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Adams-Bashforth implicit scheme for time.

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Old   July 19, 2013, 07:30
Default Adams-Bashforth implicit scheme for time.
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Amin
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Hello

I would like to use a second order accurate Adams-Bashforth implicit scheme for time.
I searched in the Internet, how to implement this scheme in OpenFOAM but i did not find any Information about it...

Can we use this kind of scheme in OpenFOAM ?
Is there any option to use other scheme, which works in the same way ?
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Old   July 22, 2013, 05:35
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Artem Shaklein
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Hello, Mirage12.

For example, I want to solve ∂y/∂t + ∂(yU_i)/∂x_i = 0. To use Adams-Bashforth, I should do next

y^(n+1) = y^(n) - dt*(3/2*( ∂(y^(n+1)U_i)/∂x_i) - 0.5*( ∂(y^(n)U_i)/∂x_i)). That seems right, yes?

So, implementation would be

Code:
phi = U & mesh.Sf();
...
yEqn
(
     fvm::ddt(y)
 + 1.5*fvm::div(phi, y)
  - 0.5*fvc::div(phi, y)
);
with "Euler" word used in OF ddtScheme dictionary.
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Old   July 23, 2013, 00:57
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I don t know ...
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Old   July 23, 2013, 05:42
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Artem Shaklein
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Of course, you can study how CrankNicholson scheme is implemented in OF and create AB from it, but this is the fastest way.
By the way, Crank-Nicholson scheme is easy to implement too
Code:
yEqn
(
     fvm::ddt(y)
  + 0.5*fvm::div(phi, y)
  + 0.5*fvc::div(phi, y)
);
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Old   July 23, 2013, 06:11
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Amin
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could you please specify where should i implement the code ?
i am not really an expert...i am just a beginner
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Old   July 23, 2013, 06:23
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Artem Shaklein
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Okay, e.g., let's take icoFoam and use AB for momentum time discretisation.

icoFoam.C looks like:
Code:
...
        fvVectorMatrix UEqn
        (
            fvm::ddt(U)
          + fvm::div(phi, U)
          - fvm::laplacian(nu, U)
        );
...
So, we just rewrite this part of code (it's better to copy all icoFoam folder to icoFoamAB e.g. for keeping original files untouched).
Code:
...
        fvVectorMatrix UEqn
        (
            fvm::ddt(U)
          +1.5*fvm::div(phi, U)
           -0.5*fvc::div(phi, U)
           - fvm::laplacian(nu, U)
        );
...
Here I used AB time advance scheme for convective fluxes and Euler implicit for diffusive fluxes.
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Old   July 23, 2013, 07:03
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Thx , i wil try it
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