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June 13, 2006, 07:20 
dear Friends,
I have highly

#1 
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rafal zietara
Join Date: Mar 2009
Location: Manchester, UK
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dear Friends,
I have highly nonlinear problem that I want to solve in OF. please help me with implementation. This problem is in steady state derived from system where three forces act on fluid (capillary, gravity and viscosity forces). I simplified problem to be tackable numerically (the equation is dimmensionless form). The continuity equation is expressed as: div(A*u)=0 (1) and u as: u=  K/sqrt(A) grad A  g/mag(g) A + v (2) where: (variables given in the order name  meaning, unit; type of variable(field) in OF) u  liquid velocity, dimless; volVectorField defined on mesh v  gas velocity, dimless; volVectorField defined on mesh K  constant , m^1 ; dimensionedScalar A  area , dimless; volScalarField defined on mesh g  gravity const. , ms1 ; dimensionedVector From those two equations i would like to calculate A. when i plug (2) to (1), i get: div(K*sqrt(A) grad A  g/mag(g) A^2 + A v )=0 (3) if we try to expand div we get:  0.5K/sqrt(A) grad A grad A  K*sqrt(A) laplacian(A)  2A g/mag(g) grad(A) + A div(v) + v grad(A)=0 (4) as you see in equation (4) we have almost no implicit terms. How to tackle the problem? How to implement this in OpenFoam? Where to look for a solutions of a similar problems? Any suggestions appreciated. Thank you in advance. /Rafal one thing more Significance of terms in equation (3). ( K*sqrt(A) grad A)  plays key role near 2 out of 5 of the boundaries in the rest of the domain neglegible. ( g/mag(g) A^2)  significant in most of the domain A v  an order less than previous 

June 13, 2006, 17:32 
Hi Rafal!
At first the equa

#2 
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Bernhard Gschaider
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Hi Rafal!
At first the equations looked to me like something I have seen before (two phase flow in porous media), but then again they didn't. Questions I have at a first glance:  dimensionless velocities? (I know physicicsts do it all the time, usually by normalizing with c, but engineers?)  the relative densities of liquid and gas go into K?  which leads to the next question: both (gas and liquid) are incompressible?  in (2) you wanted to write K/(sqrt(A) grad(A))? Otherwise I can't match the dimensions.  You are looking for a stationary solution? I think it can be done in OF, but I'm not aware of a solver in the distribution that is similar to your problem.
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June 14, 2006, 07:02 
Hi Bernhard,
Thanks for ans

#3 
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rafal zietara
Join Date: Mar 2009
Location: Manchester, UK
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Hi Bernhard,
Thanks for answer. I didn't want to provide to much details about the system not to complicate the problem to much. Good intuition. Those equation describe motion of liquid in a soap foam (drainage of water from a foam due to gravity), which is similar to flow in porous media in a sens that we have also channels in which our fluid flows through static material. In this case material consist of close packed air bubbles moving upwards (velocity of gas v in eq.(2)). Channels are located in the junction of three bubbles. First of all word of apology. I mistook dimension of K which is m (and NOT m1 as i wrote above), sorry for confusion. To give you more details about the equation and provide more comprehensive description of the problem i have prepared it in attachment with derivation of equations. derivation.dvi Velocity of gas (v) i assumed is influenced by water drainage. v is calculated separately (done this before). in this discussion we can assume is known. I assume also that both fluids (gas,liquid) are incompressible. I am looking for steady state solution. Why normalisation to get dimensionless velocities? A (crosssection area through channel) in case of foam is in order of 105 with velocities in the order of 101 may give numerical problems. I do not stick to this normalization it is only idea i read somewhere about. If it is a problem i can remove it. Do not hasitate to ask for more details. All help is appreciated. Thank you in advance for all suggestions and i invite everyone to discussion. rafal 

June 14, 2006, 07:09 
IS: Velocity of gas (v) i assu

#4 
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rafal zietara
Join Date: Mar 2009
Location: Manchester, UK
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IS: Velocity of gas (v) i assumed is influenced by water drainage
SHOULD BE: Velocity of gas (v) i assumed is NOT influenced by water drainage 

April 24, 2008, 09:11 
hi all,
i am supposed to modi

#5 
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davey david
Join Date: Mar 2009
Posts: 54
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hi all,
i am supposed to modify a code into a dimensionless one.how do i go about it? thanks in advance 

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