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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.
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Dr. Alexander VAKHRUSHEV

Christian Doppler Laboratory for "Advanced Process Simulation of
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Simulation and Modelling of Metallurgical Processes
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