- axis-1The axis used (0, 1, or 2 for x, y, or z).
Default:-1
C++ Type:int
Controllable:No
Description:The axis used (0, 1, or 2 for x, y, or z).
- data_fileFile holding csv data for use with PiecewiseBilinear
C++ Type:FileName
Controllable:No
Description:File holding csv data for use with PiecewiseBilinear
- execute_onLINEARThe list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM.
Default:LINEAR
C++ Type:ExecFlagEnum
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM.
- radialFalseSet to true if you want to interpolate along a radius rather that along a specific axis, and note that you have to define xaxis and yaxis in the input file
Default:False
C++ Type:bool
Controllable:No
Description:Set to true if you want to interpolate along a radius rather that along a specific axis, and note that you have to define xaxis and yaxis in the input file
- scale_factor1Scale factor to be applied to the axis, yaxis, or xaxis values
Default:1
C++ Type:double
Controllable:No
Description:Scale factor to be applied to the axis, yaxis, or xaxis values
- xThe x abscissa values
C++ Type:std::vector<double>
Controllable:No
Description:The x abscissa values
- xaxis-1The coordinate used for x-axis data (0, 1, or 2 for x, y, or z).
Default:-1
C++ Type:int
Controllable:No
Description:The coordinate used for x-axis data (0, 1, or 2 for x, y, or z).
- yThe y abscissa values
C++ Type:std::vector<double>
Controllable:No
Description:The y abscissa values
- yaxis-1The coordinate used for y-axis data (0, 1, or 2 for x, y, or z).
Default:-1
C++ Type:int
Controllable:No
Description:The coordinate used for y-axis data (0, 1, or 2 for x, y, or z).
- zThe ordinate values
C++ Type:std::vector<double>
Controllable:No
Description:The ordinate values
PiecewiseBilinear
Interpolates values from a csv file
Description
The PiecewiseBilinear
function reads a csv file and interpolates values based on the data in the file. The interpolation is based on x-y pairs. If axis
is given, time is used as the y index. Either xaxis
or yaxis
or both may be given. Time is used as the other index if one of them is not given. If radius
is given, xaxis
and yaxis
are used to orient a cylindrical coordinate system, and the x-y pair used in the query will be the radial coordinate and time.
The csv file data_file
format expected is:
first line holds the
x
values.each subsequent line holds the
y
value then the list ofz
values for thisy
and all values ofx
.
The csv file data_file
may be substituted by specifying the x
, y
and z
parameters.
Example Input Syntax
[Functions]
[./u]
type = PiecewiseBilinear
#x = '0 1 3' # Testing this error
y = '0 1 3'
z = '0 0 0 0 1 3 0 5 7'
axis = 0 # End Functions
[../]
[]
(test/tests/utils/2d_linear_interpolation/xyz_error.i)Input Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.
Advanced Parameters
Input Files
(test/tests/utils/2d_linear_interpolation/xyz_error.i)
[Mesh]
file = cube.e
# This problem only has 1 element, so using DistributedMesh in parallel
# isn't really an option, and we don't care that much about DistributedMesh
# in serial.
parallel_type = replicated
[]
[Variables]
[./u]
order = FIRST
family = LAGRANGE
[../]
[]
[Functions]
[./u]
type = PiecewiseBilinear
#x = '0 1 3' # Testing this error
y = '0 1 3'
z = '0 0 0 0 1 3 0 5 7'
axis = 0
[../]
[] # End Functions
[Kernels]
[./diffu]
type = Diffusion
variable = u
[../]
[]
[BCs]
[./u]
type = FunctionDirichletBC
variable = u
boundary = '1'
function = u
[../]
[]
[Executioner]
type = Transient
dt = 1
end_time = 2
nl_rel_tol = 1e-12
[]
(test/tests/utils/2d_linear_interpolation/2d_linear_interpolation_test.i)
