SAMR Phase Field Modeling (2007/08/15)
Results for uniform grid case: theta = 20, 9pt Laplacian Stencil
- Computational domain: [-2.5,2.5]x[-2.5,2.5]
- Domain size: 200x200
- Grid spacing: 0.025
- Time step size (dt): 0.000140625 (computed in terms of dx, etc.)
- Time integration scheme: explicit 2nd-order Runge-Kutta
- Spatial discretization: all 2nd-order, effective Laplacian is 9pt
- Mobility: 3000
- Strength of anisotropy: delta = 0.04
- Number of symmetry planes: j = 6
- Dimensionless latent heat: K = 2
- Dimensionless thermal conductivity: kappa = 1
- Initial undercooling: T0 = 272
- Equilibrium temperature: Teq = 273
- Rotation of system: theta = 20 degrees
- Initial solid: circle of radius 0.05
- No heat flux at boundaries. Homogeneous Neumann boundary conditions for phase field.
NOTES
- I didn't put the results after the simulation hit the wall because my computational cell is larger than the one Chin Yi used.
- Click on image to see enlarged figure.
|
Time = 0.0000 Area = 0.0075 |
|
|
Time = 0.0210937 Area = 0.199508 |
|
|
Time = 0.05625 Area = 0.637101 |
|
|
Time = 0.105469 Area = 1.42967 |
|
|
Time = 0.203906 Area = 3.6625 |
|
|
Time = 0.302344 Area = 6.72751 |
|
Area vs. Time
Results for uniform grid case: theta = 20, 5pt Laplacian Stencil
- Computational domain: [-2.5,2.5]x[-2.5,2.5]
- Domain size: 200x200
- Grid spacing: 0.025
- Time step size (dt): 0.000117188 (computed in terms of dx, etc.)
- Time integration scheme: explicit 2nd-order Runge-Kutta
- Spatial discretization: all 2nd-order, effective Laplacian is 5pt
- Mobility: 3000
- Strength of anisotropy: delta = 0.04
- Number of symmetry planes: j = 6
- Dimensionless latent heat: K = 2
- Dimensionless thermal conductivity: kappa = 1
- Initial undercooling: T0 = 272
- Equilibrium temperature: Teq = 273
- Rotation of system: theta = 20 degrees
- Initial solid: circle of radius 0.05
- No heat flux at boundaries. Homogeneous Neumann boundary conditions for phase field.
NOTES
- I didn't put the results after the simulation hit the wall because my computational cell is larger than the one Chin Yi used.
- Click on image to see enlarged figure.
|
Time = 0.0000 Area = 0.0075 |
|
|
Time = 0.0175781 Area = 0.163109 |
|
|
Time = 0.0527344 Area = 0.598438 |
|
|
Time = 0.0996094 Area = 1.3513 |
|
|
Time = 0.199219 Area = 3.654 |
|
|
Time = 0.304688 Area = 7.06439 |
|
Area vs. Time
Results for uniform grid case: theta = 90, 9pt Laplacian Stencil
- Computational domain: [-2.5,2.5]x[-2.5,2.5]
- Domain size: 200x200
- Grid spacing: 0.025
- Time step size (dt): 0.000140625 (computed in terms of dx, etc.)
- Time integration scheme: explicit 2nd-order Runge-Kutta
- Spatial discretization: all 2nd-order, effective Laplacian is 9pt
- Mobility: 3000
- Strength of anisotropy: delta = 0.04
- Number of symmetry planes: j = 6
- Dimensionless latent heat: K = 2
- Dimensionless thermal conductivity: kappa = 1
- Initial undercooling: T0 = 272
- Equilibrium temperature: Teq = 273
- Rotation of system: theta = 90 degrees
- Initial solid: circle of radius 0.05
- No heat flux at boundaries. Homogeneous Neumann boundary conditions for phase field.
NOTES
- I didn't put the results after the simulation hit the wall because my computational cell is larger than the one Chin Yi used.
- Click on image to see enlarged figure.
|
Time = 0.0000 Area = 0.0075 |
|
|
Time = 0.0210937 Area = 0.19964 |
|
|
Time = 0.05625 Area = 0.637811 |
|
|
Time = 0.105469 Area = 1.43246 |
|
|
Time = 0.203906 Area = 3.66889 |
|
|
Time = 0.302344 Area = 6.7312 |
|
Area vs. Time
Results for uniform grid case: theta = 90, 5pt Laplacian Stencil
- Computational domain: [-2.5,2.5]x[-2.5,2.5]
- Domain size: 200x200
- Grid spacing: 0.025
- Time step size (dt): 0.000117188 (computed in terms of dx, etc.)
