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Original PDE of a runge-kutta descritized equation

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Old   February 10, 2014, 12:20
Default Original PDE of a runge-kutta descritized equation
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ooo
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I would like to convert back this descritized equation in time(which was done by 3step runge-kutta) to its original PDE form (To descritize this equation with a 1-step time scheme afterwards).
The first equation is the Navier-Stokes 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(k-1) and U(~)).
Because i think if i want to use a 1-step 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!
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Old   February 10, 2014, 12:23
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Filippo Maria Denaro
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Quote:
Originally Posted by ooo View Post
I would like to convert back this descritized equation in time(which was done by 3step runge-kutta) to its original PDE form (To descritize this equation with a 1-step time scheme afterwards).
The first equation is the Navier-Stokes 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(k-1) and U(~)).
Because i think if i want to use a 1-step 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!

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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