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 2ndorder RungeKutta
 Spatial discretization: all 2ndorder, 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 2ndorder RungeKutta
 Spatial discretization: all 2ndorder, 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 2ndorder RungeKutta
 Spatial discretization: all 2ndorder, 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 2ndorder RungeKutta
 Spatial discretization: all 2ndorder, 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): 8.78906e06 (computed in terms of dx, etc.)
 Time integration scheme: explicit 2ndorder RungeKutta
 Spatial discretization: all 2ndorder, 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): 8.78906e06 (computed in terms of dx, etc.)
 Time integration scheme: explicit 2ndorder RungeKutta
 Spatial discretization: all 2ndorder, 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 