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

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

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

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

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

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