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how to implement k-epsilon equations in ADI method

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Old   July 16, 2014, 17:46
Default how to implement k-epsilon equations in ADI method
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Mey
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Hi
I have developed a code which uses adi method to simulate shallow water equations. For turbulence modelling I have used a basic mixing length concept and it works.
This turbulence model is a zero-equation model, so no additional equations shall be solved and I have no problem in solving the tridiagonal systems of equations.
But k-epsilon model adds two other unknowns.
I have no idea how to add these equations to my model. How can I descritize K-epsilon equations? How can I solve the new system of equations which includes 5 unknowns (water depth, velocities in two x and y directions,k and epsilon).
Does someone have any idea or can somebody introduce a reference on the subject.
Thank you
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Old   July 17, 2014, 10:57
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If you are currently solving your three equations with a block ADI solver, then simply extend the size of the blocks you use in the ADI solver. If you are solving your current equation set in a sequential fashion then you probably want to look for information on block ADI solvers. The basic formulation is a fairly straightforward extension of the single equation algorithm.
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Old   July 17, 2014, 17:13
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Quote:
Originally Posted by agd View Post
If you are currently solving your three equations with a block ADI solver, then simply extend the size of the blocks you use in the ADI solver. If you are solving your current equation set in a sequential fashion then you probably want to look for information on block ADI solvers. The basic formulation is a fairly straightforward extension of the single equation algorithm.
I use a simple thomas algorithm to solve the equations. Two equations (continuity and momentum in one direction) are solved in each half step.
I don't know what a block ADI solver is but by googling I assume it has something to do with parallel solving. Since I am not familiar with parallel solving I'd be happy to know where should I start from.

Is there a reasonable way to solve k-epsilon equations explicitly in each time step by some kind of iteration technique, or using block adi solver is the only answer?

Thanks
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