Ex_011 Parameterised boundary

 

Preliminary Note: Usage of parameterised boundaries is compatible with Parallel simulations, with deposition and remeshing. Thus, such functionality is available for forward modeling over geological time scales.

 

 

This tutorial example aims to demonstrate usage of Parameterised_boundary data, which is used in conjunction with Spatial_boundary to enable a distribution of displacements to be applied to a boundary as depicted in the figure below. To this end the same geometry from MEM_001 tutorial will be used.

Ex_011_Fig01

Geometry for all the cases with the 3 distribution axis defined (left). Example of displacement distribution applied to a boundary for Case01 (right)

 

 

 

 

The simulations will be performed using the implicit solver for the mechanical field and will encompass a gravity initialisation stage followed by a tectonic displacement stage. The data files for all the cases are provided in ParaGeo Examples\General Examples\Ex_011\Data with the results being provided in the corresponding \Results sub-folder.

 

It is noted that if the boundary displacements are not meant to be applied at the first simulation stage, a "bare" Parameterised_boundary data identifying the Geometry_set associated with the Parameterised_boundary must be defined in the first stage as shown below in the data taken from Case01.

 

 

Data File

 

* Parameterised_boundary           NUM=1

! ---------------------------------------

 Geometry_set             "North"

 

 

* Control_data

! =======================================

 Control_title                "init"

  (...)

 

 

 

 

* Spatial_boundary NUM=2

! ----------------------------------------

 Name                  "Para_bound"

 Boundary_type       "Spatial_grid"

 Value_type              "Absolute"

 Parameterised_boundaries   IDM=1

   1

 Prescribed_components IDM=1 JDM=1

   2

 

 

* Parameterised_boundary           NUM=1

! ----------------------------------------

 Geometry_set            "North"

 Distribution_axis       1

 Prescribed_values       IDM=2

   -25    -75

 

* Control_data

! =======================================

 Control_title              "Tectonic"

  (...)

 

 

 

1.A "bare" Parameterised_boundary data associated to "North" boundary is defined in the initial stage.

 

2.In the second stage the displacements are being applied. Thus Parameterised_boundary and Spatial_boundary are defined with the appropriate data as required.

 

3.In Spatial_boundary we define:

 

i.Boundary_type must be set to Spatial_grid as internally ParaGeo will create a spatial grid with which the displacements will be mapped to the boundary nodes.

 

ii.In Parameterisend_boundaries keyword we define the list of ID numbers corresponding to the parametrised boundaries associated with the present Spatial_boundary

 

iii.In Prescribed_components we define which displacement components will be prescribed for each of the associated parametrised boundaries listed within the keyword Parameterisend_boundaries. Note that component numbers 1, 2 and 3 correspond to X, Y and Z respectively. Note that the the IDM dimension corresponds to the number of prescribed components whereas JDM dimension corresponds to the number of parametrised boundaries associated to the present Spatial_boundary .

 

4.In Parameterised_boundary we define:

 

i.The associated Geometry_set which in this case is "North"

 

ii.In Distribution_axis we define the number corresponding to the axis along which the displacements will be distributed. Axis numbers 1, 2 and 3 correspond to X, Y and Z directions respectively.

 

iii.The Prescribed_values are used to define the amount of displacement applied to from the minimum to the maximum coordinate of the specified Distribution_axis for the associated boundary Geometry_set (case with 2 Prescribed_values)

 

5.Thus, in the present example a linear distributions of displacements along the X axis is applied in the negative Y direction for the North boundary, ranging from a displacement of -25 m in X = 0 m to a displacement of -75 m at X=8000 m.

 

 

 

Below the displacement results for different data set ups corresponding to the different provided cases are shown.

 

 

Case01

 

Data File

 

* Spatial_boundary NUM=2

! ----------------------------------------

 Name                  "Para_bound"

 Boundary_type       "Spatial_grid"

 Value_type              "Absolute"

 Parameterised_boundaries   IDM=1

   1

 Prescribed_components IDM=1 JDM=1

   2

 

 

* Parameterised_boundary           NUM=1

! ----------------------------------------

 Geometry_set            "North"

 Distribution_axis       1

 Prescribed_values       IDM=2

   -25    -75

 

1.Case01 considers a linear distributions of displacements along the X axis applied in the negative Y direction for the North boundary, ranging from a displacement of -25 m in X = 0 m to a displacement of -75 m at X=8000 m.

 

Ex_011_Fig02a

 

 

 

 

Case01b

 

Data File

 

* Spatial_boundary NUM=2

! ----------------------------------------

 Name                  "Para_bound"

 Boundary_type       "Spatial_grid"

 Value_type              "Absolute"

 Parameterised_boundaries   IDM=1

   1

 Prescribed_components IDM=1 JDM=1

   2

 

 

* Parameterised_boundary           NUM=1

! ----------------------------------------

 Geometry_set            "North"

 Distribution_axis       1

 Prescribed_values       IDM=2

   -75    -25

 

 

1.Case01b considers a linear distribution of displacements along the X axis applied in the negative Y direction for the North boundary, ranging from a displacement of -75 m in X = 0 m to a displacement of -25 m at X=8000 m.

