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Integral of pressure constraint in dense suspension tutorial

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Hi,

I'm trying to figure out the meaning of the weak constraint on the integral of the pressure in the tutorial Two-phase modeling of a dense suspension.

Mainly, a total force is defined via Fp_tot = intop1(p) where p is the pressure and then a weak constraint (at a point) is added via test(Fp_tot); this constraint ensuring that the integral of the pressure is equal to zero.

Does anyone know why this procedure is adopted? I thought it might be because no pressure is defined as a boundary condition, but I'm unsure about this particular procedure with the addition of a weak constraint.

Thanks in advance,

Best, J

3 Replies Last Post 05.08.2015, 06:33 GMT-4
Nils Malm COMSOL Employee

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Posted: 1 decade ago 25.09.2012, 04:17 GMT-4
Hello,
As you have guessed, the reason you need to add an extra pressure constraint is that the boundary conditions in this type of model do not provide any pressure reference level. Therefore, you need to provide a reference level explicitly, one way or another.

From the theoretical point of view, it should not really matter how you specify the pressure: a point constraint in any point in the model, or an integral constraint, should in principle give the same result. However, for numerical reasons, point constraints can sometimes have bad effects on the solution, introducing visible artefacts or preventing convergence. Then an integral constraint can be a better solution, since it will distribute the reaction terms enforcing the constraint evenly over the model - which can matter in practice even if the reaction terms theoretically are zero. In this particular model, a weak integral constraint was chosen. A pointwise constraint is also, in principle, possible, but may increase the memory use.

By the way, you don't have to set the Constraint type to "User defined" and specify the constraint force expression. Just leave the constraint type at "Bidirectional, symmetric"; it will have exactly the same effect.

best regards
Nils Malm
COMSOL AB
Hello, As you have guessed, the reason you need to add an extra pressure constraint is that the boundary conditions in this type of model do not provide any pressure reference level. Therefore, you need to provide a reference level explicitly, one way or another. From the theoretical point of view, it should not really matter how you specify the pressure: a point constraint in any point in the model, or an integral constraint, should in principle give the same result. However, for numerical reasons, point constraints can sometimes have bad effects on the solution, introducing visible artefacts or preventing convergence. Then an integral constraint can be a better solution, since it will distribute the reaction terms enforcing the constraint evenly over the model - which can matter in practice even if the reaction terms theoretically are zero. In this particular model, a weak integral constraint was chosen. A pointwise constraint is also, in principle, possible, but may increase the memory use. By the way, you don't have to set the Constraint type to "User defined" and specify the constraint force expression. Just leave the constraint type at "Bidirectional, symmetric"; it will have exactly the same effect. best regards Nils Malm COMSOL AB

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Posted: 1 decade ago 25.09.2012, 07:13 GMT-4
Hi Nils,

thanks for your reply!

I posted another question related to the same tutorial with subject "Shear rate discretization in "Two-phase flow modeling of a dense suspension" tutorial". Would be possible for you to have a look at that too?

Thanks!

J
Hi Nils, thanks for your reply! I posted another question related to the same tutorial with subject "Shear rate discretization in "Two-phase flow modeling of a dense suspension" tutorial". Would be possible for you to have a look at that too? Thanks! J

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Posted: 9 years ago 05.08.2015, 06:33 GMT-4
I was going through the same tutorial and have a doubt in one of the steps. For the uniform concentration, there is no term "eps" in the expression for gamma. But in Case 2 there is a term eps added to it.

What does this eps stand for? I assumed it was the turbulent dissipation rate, but we are working in the laminar flow regime.

Also, in the equations given in the model there is a term mdc/rhod and mdc/rhoc about which there is no mention in the tutorial pdf file. Is that taken as 0.

I would also like to add small alterations to the equations in this model to suit the system im working on. Solving PDEs from scratch seems a daunting task to me. All i have got to know about modifying equations is that I should go to the equations view. Is it the week function section that I have to modify. I am not able to decipher the syntax of the expressions. Do you have links to materials I could go through to understand the syntax of week functions or anything on modifying equations in equation view?

I would be very grateful for any help.
I was going through the same tutorial and have a doubt in one of the steps. For the uniform concentration, there is no term "eps" in the expression for gamma. But in Case 2 there is a term eps added to it. What does this eps stand for? I assumed it was the turbulent dissipation rate, but we are working in the laminar flow regime. Also, in the equations given in the model there is a term mdc/rhod and mdc/rhoc about which there is no mention in the tutorial pdf file. Is that taken as 0. I would also like to add small alterations to the equations in this model to suit the system im working on. Solving PDEs from scratch seems a daunting task to me. All i have got to know about modifying equations is that I should go to the equations view. Is it the week function section that I have to modify. I am not able to decipher the syntax of the expressions. Do you have links to materials I could go through to understand the syntax of week functions or anything on modifying equations in equation view? I would be very grateful for any help.

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