Hyperbolic equasion solver or How OF works

j-avdeev · October 30, 2013, 09:07

Hello,
I have working hyperbolic equasion solver (hyper1Foam in attachment - works in OF 2.1.0).

Main equation:
$\frac{\partial\psi }{\partial t}+C{\frac{\partial \psi}{\partial x}}=0$
accordingly

Code:

        solve
        (
	    fvm::ddt(psi)
	    +
	    fvm::div(phi,psi)
        );

and in fvShemes

Code:

ddtSchemes
{
    ddt(psi) Euler;
}
divSchemes
{
    div(phi,psi) Gauss linear;
}

Working geometry - coube 1x1x1 diveded on 5 equal parts along oZ axe.

Main equation in discretized form:

[LaTeX Error: Syntax error]
$C_i=\frac{V\phi_i}{\Delta t}$
where
$\psi_i - old ~value ~of ~phi ~in ~cell ~i$
$\psi^n_i - new ~value$

In my case

V = const = 1/5 = 0.2 ~~ volume ~of ~single ~cell

$\Delta t = 0.1 ~time ~step$

And when I insert result of phi from one of time directories...

$for ~\phi_i = 0,434805$
$\frac{0.2 *0,749653 - 0.2*0,434805}{0.1 } + (0,2/0,1)*0,434805*{\frac{0,206803 - 1}{0.2}} =$

Not zero!
I khow that hyperbolic equation will not =0, because it is iterational method. Is it residual?

I want to understand - how OpenFOAM count values of phi from one iteration to another - how to get new phi from old values:
phi_new = ... ... ...

And what initial values of phi?

Results: Table of results on GoogleDocs

j-avdeev · October 30, 2013, 09:12

second file of equatins

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October 30, 2013, 09:12		#2
j-avdeev Member Avdeev Evgeniy Join Date: Jan 2011 Location: Togliatty, Russia Posts: 69 Blog Entries: 1 Rep Power: 21	second file of equatins