# Test description - view this file in emacs and adjust the window size to view the file as it was created.
#
# This problem tests the MOOSE function PiecewiseBilinear and the MOOSE utility BilinearInterpolation, which are
# used to solve 2D linear interpolation problems.
#
# The problem is one element with node coordinate locations in x,y,z space as indicated in the ASCII art:
#
#
# ^
# |
# z
# |
#
# (1,1,2) (1,2,2)
# *--------------*
# / | / |
# / | (2,2,2) / |
# (2,1,2) *--------------* |
# | | | |
# | *---------|----* (1,2,1) --y-->
# | / (1,1,1) | /
# |/ |/
# *--------------*
# / (2,1,1) (2,2,1)
# /
# x
# /
# |_
#
# problem time ...0...1...2
#
#
# There are four variables and four functions of the same name, u,v,w, and A. The diffusion equation is solved
# for each of these variables with a boundary condition of type FunctionDirchletBC applied to a boundary
# (i.e. node set) that includes every node in the element. Each boundary condition uses a function of type
# PiecewiseBilinear that gets its value from a file named fred.csv.
#
# fred is a matrix of data whose first row and first column are vectors that can refer to either spacial positions
# corresponding to an axis or values of time. The remaining data are values of fred for a given row and column pair.
#
#
# Visualize fred like this:
#
# 0 1 3 where fred is a csv file that actually looks like this 0,1,3
# 0 0 0 0 0,0,0,0
# 1 0 1 3 1,0,1,3
# 3 0 5 7 3,0,5,7
#
# Another way to think of fred is:
#
# |0 1 3| - These values can be spacial positions corresponding to
# axis= 0,1, or 2, or time
#
#
# |0| |0 0 0|
# These values can be - |1| |0 1 3| - values of fred corresponding to row-column pairs
# time or spacial |3| |0 5 7|
# positions corresponding
# to axis= 0,1, or 2
#
#
# The parameters and possible values for the function PiecewiseBilinear are:
#
# data_file = fred.csv
# axis = 0, 1, or 2
# xaxis = 0, 1, or 2
# yaxis = 0, 1, or 2
# radial = true or false (false is default)
#
# where 0, 1, or 2 refer to the x, y, or z axis.
#
# If the parameter axis is defined, then the first row of fred are spacial position and the first column
# of fred are the values of time.
#
# If the parameter xaxis is defined, then the first row of fred are spacial positions and the first column
# of fred are the values of time ... just like defining the parameter axis.
#
# If the parameter yaxis is defined, then the first row of fred are time values and the first column of fred
# are spacial positions.
#
# If parameters axis AND EITHER xaxis or yaxis are defined together you'll get a moose error.
# i.e.
# axis = 0
# xaxis = 1
# results in an error. So, if you use the parameter axis, don't use xaxis or yaxis.
#
# If parameters xaxis and yaxis are defined (and radial is false), then the first row of fred are spacial positions corresponding to xaxis value,
# and the first column are spacial positions corresponding to the yaxis value.
#
# If xaxis and yaxis are defined and radial is true, the first row of fred contains values
# corresponding to the radius calculated from the coordinates of each point. Note that
# the definition of xaxis and yaxis define the "plane" of the radius. For example,
# xaxis = 0 and yaxis = 1 means that x and y components of the point are use to
# calculate the radius. xaxis = 1 and yaxis = 2 means that x and z components are used.
# The first column is for time in this case. xaxis and yaxis have to be specified and
# radial = true for this to work, otherwise a MOOSE error will result.
# This was developed so that an axisymmetric function could be defined for a 3D mesh.
#
[Mesh]
file = cube.e
# This problem only has 1 element, so using DistributedMesh in parallel
# isn't really an option, and we don't care that much about DistributedMesh
# in serial.
parallel_type = replicated
[]
[Variables]
[./u]
order = FIRST
family = LAGRANGE
[../]
[./v]
order = FIRST
family = LAGRANGE
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./A]
order = FIRST
family = LAGRANGE
[../]
[./scaled_u]
order = FIRST
family = LAGRANGE
[../]
[./R]
order = FIRST
family = LAGRANGE
[../]
[]
[Functions]
[./u]
type = PiecewiseBilinear
data_file = fred.csv
axis = 0
[../]
#
# Example 1 - variable u
#
# In this example, the first variable is u and the parameter axis is given the value 0. For such a case, the first
# row of fred refers to nodal x-coordinate values and the first column of fred (after the first row) refers to the
# times 0, 1, and 3.
#
# So, at time = 0, the value of u at each node is 0, because that's the value of fred for all x-coordinate values at time=0.
