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Weak form of Naveir Stokes equations in COMSOL.
Posted Oct 15, 2018, 8:22 a.m. EDT Fluid & Heat, Heat Transfer & Phase Change, Computational Fluid Dynamics (CFD) 6 Replies
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If a physical model is not listed in the wizard, we can use Comsol's weak form to enter PDE's (governing equations of a system) in their weak form. How can it be done ?
for example: 2 equations of momentum (2D flow) coupled with continuity equation
ρ v.∇v=−∇p+μ∇2v
∇.v=0
This model (well-known) is for calculating velocity and pressure fields. How to make weak form and then enter to comsol for solution?. Your help will be strongly appriciated.
-------------------Munir
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The Navier Stokes equation is available from the Model Wizard. In the Select Physics panel, select Fluid Flow > Single-Phase Flow > Laminar Flow .
Best regards,
Jeff
-------------------Jeff Hiller
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Thank you so much for your quick reply. The problem is that I am solving these equations for two phase (gas-fluid) flow and I need to enter comsol my modified equations, such that I solve for velocity and pressure. Now I do not know the mechanisom to solve for three dependent variaables (u,v and p), as I need to write three coupled weak form pdes. Please, how to solve this equations as coupled pdes?.
-------------------Munir
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The software also supports multiphase flow with the CFD Module, see https://www.comsol.com/blogs/which-multiphase-flow-interface-should-i-use/ for an introduction to those interfaces.
Generally speaking, setting up multiphase flow outside of the pre-implemented physics interfaces is far from trivial, as you have to deal not only with formulating the equations in the weak form, but also with mixed interpolation, stabilization, etc, so that you'll want to use a pre-implemented interface if at all possible. With that said, there is a blog series on the weak form available starting here, though I must say that it does not address those secondary issues specific to flows that I just mentioned.
Best,
Jeff
-------------------Jeff Hiller
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Please, I cannot understand from your blogs. Can you send or post blogs understandable for two phase flow using NS equations, such as
https://cn.comsol.com/blogs/implementing-the-weak-form-in-comsol-multiphysics/. or Lab 1: Equation-based Modeling in Comsol Multiphysics
for the mentioned equations. Thanks.
-------------------Munir
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Hello Bacha Munir. If you use just the main module it includes the single phase, Laminar flow, form of the Navier Stokes equations; i.e,, Fluid Flow > Single-Phase Flow > Laminar Flow as Jeff Hiller stated. Within the model tree, you can view all the equations as they appear in weak form (click on view equations in the options). This defines how COMSOL solves the Navier Stokes equations in weak form which was your original question. If you want to do two-phase without purchasing the CFD module, or just want to solve it a different way yourself, you can duplicate the equations as they are by giving a different name to the 2nd set of equations for liquid and gas. Then you will need to define the interaction between gas and liquid yourself. You should be able to figure out the weak form of these additional terms by examining the liquid and gas equations yourself. Hope this helps.
-------------------James D. Freels, Ph.D., P.E.
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Thank you Sir James D. Freels for your kind suggissions. I almost found the solution of that equations on the web. But now I have some problem in implementation the weak constraints on the air liquid interface directly using COMSOL. Do you have some experiance in weak constraints, how to implement?. I want to applying weak constraints directly to air liquid interface, which requaired for my paper under study. Please share. Thanks.
-------------------Munir