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solving for denstiy and velocity implicitly

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Old   June 1, 2012, 05:49
Default solving for denstiy and velocity implicitly
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Hi,

I have been trying to solve the following systems of equations implicitly:

\frac{\partial\rho}{\partial t}=f\left(\rho,t\right)

\frac{\partial \rho v}{\partial t}=g\left(\rho,v,t\right)


I don't want to change the second equation to:
\frac{\partial(\rho v)}{\partial t}=\rho\frac{\partial(v)}{\partial t}+v\frac{\partial(\rho)}{\partial t}

I have the initial variables and \rho and v are vectors. I have solved the equations explicitly and I have solved one system of equations implicitly before but not sure how to approach this problem with two systems of equations implicitly. Do I need to turn them all into one system of equations?

Thanks!
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Old   June 1, 2012, 06:14
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Originally Posted by Hooman View Post
Hi,

I have been trying to solve the following systems of equations implicitly:

\frac{\partial\rho}{\partial t}=f\left(\rho,t\right)

\frac{\partial \rho v}{\partial t}=g\left(\rho,v,t\right)


I don't want to change the second equation to:
\frac{\partial(\rho v)}{\partial t}=\rho\frac{\partial(v)}{\partial t}+v\frac{\partial(\rho)}{\partial t}

I have the initial variables and \rho and v are vectors. I have solved the equations explicitly and I have solved one system of equations implicitly before but not sure how to approach this problem with two systems of equations implicitly. Do I need to turn them all into one system of equations?

Thanks!
but I think that your system requires the energy equation, too... for the compressible flow model the pressure is thermodinamic and you need to supply the state equation ...
However, your system is intrinsicly coupled, you can use several methods to solve it
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Old   June 1, 2012, 06:30
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I know about the energy equation to solve for pressure.
Right now I just need to know how to approach solving these two equations in the form that they are and with only rho and v the variable.

Can you name some of these methods please?

Thanks!
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Old   June 1, 2012, 07:04
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Filippo Maria Denaro
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Originally Posted by Hooman View Post
I know about the energy equation to solve for pressure.
Right now I just need to know how to approach solving these two equations in the form that they are and with only rho and v the variable.

Can you name some of these methods please?

Thanks!
you can see: Chung T.J. Computational fluid dynamics (CUP, 2002)
and look at the PISO method
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Old   June 4, 2012, 09:30
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Thanks for this. I looked it up.

Can I just ask if I had a nonlinear term in the right hand side of the second equation, for instance \rho v^2, would I need to linearize it somehow or can I just leave it as it is?

Thanks again!
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Old   June 7, 2012, 04:46
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Hi again,

I just had a look at some books and articles and from what I understood correction methods such as PISO and SIMPLE are used when the pressure-based approach is used in solving compressible flows. When using density-based approaches are used there is no need to use these equations we have the continuity equation. I was wondering if you could correct me if I'm mistaken about this and also how I can go on about solving these equations using when using the density-based approach?

I hope u see this message.

Thanks again.
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