#
# At time = 1, the value of u at nodes with x-coordinate = 1 is 1.
# , the value of u at nodes with x-coordinate = 2 is 2.
#
# You can check this value with your own 2D linear interpolation calculation. Go ahead and check all the examples!
#
# At time = 2, the value of u at nodes with x-coordinate = 1 is 3.
# , the value of u at nodes with x-coordinate = 2 is 4.
#
[./v]
type = PiecewiseBilinear
data_file = fred.csv
xaxis = 1
[../]
#
# Example 2 - variable v
#
# In this example, the variable is v and the parameter xaxis is given the value 1. For such a case, the first
# row of fred refers to nodal y-coordinate values and the first column of fred (after the first row) refers to the
# times 0, 1, and 3.
#
# At time = 0, the value of v at each node is 0, because that's the value of fred for all y-coordinate values at time=0.
#
# At time = 1, the value of v at nodes with y-coordinate = 1 is 1.
# , the value of v at nodes with y-coordinate = 2 is 2.
#
# At time = 2, the value of v at nodes with y-coordinate = 1 is 3.
# , the value of v at nodes with y-coordinate = 2 is 4.
#
[./w]
type = PiecewiseBilinear
data_file = fred.csv
yaxis = 2
[../]
#
# Example 3 - variable w
#
# In this example, the variable is w and the parameter yaxis is given the value 2. For such a case, the first
# row of fred refers to times 0, 1, and 3. The first column of fred (after the first row) refers to the nodal
# z-coordinate values.
#
# At time = 0, the value of w at each node is 0, because that's the value of fred for all z-coordinate values at time=0.
#
# At time = 1, the value of w at nodes with z-coordinate = 1 is 1.
# , the value of w at nodes with z-coordinate = 2 is 3.
#
# At time = 2, the value of w at nodes with z-coordinate = 1 is 2.
# , the value of w at nodes with z-coordinate = 2 is 4.
#
[./A]
type = PiecewiseBilinear
data_file = fred.csv
xaxis = 0
yaxis = 1
[../]
#
# Example 4 - variable A
#
# In this example, the variable is A and the parameters xaxis AND yaxis BOTH defined and given the values 0 and 1 respectivley.
# For such a case, the first row of fred refers to nodal x-coordinate values.
# The first column refers to nodal y-coordinate values.
#
# In this example the values are the same for every time (except time=0 where the values are undefined)
#
# For nodal coordinates with x=1, y=1 A = 1
# x=2, y=1 A = 2
# x=1, y=2 A = 3
# x=2, y=2 A = 4
#
# You can use this 2D linear interpolation function for anything (BC, Kernel, AuxKernel, Material) that has
# a function as one of its parameters. For example, this can be used to describe the fission peaking factors
# that vary in time and along the length of a fuel rod, or a fission rate distribution in metal fuel that varies
# as a function of x and y postion, but is constant in time.
#
#
[./scaled_u]
type = PiecewiseBilinear
data_file = fred.csv
axis = 0
scale_factor = 2
[../]
#
# Example 5 - variable scaled_u. This is just a scaled version of Example 1 to see if the scale_factor works
#
#
#
[./R]
type = PiecewiseBilinear
data_file = fred.csv
xaxis = 0
yaxis = 1
radial = true
[../]
