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October 25, 2007, 05:16 
Continuity Equation

#1 
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Hi,
I wonder why in CFX the continuity equation is not satisfied? At some points the value of (Velocity u.Gradient X+Velocity v.Gradient Y) is order of 10,20 How should I trust the results from CFX? Thanks, Selim 

October 25, 2007, 05:55 
Re: Continuity Equation

#2 
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May be you use compressible model in your calculation?


October 25, 2007, 05:58 
Re: Continuity Equation

#3 
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Hi
No, it is incompressible the density is constant Thanks, selim 

October 25, 2007, 06:37 
Re: Continuity Equation

#4 
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The conservation principals are all respected in CFX and other CFD codes. The problem is that you have to transform the conservation equations in a way that the PC can solve them. Have a look at the Wiki on this website and to the numerical methods in particular: "The objective of all discretization techniques (Finite Difference, Finite Element, Finite Volume, Boundary Element...) is to devise a mathematical formulation to transform each of these terms into an algebraic equation. Once applied to all control volumes in a given mesh, we obtain a full linear system of equations that needs to be solved". To verify that your simulation is good first of all have a look at the residuals of the solved equations(< E3, E4) and check the continuity balance (mass flow in = mass flow out). Good luck


October 25, 2007, 09:02 
Re: Continuity Equation

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Hi, I undertstand the numerics behind CFD (Finite volume..) But actauuly what I need : I took some grid points on the rectangular domain and when I write umomentum and vmomentum equations for this grid points, the result is quite interesting (my equations are not nondimensionalized but values are not exceptable) My question is quite simple? CFD codes give us results such that we cannot apply navier stokes equations in every point. It is satisfied globally(like an overall avarage) and what we see as residuals from Solver is that avarage residuals?
Is there a way to extract points (grid points) such tjhat NS is applicable to that points? May be I am wrong Please correct me Thanks Selim 

October 25, 2007, 10:49 
Re: Continuity Equation

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The procedure to calculate the Navier Stokes equations is not so simple. How do you solve the equations? It doesn't make much sense to calculate the NS in a point, it makes more sense to calculate the values across an elemnt, cell, we're talking about fluxes, conservation etc... How do you take into consideration the turbulence terms in the equation? When a code calculates the variables in a point this point may be the centroid of the cell or the node of the cell. There are the shape functions that transform these values..If the cell is distorted how do you calculate the normal to that cell? BTW are you using tetra or hexa elements? And there are also other problems to take into account. Anyway the residuals that the solver calculates and indicates in the monitor are the averaged residuals (usually weightened, see the manual). You may let CFX write the residual value for each node (not the centroid of the cell), but you have to set this in the Pre, before solving the analysis.


October 25, 2007, 14:54 
Re: Continuity Equation

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Take a look at the discretization of the NS equations, you will see that that each control volume satisfy conservation of mass and momentum. The algebraic equation of a CV consists of contributions from all the CV faces (or explicitly neighboring CVs). AN algebraic eq. (for mass or momentum) for a CV reads:
\sigma A_nb phi_nb + A_P phi_P = Q_P where A is the coefficient matrix, Q the source term phi the unknown, and indices 'nb' and P for neighbours and that particular CV, respectively. Your mistake is that you are trying to apply conservation equation like this: A_P phi_P = Q_P and this can not give you right results. In order to check the conservation locally you have to known the discretization schemes and datastructure in CFX and I think this is not open to a user. There are other indirectways to check this however these approachs are very demanding and timeconsuming. If it is not absolutely necessary for you to check local conservation, you should not waste your time and simply accept it. I hope this will help you understand your mistake. KUMAR 

October 26, 2007, 02:56 
Re: Continuity Equation

#8 
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Hi,
Thanks for the comments I need to extract some grid points from the domain (on a rectangular domain) which I can satisfy NS (momentum equations as well) locally on this grid points. Is there a way to get such grid points? Then I use this information for a model reduction scheme. Any further suggestions, Thanks Selim 

October 26, 2007, 10:51 
Re: Continuity Equation

#9 
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Hi I have defined a new coordinate system in CFX pre and I define my domain by new coordinate system
But in CFX post I cannot see my previously defined coordinate system. The ccordinate appearing in CFX post is its default one. May be that is the problem When using gradients(delta U/delta X)+delta V /delta Y) definition of ccordinate system is mixed? Thanks, Selim 

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