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Is there a time step limit for Douglas-Gunn ADI scheme

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Old   July 13, 2018, 03:37
Question Is there a time step limit for Douglas-Gunn ADI scheme
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Youjiang Wang
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Hallo, everyone.

From a text book I read that the Crank-Nicolson method is unconditionally stable for the one dimensional unsteady heat equation \frac{\partial \phi}{\partial t} = a\frac{\partial^2 \phi}{\partial x^2}. But it leads to unphysical oscillatory solution when the Mesh Fourier Number Fo_{\Delta} = \frac{a \Delta t}{\Delta x^2} is larger than one.

I just wonder, whether the Douglas-Gunn ADI scheme, which is like an extension of the C-N method in 3D, also has the same problem. If so, what is the limit for the time step?


Thank you very much for any discussion.
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Old   July 13, 2018, 11:06
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The Douglas-Gunn ADI scheme (approximate factorization) does not have a time step restriction unlike the traditional ADI methods. Other ADI methods (Peachmann) have a time step restriction when dealing with 3D.
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