#
# Example 6 - variable R
#
# In this example, the variable is R and the parameters xaxis and yaxis are defined and
# given the values 0 and 1 respectivley. The parameter radial is also defined and given
# the value true. In this case, the x and y components of each point are used to
# calculate a radius. This radius is used in the call to BilinearInterpolation.
# In fred.csv, the first row are the radius values. The first column is time.
#
# At time = 1, the value of R at nodes with coordinates (x = 1, y = 1, or r = 1.414) is 1.414.
# , the value of R at nodes with coordinates (x = 1, y = 2, or r = 2.236) is 2.236.
# , the value of R at nodes with coordinates (x = 2, y = 2, or r = 2.828) is 2.828.
#
# At time = 2, the value of R at nodes with coordinates (x = 1, y = 1, or r = 1.414) is 3.414.
# , the value of R at nodes with coordinates (x = 1, y = 2, or r = 2.236) is 4.236.
# , the value of R at nodes with coordinates (x = 2, y = 2, or r = 2.828) is 4.828.
#
# Note that the case of x = 2, y = 1 gives the same result as x = 1, y=2.
#
#
[] # End Functions
[Kernels]
[./diffu]
type = Diffusion
variable = u
[../]
[./diffv]
type = Diffusion
variable = v
[../]
[./diffw]
type = Diffusion
variable = w
[../]
[./diffA]
type = Diffusion
variable = A
[../]
[./diff_scaled_u]
type = Diffusion
variable = scaled_u
[../]
[./diffR]
type = Diffusion
variable = R
[../]
[]
[BCs]
[./u]
type = FunctionDirichletBC
variable = u
boundary = '1'
function = u
[../]
[./v]
type = FunctionDirichletBC
variable = v
boundary = '1'
function = v
[../]
[./w]
type = FunctionDirichletBC
variable = w
boundary = '1'
function = w
[../]
[./A]
type = FunctionDirichletBC
variable = A
boundary = '1'
function = A
[../]
[./scaled_u]
type = FunctionDirichletBC
variable = scaled_u
boundary = '1'
function = scaled_u
[../]
[./R]
type = FunctionDirichletBC
variable = R
boundary = '1'
function = R
[../]
[]
[Executioner]
type = Transient
dt = 1
end_time = 2
nl_rel_tol = 1e-12
[]
[Outputs]
file_base = out
exodus = true
[]
(test/tests/utils/2d_linear_interpolation/xyz_error.i)
[Mesh]
file = cube.e
# This problem only has 1 element, so using DistributedMesh in parallel
# isn't really an option, and we don't care that much about DistributedMesh
# in serial.
parallel_type = replicated
[]
[Variables]
[./u]
order = FIRST
family = LAGRANGE
[../]
[]
[Functions]
[./u]
type = PiecewiseBilinear
#x = '0 1 3' # Testing this error
y = '0 1 3'
z = '0 0 0 0 1 3 0 5 7'
axis = 0
[../]
[] # End Functions
[Kernels]
[./diffu]
type = Diffusion
variable = u
[../]
[]
[BCs]
[./u]
type = FunctionDirichletBC
variable = u
boundary = '1'
function = u
[../]
[]
[Executioner]
type = Transient
dt = 1
end_time = 2
nl_rel_tol = 1e-12
[]
(test/tests/utils/2d_linear_interpolation/2d_linear_interpolation_test_internal.i)
