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verifying second order

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Old   November 20, 2009, 15:56
Default verifying second order
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vahid
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hi
I have written a code for wave equation with RK2.
now I want to know how I can be sure that my code is second order?
the error must be smaller than what?
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Old   November 20, 2009, 17:34
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jed
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Jed Brown
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Which wave equation? In any case, you choose a smooth solution (\cos is good) and compare your code's results at successively finer resolution (refine in both space and time). Now plot \log(\text{error}) versus \log(\Delta x), the resulting slope is the order of accuracy of your method. If you don't have an exact solution available, you can manufacture one by introducing a distributed source term that makes something simple a solution, or (generally a worse option) compute a reference solution at very high resolution (preferably with a proven code).
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Old   November 23, 2009, 17:51
Default code order
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CFDtoy
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Hi there,
Do richardson extrapolation test for grid convergence! 3 sets of results at time steps or spatial step h, h/2 ,h 4 is needed (basically 3 grids). works for structured mesh straight up ! Unstructured meshes are tricky. Since yours is a simple RK based integration procedure method..this works very well.

/CFDtoy

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Originally Posted by vahidmech View Post
hi
I have written a code for wave equation with RK2.
now I want to know how I can be sure that my code is second order?
the error must be smaller than what?
CFDtoy is offline   Reply With Quote

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