[agustinvo]

Hello

I have to solve an equation to get the turbulent Prandtl number in my case, where I have something like:



where f is a complex formula, so I see a bit hard to get an analytical solution to get the turbulent Prandtl number.

I am thinking to solve it by iterations (Newton method), but I would like to know if someone has alredy solved something similar in an equation environment.

The problem of the Newton method is I have to get the turbulent Prandtl number in each cell (is a volScalarField).

I will comment my advances

[tomislav_maric]

There are ODE solvers available that you can use for that purpose. Check out applications/test/ODE. You can compile the test with wmake and execute it like this:

Test-ODE Euler

Or like this:

Test-ODE whaaat

to get the list of available solvers. The Euler solver implements the Newton root finding method. If you open Test-ODE.C, you can see how to assemble an ODE system. In your case, you will not have 4 but one equation. And you can compute the derivatives.

If you want to solve this for a field, my guess is that you need to perform root finding on a per-cell basis. That could be quite costly, depending on the function graph - for example if it has diminishing gradients, or there is no way to find a good starting point.

[agustinvo]

Hello

thanks for your answer, tomislav_maric. I have checked the code and I have implemented the equation, but as you said and I supposed, it has a huge computational cost.

I will check if there are other possibilites.

Thanks for your help!

[chriss85]

It might be faster if you use the previous result as a starting point for the next iteration.