not using that term. My approach is the pressure projection method.

sbaffini · May 6, 2023, 06:34

You might want to take a look at this:

https://en.wikipedia.org/wiki/Froude_number

Typically, from non dimensional numbers, one can understand which terms are negligible.

Honestly, altough I rarely see applications with gravity, I've never seen an application where the pressure is just linked to the external source while convection and diffusion are both negligible. In particular, my doubts are:

1) Imagine gravity can be absorbed by the pressure as a conservative force (it can't properly with boussinesq), so you would have just the time derivative and the pressure gradient. What is the meaning here? How do you even update pressure? And why then the unsteady velocity term is relevant but not the others?

2) If convection and diffusion are not relevant in momentum, why are they in the temperature equation?

In my experience, there is always one among convection and diffusion which is relevant, otherwise they are both, and not none just because a source term is much higher. But you may want to check this better with someone who has direct experience.

May 5, 2023, 19:33	Validity of very fast boussinesq time-explicit CFD solver.	#1
ALVRM New Member Join Date: May 2023 Posts: 15 Rep Power: 3	Hello First time using this forum. I have been trying to build my own CFD code from scratch and have recently been testing the concept of a very quick time explicit solver for natural convection. In the near-zero Mach range, the buoyancy force experienced in natural convection problems dominate the total forces experienced on a discretized element. Is it reasonable to completely ignore the convection and diffusion terms for zero-Mach problems? The pressure is solved implicitly in space, and therefore, guarantees a divergence free velocity field, which makes the solution incompressible in its nature. Does anyone have a resource or white paper on this, where someone has tried to make a quick and dirty estimation of natural convection? I would like to know the potential errors involved in doing this, and also would like to know the time step constraint required. Currently, I am using the convection term time step constraint, but that seems unnecessary considering I'm not using that term. My approach is the pressure projection method.

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May 6, 2023, 06:34		#2
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,191 Blog Entries: 29 Rep Power: 39	You might want to take a look at this: https://en.wikipedia.org/wiki/Froude_number Typically, from non dimensional numbers, one can understand which terms are negligible. Honestly, altough I rarely see applications with gravity, I've never seen an application where the pressure is just linked to the external source while convection and diffusion are both negligible. In particular, my doubts are: 1) Imagine gravity can be absorbed by the pressure as a conservative force (it can't properly with boussinesq), so you would have just the time derivative and the pressure gradient. What is the meaning here? How do you even update pressure? And why then the unsteady velocity term is relevant but not the others? 2) If convection and diffusion are not relevant in momentum, why are they in the temperature equation? In my experience, there is always one among convection and diffusion which is relevant, otherwise they are both, and not none just because a source term is much higher. But you may want to check this better with someone who has direct experience.