How to deal with Gravity using SIMPLE approach

Nico42 · October 11, 2018, 15:24

Hi all,

I'm trying to have a steady-state stoke code using FVM staggered grid in 2D, with incompressibility and without inertia. So a quite reduced problem.

The only "fancy" thing that is mandatory in my problem is having a gravity source term.

From what I can understand of the SIMPLE approach, you first guess P, then solve u,v, then calculate p' using mass conservation and update u,v using p' and u',v'.

In my code, I create two loops: one outer loop for momentum eqs. and one inner loop dealing with p' and u,v corrections.

When I only iterate the inner loop, I have, what I think is a good result, though once I use that solution to iterate the outer loop my solutions becomes totally wrong, and my overall pressure increases by a factor of 100-1000...

I cannot understand how to fix it, but I am pretty sure it is coming from the gravity term which makes the things complicated...

The matlab test code is attached, hope you can help me! I am getting very frustrated about it.

Thank you!

Eifoehn4 · October 12, 2018, 16:27

Dear Nico42,

add your gravity source explicitly after or before your simple approach. There should'nt be any special treatment.

Regards

Nico42 · October 12, 2018, 19:13

Dear Eifoehn4,

Thank you for your answer!

However, I don't quite get it. How can I treat the gravity forces after using the SIMPLE algorithm?

It should be part of the formulation to have correction pressure no?

In the model I am trying to make, I want buoyancy to drive the flow. This in order to model, for instance, a heavy viscous ball sinking inside a less dense viscous field, or a light ball ascending through that same viscous field.
Therefore we get a pressure within the model that depends on the weight of the material (rho*g*h) and we get a stoke pressure which depends on the flow triggered by the density contrast between the ball and the viscous medium.

The problem I am having right now is to get a correct pressure solution, as it seems that when I treat the body forces outside the pressure term it does not work between outer iterations.

Thank you again for your answer, I hope my problem is now clearer

Nico

October 12, 2018, 16:27		#2
Eifoehn4 Senior Member - Join Date: Jul 2012 Location: Germany Posts: 184 Rep Power: 14	Dear Nico42, add your gravity source explicitly after or before your simple approach. There should'nt be any special treatment. Regards __________________ Check out my side project: A multiphysics discontinuous Galerkin framework: Youtube, Gitlab.

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October 12, 2018, 19:13		#3
Nico42 New Member Join Date: Oct 2018 Posts: 2 Rep Power: 0	Dear Eifoehn4, Thank you for your answer! However, I don't quite get it. How can I treat the gravity forces after using the SIMPLE algorithm? It should be part of the formulation to have correction pressure no? In the model I am trying to make, I want buoyancy to drive the flow. This in order to model, for instance, a heavy viscous ball sinking inside a less dense viscous field, or a light ball ascending through that same viscous field. Therefore we get a pressure within the model that depends on the weight of the material (rhogh) and we get a stoke pressure which depends on the flow triggered by the density contrast between the ball and the viscous medium. The problem I am having right now is to get a correct pressure solution, as it seems that when I treat the body forces outside the pressure term it does not work between outer iterations. Thank you again for your answer, I hope my problem is now clearer Nico