# how to implement k-epsilon equations in ADI method

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 July 16, 2014, 17:46 how to implement k-epsilon equations in ADI method #1 New Member   Mey Join Date: Jul 2014 Posts: 3 Rep Power: 11 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

 July 17, 2014, 10:57 #2 Senior Member   Join Date: Jul 2009 Posts: 357 Rep Power: 18 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. kiamey likes this.

July 17, 2014, 17:13
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Mey
Join Date: Jul 2014
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Rep Power: 11
Quote:
 Originally Posted by agd 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

 Tags adi, k-epsilon model, shallow water