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November 12, 2009, 07:15 |
OpenFOAM - 2nd order of discretization?
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#1 |
Senior Member
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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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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 http://smmp.unileoben.ac.at |
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