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

wyj216 · July 13, 2018, 03:37

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.

selig5576 · July 13, 2018, 11:06

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.

July 13, 2018, 03:37	Is there a time step limit for Douglas-Gunn ADI scheme	#1
wyj216 New Member Youjiang Wang Join Date: Apr 2015 Location: Hamburg Posts: 22 Rep Power: 10	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.

July 13, 2018, 11:06	adi	#2
selig5576 Senior Member Selig Join Date: Jul 2016 Posts: 213 Rep Power: 10	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. wyj216 likes this.

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