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mass balance over a cell _ urgent help

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Old   August 4, 2007, 08:28
Default mass balance over a cell _ urgent help
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I am a little bit confused due to the result i am getting using a finite volume SIMPLE like code.

Considering an incompressible code, for a fully converged and (simplifying assuming steady state condition) I think the continuity equation should be fulfilled at each cell, either as the finite difference or finite volume form.

so i expect (u(i+1,j)-u(i,j))/(0.5*(dx(i+1)+dx(i)) + (v(i,j+1)-vg(i,j))/(0.5*(dy(i+1)+dy(i)) = 0 at each cell;

But my code gives me this value for the corrected u and v only.

I used non staggered grid, but even if I use the staggered I think that wouldn't be different.

I am just solving the flat plate laminar flow problem, so there is no complex flow here. For instance I decreased the residual criterion but not helped. I also increased the no iteration for the momentum the pressure routines still no difference.



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Old   August 4, 2007, 10:12
Default Re: mass balance over a cell _ urgent help
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My understanding is that SIMPLE works sort of like a predictor-corrector for each iteration.

In the first step, an improved estimate for the velocities is calculated - 'improved' meaning that the answers are a bit closer to those that satisfy the momentum balances.

In the second step, the pressures and velocities are adjusted so that mass conservation is solved. But, since the second step changes the momentum-satisfying velocities, the momentum equations are a bit out of balance (but hopefully closer than before the first step).

This dance is repeated as needed until both mass and momenta balances are within tolerance.

I haven't checked your continuity equation in detail, but I think what you describe is to be expected. You'll have agreement in momentum and continuity equations only after you've cycled through both sets of equations many times.

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Old   August 5, 2007, 00:32
Default Re: mass balance over a cell _ urgent help
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Thankyou sir, your quick valued response helped me to look thru what I did, the following form:

(u(i+1,j)-u(i,j))/(0.5*(dx(i+1)+dx(i)) + (v(i,j+1)-v(i,j))/(0.5*(dy(i+1)+dy(i)) = 0

should have better been written as (for my case):

(u(i+1,j)-u(i-1,j))*(0.25*(y(i+1)-y(i-1)) + (v(i,j+1)-v(i,j-1))*(0.25*(y(i+1)-y(i-1)) = 0

i.e. FV form and taking as averages.

Best regards,


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