# finite volume discretization

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 August 15, 2014, 07:26 finite volume discretization #1 New Member   ali Join Date: May 2014 Posts: 19 Rep Power: 4 how we can discretized k-epsilon equation with finite volume method thanks in advance

 August 15, 2014, 07:43 #2 Senior Member   Hamid Zoka Join Date: Nov 2009 Posts: 199 Rep Power: 10 it is normally similar to descritizing the energy equation sciense likes this.

 August 15, 2014, 08:14 #3 New Member   ali Join Date: May 2014 Posts: 19 Rep Power: 4 thanks are we need to linearize ( epsilon^2) term in epsilon equation?

 August 15, 2014, 15:43 #4 Senior Member   Joachim Join Date: Mar 2012 Location: Atlanta Posts: 140 Rep Power: 7 Hey, You do not need to linearize anything when computing the fluxes, source terms, etc. You should only need the linearized fluxes if you are using an implicit scheme (when computing the Jacobian matrices). If you are unfamiliar with finite volume methods, I suggest you have a look at the following book: Computational Fluid Dynamics: Principles and Applications by Blazek Really nice book, in which the finite volume version of the k-epsilon model is described. Good luck, Joachim sciense likes this.

 August 15, 2014, 16:50 #5 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 2,692 Rep Power: 33 The general guideline is that the differential equation must be written in divergence form so, that once integrated over a finite volume, you can express the surface integral of the normal component of the fluxes. Such equation can be discretized using some quadrature rule for the integral and some numerical reconstrction for the fluxes

August 16, 2014, 14:26
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Quote:
 Originally Posted by sciense how we can discretized k-epsilon equation with finite volume method thanks in advance
k-espilon equation are general transport equations so you just have to discretize convective flux, diffusive flux temporal term and source term.
epsilon^2 will be considered as sourceterm in the right hand side of your matrix system (if you use an implicit temporal scheme).

 August 20, 2014, 08:54 #7 New Member   ali Join Date: May 2014 Posts: 19 Rep Power: 4 what is the discretization of (du/dx)^2 term in finite volume method thanks for your reply

August 20, 2014, 11:18
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Filippo Maria Denaro
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Quote:
 Originally Posted by sciense what is the discretization of (du/dx)^2 term in finite volume method thanks for your reply

it cannot be written in divergence form but must be integrated over a finite volume as a source term. Then you can use some quadrature rule for the discretization of the integral (see the book of Peric & Ferziger)

 August 25, 2014, 08:02 #9 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 613 Blog Entries: 17 Rep Power: 20 You can also do the following transformation (i don't know if it helps stability): du/dx*du/dx = d/dx(u*du/dx) - u*d/dx(du/dx) sciense likes this.

August 25, 2014, 08:39
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ali
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 Originally Posted by sbaffini You can also do the following transformation (i don't know if it helps stability): du/dx*du/dx = d/dx(u*du/dx) - u*d/dx(du/dx)
what a about the [(du/dx)+(dv/dy)]^2 term?

Last edited by sciense; August 25, 2014 at 12:10.

 August 25, 2014, 12:02 #11 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 613 Blog Entries: 17 Rep Power: 20 Actually, the previous example only applies to terms like: du_j/dx_i * du_k/dx_i = d/dx_i(u_j*du_k/dx_i) - u_j*d2u_k/dx_i^2 If you can fit your term in this template then it still applies.

 August 26, 2014, 05:04 #12 New Member   Parth Thaker Join Date: Mar 2014 Location: Surat , Gujarat , INDIA Posts: 26 Rep Power: 4 how to descretise orlanski's boundary condition (CBC) using FVM??? thnx in advance

 Tags finite volume method, k-epsilon model

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