- Time integration scheme: explicit 2nd-order Runge-Kutta
- Spatial discretization: all 2nd-order, effective Laplacian is 5pt
- Mobility: 3000
- Strength of anisotropy: delta = 0.04
- Number of symmetry planes: j = 6
- Dimensionless latent heat: K = 2
- Dimensionless thermal conductivity: kappa = 1
- Initial undercooling: T0 = 272
- Equilibrium temperature: Teq = 273
- Rotation of system: theta = 90 degrees
- Initial solid: circle of radius 0.05
- No heat flux at boundaries. Homogeneous Neumann boundary conditions for phase field.
NOTES
- I didn't put the results after the simulation hit the wall because my computational cell is larger than the one Chin Yi used.
- Click on image to see enlarged figure.
|
Time = 0.0000 Area = 0.0075 |
|
|
Time = 0.0175781 Area = 0.163218 |
|
|
Time = 0.0527344 Area = 0.598987 |
|
|
Time = 0.0996094 Area = 1.35343 |
|
|
Time = 0.199219 Area = 3.65965 |
|
|
Time = 0.304688 Area = 7.0754 |
|
Area vs. Time
Results for SAMR grid case: theta = 20, 9pt Laplacian Stencil
- Computational domain: [-2.5,2.5]x[-2.5,2.5]
- Domain size on coarsest level: 100x100
- Coarsest grid spacing: 0.05
- Finest grid spacing: 0.00625
- Time step size (dt): 8.78906e-06 (computed in terms of dx, etc.)
- Time integration scheme: explicit 2nd-order Runge-Kutta
- Spatial discretization: all 2nd-order, effective Laplacian is 9pt
- Mobility: 3000
- Strength of anisotropy: delta = 0.04
- Number of symmetry planes: j = 6
- Dimensionless latent heat: K = 2
- Dimensionless thermal conductivity: kappa = 1
- Initial undercooling: T0 = 272
- Equilibrium temperature: Teq = 273
- Rotation of system: theta = 20 degrees
- Initial solid: circle of radius 0.05
- No heat flux at boundaries. Homogeneous Neumann boundary conditions for phase field.
NOTES
- I didn't put the results after the simulation hit the wall because my computational cell is larger than the one Chin Yi used.
- The green boxes are the first level of refinement (4 times finer than coarsest level). The black boxes are the second level of refinement (2 times finer than first refinement level).
- Click on image to see enlarged figure.
|
Time = 0.0000 Area = 0.0075 |
|
|
Time = 0.0219727 Area = 0.225174 |
|
|
Time = 0.0505371 Area = 0.594014 |
|
|
Time = 0.101074 Area = 1.43602 |
|
|
Time = 0.202148 Area = 3.8775 |
|
|
Time = 0.3 Area = 7.18016 |
|
Area vs. Time
Results for SAMR grid case: theta = 90, 9pt Laplacian Stencil
- Computational domain: [-2.5,2.5]x[-2.5,2.5]
- Domain size on coarsest level: 100x100
- Coarsest grid spacing: 0.05
- Finest grid spacing: 0.00625
- Time step size (dt): 8.78906e-06 (computed in terms of dx, etc.)
- Time integration scheme: explicit 2nd-order Runge-Kutta
- Spatial discretization: all 2nd-order, effective Laplacian is 9pt
- Mobility: 3000
- Strength of anisotropy: delta = 0.04
- Number of symmetry planes: j = 6
- Dimensionless latent heat: K = 2
- Dimensionless thermal conductivity: kappa = 1
- Initial undercooling: T0 = 272
- Equilibrium temperature: Teq = 273
- Rotation of system: theta = 90 degrees
- Initial solid: circle of radius 0.05
- No heat flux at boundaries. Homogeneous Neumann boundary conditions for phase field.
NOTES
- I didn't put the results after the simulation hit the wall because my computational cell is larger than the one Chin Yi used.
- The green boxes are the first level of refinement (4 times finer than coarsest level). The black boxes are the second level of refinement (2 times finer than first refinement level).
- Click on image to see enlarged figure.
|
Time = 0.0000 Area = 0.0075 |
|
|
Time = 0.0219727 Area = 0.225186 |
|
|
Time = 0.0505371 Area = 0.594048 |
|
|
Time = 0.101074 Area = 1.43616 |
|
|
Time = 0.202148 Area = 3.87751 |
|
|
Time = 0.3 Area = 7.17499 |
|
Area vs. Time
