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February 10, 2014, 12:20 
Original PDE of a rungekutta descritized equation

#1 
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Join Date: Feb 2012
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I would like to convert back this descritized equation in time(which was done by 3step rungekutta) to its original PDE form (To descritize this equation with a 1step time scheme afterwards).
The first equation is the NavierStokes equation but i don't know what is the exact original form of the second equation.(The term 'f' for the second equation is known) One of The confusing part for me is the existence of the two laplacian terms.Why do we have two kinds of initial(previous timestep) term there. (U(k1) and U(~)). Because i think if i want to use a 1step scheme, then both terms acts as a value of previous time step. I want to be sure if the original form is : (du/dt = laplacian(nu,u) + f) or not! 

February 10, 2014, 12:23 

#2  
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
for the consistence property, any discrete scheme must tend to the differential form for all the discretization parameters going to zero... 

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