# Test description - view this file in emacs and adjust the window size to view the file as it was created.
#
# This problem tests the MOOSE function PiecewiseBilinear and the MOOSE utility BilinearInterpolation, which are
# used to solve 2D linear interpolation problems.
#
# The problem is one element with node coordinate locations in x,y,z space as indicated in the ASCII art:
#
#
# ^
# |
# z
# |
#
# (1,1,2) (1,2,2)
# *--------------*
# / | / |
# / | (2,2,2) / |
# (2,1,2) *--------------* |
# | | | |
# | *---------|----* (1,2,1) --y-->
# | / (1,1,1) | /
# |/ |/
# *--------------*
# / (2,1,1) (2,2,1)
# /
# x
# /
# |_
#
# problem time ...0...1...2
#
#
# There are four variables and four functions of the same name, u,v,w, and A. The diffusion equation is solved
# for each of these variables with a boundary condition of type FunctionDirchletBC applied to a boundary
# (i.e. node set) that includes every node in the element. Each boundary condition uses a function of type
# PiecewiseBilinear that gets its value from the specified x, y, and z values.
#
# fred is a matrix of data whose first row and first column are vectors that can refer to either spacial positions
# corresponding to an axis or values of time. The remaining data are values of fred for a given row and column pair.
#
#
# Visualize fred like this:
#
# 0 1 3 where fred is a csv file that actually looks like this 0,1,3
# 0 0 0 0 0,0,0,0
# 1 0 1 3 1,0,1,3
# 3 0 5 7 3,0,5,7
#
# Another way to think of fred is:
#
# |0 1 3| - These values can be spacial positions corresponding to
# axis= 0,1, or 2, or time
#
#
# |0| |0 0 0|
# These values can be - |1| |0 1 3| - values of fred corresponding to row-column pairs
# time or spacial |3| |0 5 7|
# positions corresponding
# to axis= 0,1, or 2
#
#
# The parameters and possible values for the function PiecewiseBilinear are:
#
# x = '0 1 3'
# y = '0 1 3'
# z = '0 0 0 0 1 3 0 5 7'
# axis = 0, 1, or 2
# xaxis = 0, 1, or 2
# yaxis = 0, 1, or 2
# radial = true or false (false is default)
#
# where 0, 1, or 2 refer to the x, y, or z axis.
#
# If the parameter axis is defined, then the first row of fred are spacial position and the first column
# of fred are the values of time.
#
# If the parameter xaxis is defined, then the first row of fred are spacial positions and the first column
# of fred are the values of time ... just like defining the parameter axis.
#
# If the parameter yaxis is defined, then the first row of fred are time values and the first column of fred
# are spacial positions.
#
# If parameters axis AND EITHER xaxis or yaxis are defined together you'll get a moose error.
# i.e.
# axis = 0
# xaxis = 1
# results in an error. So, if you use the parameter axis, don't use xaxis or yaxis.
#
# If parameters xaxis and yaxis are defined (and radial is false), then the first row of fred are spacial positions corresponding to xaxis value,
# and the first column are spacial positions corresponding to the yaxis value.
#
# If xaxis and yaxis are defined and radial is true, the first row of fred contains values
# corresponding to the radius calculated from the coordinates of each point. Note that
# the definition of xaxis and yaxis define the "plane" of the radius. For example,
# xaxis = 0 and yaxis = 1 means that x and y components of the point are use to
# calculate the radius. xaxis = 1 and yaxis = 2 means that x and z components are used.
# The first column is for time in this case. xaxis and yaxis have to be specified and
# radial = true for this to work, otherwise a MOOSE error will result.
# This was developed so that an axisymmetric function could be defined for a 3D mesh.
#
[Mesh]
file = cube.e
# This problem only has 1 element, so using DistributedMesh in parallel
# isn't really an option, and we don't care that much about DistributedMesh
# in serial.
parallel_type = replicated
[]
[Variables]
[./u]
order = FIRST
family = LAGRANGE
[../]
[./v]
order = FIRST
family = LAGRANGE
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./A]
order = FIRST
family = LAGRANGE
[../]
[./scaled_u]
order = FIRST
family = LAGRANGE
[../]
[./R]
order = FIRST
family = LAGRANGE
[../]
[]
[Functions]
[./u]
type = PiecewiseBilinear
x = '0 1 3'
y = '0 1 3'
z = '0 0 0 0 1 3 0 5 7'
axis = 0
[../]
#
# Example 1 - variable u
#
# In this example, the first variable is u and the parameter axis is given the value 0. For such a case, the first
# row of fred refers to nodal x-coordinate values and the first column of fred (after the first row) refers to the
# times 0, 1, and 3.
#
# So, at time = 0, the value of u at each node is 0, because that's the value of fred for all x-coordinate values at time=0.
#
# At time = 1, the value of u at nodes with x-coordinate = 1 is 1.
# , the value of u at nodes with x-coordinate = 2 is 2.
#
# You can check this value with your own 2D linear interpolation calculation. Go ahead and check all the examples!
#
# At time = 2, the value of u at nodes with x-coordinate = 1 is 3.
# , the value of u at nodes with x-coordinate = 2 is 4.
#
[./v]
type = PiecewiseBilinear
x = '0 1 3'
y = '0 1 3'
z = '0 0 0 0 1 3 0 5 7'
xaxis = 1
[../]
#
# Example 2 - variable v
#
# In this example, the variable is v and the parameter xaxis is given the value 1. For such a case, the first
# row of fred refers to nodal y-coordinate values and the first column of fred (after the first row) refers to the
# times 0, 1, and 3.
#
# At time = 0, the value of v at each node is 0, because that's the value of fred for all y-coordinate values at time=0.
#
# At time = 1, the value of v at nodes with y-coordinate = 1 is 1.
# , the value of v at nodes with y-coordinate = 2 is 2.
#
# At time = 2, the value of v at nodes with y-coordinate = 1 is 3.
# , the value of v at nodes with y-coordinate = 2 is 4.
#
[./w]
type = PiecewiseBilinear
x = '0 1 3'
y = '0 1 3'
z = '0 0 0 0 1 3 0 5 7'
yaxis = 2
[../]
