What is the meaning of the “insulation” in “# Boundary conditions for phase field in each direction”?

Applying this option, how does MICRESS calculate the second derivative of the phase field parameter in the node at the boundary?

## Insulation

### Re: Insulation

Dear mtoloui,

insulation/isolation means that the boundary cell (the next imaginary cell which is not part of the simulation domain) is assumed to have the same field value (e.g. phase-field parameter) as its direct neighbour (the outermost cell of the domain). The name is like that because, e.g. for the concentration field, no gradients and, consequently, not fluxes occur between the boundary cell and its neighbour in the simulation domain.

This value for the boundary neigbour which is assumed according to the type of boundary condition is used for calculation of the derivatives.

To the contrary, the symmetric boundary condition (s) defines the field value of the boundary cell to be identical to its second neighbour in the simulation domain, thus implying a symmetry plane through the center of the outermost cells of the domain.

Bernd

insulation/isolation means that the boundary cell (the next imaginary cell which is not part of the simulation domain) is assumed to have the same field value (e.g. phase-field parameter) as its direct neighbour (the outermost cell of the domain). The name is like that because, e.g. for the concentration field, no gradients and, consequently, not fluxes occur between the boundary cell and its neighbour in the simulation domain.

This value for the boundary neigbour which is assumed according to the type of boundary condition is used for calculation of the derivatives.

To the contrary, the symmetric boundary condition (s) defines the field value of the boundary cell to be identical to its second neighbour in the simulation domain, thus implying a symmetry plane through the center of the outermost cells of the domain.

Bernd

### Re: Insulation

Dear Bernd,

So how is the 'Insulation' condition implemented when switching on the moving frame? Still no fluxes occur between the boundary cell and its neighbor in the simulation domain? Or just keep the relations as previous time?

Thank you!

Kind regards

Rody

So how is the 'Insulation' condition implemented when switching on the moving frame? Still no fluxes occur between the boundary cell and its neighbor in the simulation domain? Or just keep the relations as previous time?

Thank you!

Kind regards

Rody

### Re: Insulation

Dear Rody,

the boundary conditions in MICRESS are implemented as an additional shell of cells around the simulation domain. Moving frame is working in z direction, the simulation domain is shifted downwards stepwise by one cell if the shifting condition (distance to top or temperature at the bottom) is fullfilled. If shifting occurs, the top boundary cells are shifted to the uppermost line of the domain and afterwards replicated to the top boundary cells by application of the boundary condition. In case of isolation in top direction, the boundary cells and the corresponding cells in the upper line of the domain are identical for the considered field value, so no extra flux is occuring due to shifting. The same holds for the bottom boundary. But, of course, if the field values of the cells moving in at the top and those of the cells moving out at the bottom are not identical, the field value is not conserved in the simulation domain!

I am not sure whether this answers your question.

In the most common application of the moving frame feature, which probably is directional solidification, it is not recommendable to use the isolation condition at the top, a fixed condition should be used instead, eventually in combination with 1d_far_field!

Bernd

the boundary conditions in MICRESS are implemented as an additional shell of cells around the simulation domain. Moving frame is working in z direction, the simulation domain is shifted downwards stepwise by one cell if the shifting condition (distance to top or temperature at the bottom) is fullfilled. If shifting occurs, the top boundary cells are shifted to the uppermost line of the domain and afterwards replicated to the top boundary cells by application of the boundary condition. In case of isolation in top direction, the boundary cells and the corresponding cells in the upper line of the domain are identical for the considered field value, so no extra flux is occuring due to shifting. The same holds for the bottom boundary. But, of course, if the field values of the cells moving in at the top and those of the cells moving out at the bottom are not identical, the field value is not conserved in the simulation domain!

I am not sure whether this answers your question.

In the most common application of the moving frame feature, which probably is directional solidification, it is not recommendable to use the isolation condition at the top, a fixed condition should be used instead, eventually in combination with 1d_far_field!

Bernd