Hello!
In the driving files of the example files of MICRESS, the "type of potential" is usually selected as "double_obstacle". I, however, look sometimes for the potential function to be defined as "double_well" in basic textbooks and/or articles dealing with the phase field model.
Please explain that how difference is the "double_obstacle" from "double_well" and what is advantage to select the "double_obstacle".
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original message from Sukeharu Nomoto
What is "double_obstacle" of potential ?
Re: What is "double_obstacle" of potential ?
double_well and double_obstacle denote the typ of potential which is assumed for the free energy description of the diffuse interface. Their is no short answer to the question above and there are many items about pros and cons of each potential in theory and numerical aplications ...
Maybe the essentials are:
Both potentials lead to a bit different phase field equation, e.g. the polynomal part and the weight factor for the driving force is different.
The equations look like:
DW:d phi/dt ~ sigma (laplace phi + 36/eta**2 phi (1-phi) (2phi-1)) + 30/eta phi**2 (1-phi)**2 delta G
DO: d phi/dt ~ sigma (laplace phi + Pi**2/eta**2 (phi-1/2)) + Pi/eta sqrt(phi (1-phi)) delta G
As a consequence the steady state solution for the interface contours are different (Try with MICRESS!)
DW: solution is a hyperbolic-tangent profile
DO: solution is a sine (ore cosine)-profile, of course only half a period!
Both contours are quite similar in the middle of the interface (same gradients), but differ at the outer parts. The sine-function is steeper and gives a finite interface thickness (controlled by the input parameter "interface thickness"), the hyperbolic tangent has no finite thickness! However, to keep the multi-phase/grain problem numerical feasible we cut the tanh-profile at phi="phase minimum". Nevertheless the interface is thicker for the same "interface thickness", rather twice as the specified value. Therefore one advantage of DO is that it computes faster, especially for pur grain growth problems or when thermodynamic calculations on the interface are the dominating effort.
A thinner interface can have further numerical advantages in situations when the limitation of a "constant driving force across the interface" is violated.
But again their is now general advise, just try!
hope that answers the question
Markus
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original message from Markus
Maybe the essentials are:
Both potentials lead to a bit different phase field equation, e.g. the polynomal part and the weight factor for the driving force is different.
The equations look like:
DW:d phi/dt ~ sigma (laplace phi + 36/eta**2 phi (1-phi) (2phi-1)) + 30/eta phi**2 (1-phi)**2 delta G
DO: d phi/dt ~ sigma (laplace phi + Pi**2/eta**2 (phi-1/2)) + Pi/eta sqrt(phi (1-phi)) delta G
As a consequence the steady state solution for the interface contours are different (Try with MICRESS!)
DW: solution is a hyperbolic-tangent profile
DO: solution is a sine (ore cosine)-profile, of course only half a period!
Both contours are quite similar in the middle of the interface (same gradients), but differ at the outer parts. The sine-function is steeper and gives a finite interface thickness (controlled by the input parameter "interface thickness"), the hyperbolic tangent has no finite thickness! However, to keep the multi-phase/grain problem numerical feasible we cut the tanh-profile at phi="phase minimum". Nevertheless the interface is thicker for the same "interface thickness", rather twice as the specified value. Therefore one advantage of DO is that it computes faster, especially for pur grain growth problems or when thermodynamic calculations on the interface are the dominating effort.
A thinner interface can have further numerical advantages in situations when the limitation of a "constant driving force across the interface" is violated.
But again their is now general advise, just try!
hope that answers the question
Markus
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original message from Markus
Re: What is "double_obstacle" of potential ?
Thank you very much for your answers.
It impressed on me that the sine-profile is better than the hyperbolic-tangent profile for expressing the steady interface contour.
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original message from Sukeharu Nomoto
It impressed on me that the sine-profile is better than the hyperbolic-tangent profile for expressing the steady interface contour.
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original message from Sukeharu Nomoto