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August 15, 2014, 07:26 
finite volume discretization

#1 
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ali
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how we can discretized kepsilon equation with finite volume method
thanks in advance 

August 15, 2014, 07:43 

#2 
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Hamid Zoka
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it is normally similar to descritizing the energy equation


August 15, 2014, 08:14 

#3 
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ali
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thanks
are we need to linearize ( epsilon^2) term in epsilon equation? 

August 15, 2014, 15:43 

#4 
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Joachim
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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 kepsilon model is described. Good luck, Joachim 

August 15, 2014, 16:50 

#5 
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Filippo Maria Denaro
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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 

#6  
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Quote:
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 
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ali
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what is the discretization of (du/dx)^2 term in finite volume method
thanks for your reply 

August 20, 2014, 11:18 

#8  
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Filippo Maria Denaro
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Quote:
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, 08:39 

#10  
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ali
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Quote:
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

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 
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Parth Thaker
Join Date: Mar 2014
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how to descretise orlanski's boundary condition (CBC) using FVM???
thnx in advance 

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finite volume method, kepsilon model 
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