finite volume discretization
 

how we can discretized k-epsilon equation with finite volume method
thanks in advance

it is normally similar to descritizing the energy equation

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

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

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

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).

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)

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)

thanks for your realy helpfull guidance
what a about the [(du/dx)+(dv/dy)]^2 term?

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.

how to descretise orlanski's boundary condition (CBC) using FVM???

thnx in advance