#
# Example 3 - variable w
#
# In this example, the variable is w and the parameter yaxis is given the value 2. For such a case, the first
# row of fred refers to times 0, 1, and 3. The first column of fred (after the first row) refers to the nodal
# z-coordinate values.
#
# At time = 0, the value of w at each node is 0, because that's the value of fred for all z-coordinate values at time=0.
#
# At time = 1, the value of w at nodes with z-coordinate = 1 is 1.
# , the value of w at nodes with z-coordinate = 2 is 3.
#
# At time = 2, the value of w at nodes with z-coordinate = 1 is 2.
# , the value of w at nodes with z-coordinate = 2 is 4.
#
[./A]
type = PiecewiseBilinear
x = '0 1 3'
y = '0 1 3'
z = '0 0 0 0 1 3 0 5 7'
xaxis = 0
yaxis = 1
[../]
#
# Example 4 - variable A
#
# In this example, the variable is A and the parameters xaxis AND yaxis BOTH defined and given the values 0 and 1 respectivley.
# For such a case, the first row of fred refers to nodal x-coordinate values.
# The first column refers to nodal y-coordinate values.
#
# In this example the values are the same for every time (except time=0 where the values are undefined)
#
# For nodal coordinates with x=1, y=1 A = 1
# x=2, y=1 A = 2
# x=1, y=2 A = 3
# x=2, y=2 A = 4
#
# You can use this 2D linear interpolation function for anything (BC, Kernel, AuxKernel, Material) that has
# a function as one of its parameters. For example, this can be used to describe the fission peaking factors
# that vary in time and along the length of a fuel rod, or a fission rate distribution in metal fuel that varies
# as a function of x and y postion, but is constant in time.
#
#
[./scaled_u]
type = PiecewiseBilinear
x = '0 1 3'
y = '0 1 3'
z = '0 0 0 0 1 3 0 5 7'
axis = 0
scale_factor = 2
[../]
#
# Example 5 - variable scaled_u. This is just a scaled version of Example 1 to see if the scale_factor works
#
#
#
[./R]
type = PiecewiseBilinear
x = '0 1 3'
y = '0 1 3'
z = '0 0 0 0 1 3 0 5 7'
xaxis = 0
yaxis = 1
radial = true
[../]
#
# Example 6 - variable R
#
# In this example, the variable is R and the parameters xaxis and yaxis are defined and
# given the values 0 and 1 respectivley. The parameter radial is also defined and given
# the value true. In this case, the x and y components of each point are used to
# calculate a radius. This radius is used in the call to BilinearInterpolation.
# In fred.csv, the first row are the radius values. The first column is time.
#
# At time = 1, the value of R at nodes with coordinates (x = 1, y = 1, or r = 1.414) is 1.414.
# , the value of R at nodes with coordinates (x = 1, y = 2, or r = 2.236) is 2.236.
# , the value of R at nodes with coordinates (x = 2, y = 2, or r = 2.828) is 2.828.
#
# At time = 2, the value of R at nodes with coordinates (x = 1, y = 1, or r = 1.414) is 3.414.
# , the value of R at nodes with coordinates (x = 1, y = 2, or r = 2.236) is 4.236.
# , the value of R at nodes with coordinates (x = 2, y = 2, or r = 2.828) is 4.828.
#
# Note that the case of x = 2, y = 1 gives the same result as x = 1, y=2.
#
#
[] # End Functions
[Kernels]
[./diffu]
type = Diffusion
variable = u
[../]
[./diffv]
type = Diffusion
variable = v
[../]
[./diffw]
type = Diffusion
variable = w
[../]
[./diffA]
type = Diffusion
variable = A
[../]
[./diff_scaled_u]
type = Diffusion
variable = scaled_u
[../]
[./diffR]
type = Diffusion
variable = R
[../]
[]
[BCs]
[./u]
type = FunctionDirichletBC
variable = u
boundary = '1'
function = u
[../]
[./v]
type = FunctionDirichletBC
variable = v
boundary = '1'
function = v
[../]
[./w]
type = FunctionDirichletBC
variable = w
boundary = '1'
function = w
[../]
[./A]
type = FunctionDirichletBC
variable = A
boundary = '1'
function = A
[../]
[./scaled_u]
type = FunctionDirichletBC
variable = scaled_u
boundary = '1'
function = scaled_u
[../]
[./R]
type = FunctionDirichletBC
variable = R
boundary = '1'
function = R
[../]
[]
[Executioner]
type = Transient
dt = 1
end_time = 2
nl_rel_tol = 1e-12
[]
[Outputs]
file_base = out
exodus = true
[]