About Darcy-Brinkman-Forchheimer equation discretization

[FU]

Hi，

I want to solve the problem about Darcy-Brinkman-Forchheimer equations, but don't know how to discretizate this equation.

This equation has a similar N-S equation. But the discretization of the last item of the equation and the programming statements are somewhat unclear.

Yours，

FU

[Wolfgang Bangerth]

On 9/27/19 8:41 PM, FU wrote:
> I want to solve the problem about Darcy-Brinkman-Forchheimer equations, but
> don't know how to discretizate this equation.
>

> Darcy equation.png
>
> This equation has a similar N-S equation. But the discretization of the last
> item of the equation and the programming statements are somewhat unclear.

Can you be more specific about what your problem is? What do people suggest in
the literature?

Best
W.


--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Chinedu Nwaigwe]

Hi FU, 

I think,  the first step would be to multiply the entire equation by epsilon/rho. Semi-implicit treatment of the last term might work. That means to evaluate everything within the bracket at old time step n and evaluate the u factor at new time step n+1.  Hope that helps.

Chinedu

--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups "deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to dealii+un...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/4ebf110b-bb82-4aac-885e-bf1f501366dc%40googlegroups.com.

[Chinedu Nwaigwe]

On Sat, Sep 28, 2019, 03:41 FU <fudany...@gmail.com> wrote:

--

[Bruno Blais]

Hello, 

It depends of the value of the Reynolds number and the gradients of K with respect to x or t, but generally the last two terms do not generally pose problems. The first additional term to the right leads to a mass matrix, which is well conditioned.

The second term itself is trickier. If you want to use an analytical Jacobian formulation and Newton's method, you will need to calculate the Frechet derivative of the velocity magnitude. You can also use a Picard iteration for this term, which will greatly simplify the expression of the Jacobian at the cost more Newton iteration.

Issues generally arise when you have jumps the value of K in space. Then generally it is better to use some sort of upwinding to prevent oscillations in the velocity field (i.e SUPG).