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OpenFOAM - 2nd order of discretization?

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Old   November 12, 2009, 08:15
Default OpenFOAM - 2nd order of discretization?
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Dr. Alexander Vakhrushev
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Hi all!

When FVM discretization is considered in OpenFOAM manuals, it is stated that linear variation of variable within CV represents 2nd order of accuracy:

f(x) = f(x0) + (x-x0) * (grad f(x))|x=x0

But ussualy

f(x) = f(x0) represents zero order of accuracy
f(x) = f(x0) + (x-x0) * (grad f(x))|x=x0 is of the 1st order of accuracy
and so on.

The same way we get first order temporal derivative:
dt(f)/dt = (f(t_n) - f(t_n-1)) / delta t

using only first two terms in Taylor series, and is necessary to use third term
to get second order approximation:

dt(f)/dt = (3/2*f(t_n) - 2*f(t_n-1) - 1/2*f(t_n-2)) / delta t

So what does actually mean "2nd order of accuracy" then?

Thank you for your attention! Waiting for your comments.
Best regards,

Dr. Alexander VAKHRUSHEV

Christian Doppler Laboratory for "Metallurgical Applications of Magnetohydrodynamics"

Simulation and Modelling of Metallurgical Processes
Department of Metallurgy
University of Leoben
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