# Continuity Equation

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 October 25, 2007, 03:42 Continuity Equation #1 selim Guest   Posts: n/a Hi, I ran a simulation in a CFD code. When I monitor the continuity equation in the computational domain I see some regions are much greater than zero? Is there something wrong or could it like that in a numerical simulation? I am quite new to CFD Thanks, selim

 October 25, 2007, 04:10 Re: Continuity Equation #2 mic Guest   Posts: n/a Do you mean that you are monitoring the residuals of the continuity equation? If this is the case, the residuals are greater than zero but must be of the order of e-3, e-5 (depends on the code you're using and the simulation type)

 October 25, 2007, 04:17 Re: Continuity Equation #3 selim Guest   Posts: n/a Thanks for the answer I am performing an incompressible cold flow simulation. What is residual? (Continuity is not zero at each point of the domain? e.g delta(u)/delta(x) +delta(v)/delta(y)=0?) or not? At some points this exceeds 10,-10 Any further suggestions , Kind regards, selim

 October 25, 2007, 05:29 Re: Continuity Equation #4 Hatef Guest   Posts: n/a Hi Residual means the diffrence between two last iterations. for instance if you are monitoring the continuity which is simply the mass flow rate and you are getting a resdiual of the order of 10e-10 which is really a good order... then it means that the difference in result of last two iterations is of order of 10e-10. this is not a very accurate definition but it helps you to get some idea about residual.

 October 25, 2007, 06:25 Re: Continuity Equation #5 mic Guest   Posts: n/a Yes, what Hatef says may help you understand the problem. The equation that you have to solve is the one that you mention, but this is not directly integrated. And the residual is the indication of how good is your solution E-10 is really wonderful! What is important, is to verify that the massflow that enters your domain is equal to the mass flow that exits from your domain.

 October 25, 2007, 09:01 Re: Continuity Equation #6 selim Guest   Posts: n/a 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 u-momentum and v-momentum 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, 09:49 Re: Continuity Equation #7 momentum_waves Guest   Posts: n/a Perhaps you have a leak in your system? Seriously, though, do you have any mass source terms in your model? mw...

 October 25, 2007, 10:48 Re: Continuity Equation #8 agg Guest   Posts: n/a The equations must be satisfied at each and every point/control volume, not just globally. When you are evaluating the continuity equation (du/dx+dv/dy), make sure you are computing the derivatives correctly (depending on whether variables are cell centererd or face centered etc.)

 October 26, 2007, 01:05 Re: Continuity Equation #9 Shuo Guest   Posts: n/a Does the continutity condition reach a very small value for flows that are unsteady or periodic in addition to steady flows?

 October 26, 2007, 09:01 Re: Continuity Equation #10 ag Guest   Posts: n/a If the flow is incompressible then the divergence-free condition should be enforced whether the flow is steady or unsteady. In an incompressible, segregated solver div(u) = 0 needs to be satisfied locally at the end of each iteration. This leads to the pressure corrections in terms of the intermediate veloctiies, and basically ensures that continuity is also satisfied.

 October 26, 2007, 18:06 Re: Continuity Equation #11 shuo Guest   Posts: n/a How about compressible steady and unsteady flow?

 October 26, 2007, 18:08 Re: Continuity Equation #12 shuo Guest   Posts: n/a Also is continuity satisfied for finite difference schemes locally?

 October 27, 2007, 15:14 Re: Continuity Equation #13 ag Guest   Posts: n/a Continuity is always satisfied, but for a compressible flow the divergence is not zero. In a segregated scheme one would solve for the density variation using the continuity equation after computing the pressure corrections (at least that is one approach).

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