 

Ex_011_Fig02b

 

 

 

 

Case02

 

Data File

 

* Spatial_boundary NUM=2

! ----------------------------------------

 Name                  "Para_bound"

 Boundary_type       "Spatial_grid"

 Value_type              "Absolute"

 Parameterised_boundaries   IDM=1

   1

 Prescribed_components IDM=1 JDM=1

   2

 

 

* Parameterised_boundary           NUM=1

! ----------------------------------------

 Geometry_set            "North"

Distribution_axis       3

 Prescribed_values       IDM=2

   -25    -75

 

 

1.Case02 considers a linear distribution of displacements along the Z axis (Distribution_axis 3) applied in the negative Y direction for the North boundary, ranging from a displacement of -25 m at the base to a displacement of -75 m at the top.

 

Ex_011_Fig03

 

 

 

 

Case03

 

Case03 considers a quadratic distribution of displacements so that 3 prescribed values at the Minimum, Center and Maximum coordinates for the boundary are provided.

 

Data File

 

* Spatial_boundary NUM=2

! ----------------------------------------

 Name                  "Para_bound"

 Boundary_type       "Spatial_grid"

 Value_type              "Absolute"

 Parameterised_boundaries   IDM=1

   1

 Prescribed_components IDM=1 JDM=1

   2

 

 

* Parameterised_boundary           NUM=1

! ----------------------------------------

 Geometry_set            "North"

 Distribution_axis   1

Prescribed_values            IDM=3

  -25    -75    -10

 

 

1.Case03 considers a quadratic distribution of displacements along the X axis applied in the negative Y direction for the North boundary according to the specified values.

 

Ex_011_Fig04a

 

 

 

 

Case04

 

Case04 considers two parameterised boundaries, one applying compressional displacements in the North as in all the previous cases and one applying a distributed extensional displacement in the X direction along the Y axis to the East boundary. Note that in this case each Parameterised_boundary is associated to a separate Spatial_boundary. In Case04b an alternative set up that yields identical results is demonstrated.

 

Data File

 

* Spatial_boundary NUM=2

! ----------------------------------------

 Name                  "Para_bound_N"

 Boundary_type       "Spatial_grid"

 Value_type              "Absolute"

 Parameterised_boundaries   IDM=1

   1 

 Prescribed_components IDM=1 JDM=1

   2  ! disp_y

 

* Parameterised_boundary           NUM=1

! ----------------------------------------

 Geometry_set             "North"

Distribution_axis   1

 Prescribed_values                IDM=2

   -25    -75

 

 

 

* Spatial_boundary NUM=3

! ----------------------------------------

 Name                  "Para_bound_E"

 Boundary_type       "Spatial_grid"

 Value_type              "Absolute"

 Parameterised_boundaries   IDM=1

   2 

 Prescribed_components IDM=1 JDM=1

   1  ! disp_x

 

* Parameterised_boundary           NUM=2

! ----------------------------------------

 Geometry_set             "East"

Distribution_axis   2

 Prescribed_values                IDM=2

   0    35        

 

 

1.Case04 considers two parameterised boundaries:

 

i.Parameterised_boundary NUM=1 is used to prescribe displacements in the Y direction (Prescribed component 2) along the X axis (Distribution_axis 1) to the North boundary

 

ii.Parameterised_boundary NUM=2 is used to prescribe displacements in the X direction (Prescribed component 1) along the Y axis (Distribution_axis 2) to the East boundary

 

Ex_011_Fig05a

 

Ex_011_Fig05b

 

 

 

 

Case04b

 

Case04b considers an alternative set up to achieve the same results as in Case04. In this case both parametersied boundaries are associated to the same Spatial_boundary.

 

Data File

 

* Spatial_boundary NUM=2

! ----------------------------------------

 Name                  "Para_bound_N"

 Boundary_type       "Spatial_grid"

 Value_type              "Absolute"

 Parameterised_boundaries   IDM=2

   1  2 

 Prescribed_components IDM=1 JDM=1

   2  ! disp_y

   1  ! disp_x

 

* Parameterised_boundary           NUM=1

! ----------------------------------------

 Geometry_set             "North"

Distribution_axis   1

 Prescribed_values                IDM=2

   -25    -75

 

 

* Parameterised_boundary           NUM=2

! ----------------------------------------

 Geometry_set             "East"

Distribution_axis   2

 Prescribed_values                IDM=2

   0    35        

 

1.Case04b considers two parameterised boundaries:

 

i.Parameterised_boundary NUM=1 is used to prescribe displacements in the Y direction (Prescribed component 2) along the X axis (Distribution_axis 1) to the North boundary

 

ii.Parameterised_boundary NUM=2 is used to prescribe displacements in the X direction (Prescribed component 1) along the Y axis (Distribution_axis 2) to the East boundary

 

2.A single is used in this case, yielding identical results to Case04.