- curlUpdater
curlUpdater¶
Works with VSimBase, VSimEM, VSimPD, VSimPA, and VSimVE licenses.
Multifield updater operation that solves equations of the form:
\[\frac{\partial {\bf F}}{\partial t}=A\left(\nabla \times {\bf G}\right)+B{\bf H},\]
via the operation:
\[F_{i}\left(t+\Delta t\right) = F_{i}\left(t\right) + (c_0 + c_1 \Delta t) \left[ A \left( \nabla \times {\bf G} \right)_{c_{g}+i} + B H_{c_{h}+i} \right],\]
\({\bf F}\) is the writeFields
.
\({\bf G}\) is the first readFields
.
\({\bf H}\) is an optional second readFields
(if missing, the coefficient B is taken to be 0).
\(i\) is the updater component.
\(c_{0}\) and \(c_{1}\) are the dtCoefficients
values (represented in the form [\(c_{0}\) \(c_{1}\)])
\(A\) and \(B\) are the readFieldFactors
values.
\(c_{g}\) and \(c_{h}\) are the readFieldCompShifts
values (represented in the form [\(c_{g}\) \(c_{h}\)]
and usually both 0, see the note following curlUpdater Parameters).
curlUpdater Differencing Definitions¶
Forward curlUpdater differencing definition:
Backward curlUpdater differencing definition:
curlUpdater Parameters¶
The curlUpdater takes the lowerBounds
and
upperBounds
parameters of FieldUpdater, as well as
the global region modification parameters and local region
modification parameters. In
addition, curlUpdater takes the following parameters:
- readFields (required string vector)
A vector of either one or two strings. The first string is the name of the field to take the curl of, and if provided, the second is the name of the field (multiplied by the specified factors) to add to the result.
- writeFields (required string vector)
A vector containing a single element, which is the name of the field to update.
- differencing (required string)
Either
forward
orbackward
, as described above.
- useVecUpdater (optional integer, default = 0 (false))
If true, the updater will update all three components of the vector field specified in
writeFields
, beginning with the specifiedcomponent
. The updated field must therefore have at least \({\tt component} + 3\) components.
- component (optional integer, default = 0)
The field component to update, or if
useVecUpdater
istrue
, the first field component to update.
- readFieldCompShifts (optional integer vector, default = [0 0])
This vector must have the same number of elements as
readFields
. It specifies the amount by which to increment the component indices of the first field and the (optional) second field. It is equal to [\(c_g\) \(c_h\)] in the description above. For example, if a magnetic field is represented by components 3–5 of the fieldEandB
, then to calculate the curl of that magnetic field, one would specifyreadFields = [EandB]
andreadFieldCompShifts = [3]
.
- readFieldFactors (optional float vector)
If this is specified, there must be one element for each field specified in
readFields
. The terms in the update for each field are multiplied by the corresponding factors; they are the coefficients \(A\) and \(B\) in the description above. If not specified, the factors use values of \(1\) for each field.
- dtCoefficients (optional float vector, default = [1. 0.])
Two components [\(c_{0}\) \(c_{1}\)] as defined in the equation above. The result of the updater will be multiplied by (\(c_{0}\) + \(c_{1} \Delta t\)), where \(\Delta t\) is the current time step.
- gridBoundary (optional string)
If provided, only components on the interior of the specified GridBoundary will be updated. The method to define the interior is given in the
interiorness
parameters.
- interiorness (optional string, default = cellcenter)
If the
gridBoundary
parameter is specified, this is the method the used to determine whether a component is interior to the boundary. The behavior depends on theoffset
specified in the updated Field. One of:cellcenter
:If
offset = none
, oroffset = edge4v
andcomponent = 0
, then a cell is considered interior if its node is adjacent to at least one cell with center inside the boundary.If
offset = edge
, oroffset = edge4v
andcomponent
is not0
, then a cell is considered interior if the edge specified bycomponent
is adjacent to at least one cell with center inside the boundary.If
offset = face
, then a cell is considered interior if the face specified bycomponent
is adjacent to at least one cell with center inside the boundary.If
offset = center
, then a cell is considered interior if its center is inside the boundary.
deymittra
If
offset = none
, oroffset = edge4v
andcomponent = 0
, then a cell is considered interior if all nodes adjacent to (i.e. displaced by a single edge from) its node are inside the boundary.If
offset = edge
, oroffset = edge4v
andcomponent
is not0
, then a cell is considered interior if the edge specified bycomponent
has at least one adjacent node inside the boundary, and that edge is not ignored by the Dey-Mittra algorithm given thedmFrac
parameter specified in thegridBoundary
.If
offset = face
, then a cell is considered interior if all nodes adjacent to the face specified bycomponent
are inside the boundary.This
interiorness
option cannot be specified withoffset = center
.
dmnodal
This
interiorness
option is identical todeymittra
.
- lowerSkinDepth (optional integer vector)
Specifies the number of skin cells, in each direction, on the lower end of the local domain. The cells in the skin are updated before the fields specified as
messageFields
in the UpdateStep or InitialUpdateStep block are messaged. If not specified, the skin depth will be determined automatically.
- upperSkinDepth (optional integer vector)
Specifies the number of skin cells, in each direction, on the upper end of the local domain. If not specified, the skin depth will be determined automatically.
Example Yee Ampere (Ey) Update Block¶
To solve the y component of Ampere’s law with Maxwell’s correction,
via the curlUpdater opperation
where
\({\bf E}\) is the elecField, \({\bf B}\) is the magField, \({\bf J}\) is the current density, and \({\bf S}\) is the SumRhoJ field defined by
use the following code:
<FieldUpdater ampere-y>
kind = curlUpdater
component = 1
differencing = backward
writeFields = [elecField]
readFields = [magField SumRhoJ]
readFieldFactors = [$c^2$ ~$(-1/\epsilon_0)$]
dtCoefficients = [0. 1.]
readFieldCompShifts = [0 1]
</FieldUpdater>
Adding \(S_2\) is adding \(J_1\), thus the component on the SumRhoJ field must be shifted so that \(J_1\) is added to \(E_1\).