As described in Equations, as an alternative to the weak form you can enter the equation using the Coefficient Form Equation node (
).
). To add a Coefficient Form Equation, first add a Component node under Building Blocks>Components, then:
|
•
|
). |
•
|
The Settings window has the following sections:
This section displays the equation that you define by defining the coefficients in the next section.
There are eight coefficient in a coefficient form equation. You define each coefficient by defining a tensor expression that requires a certain dimension. The dimensions are defined by the dimension of the dependent variable, N, and the number of spatial dimension (always 3). The table below lists the dimensions for all eight coefficients.
|
da
|
||
|
ea
|
If the dependent variable is a scalar, you can simplify the tensor dimensions by skipping all singleton dimensions. This simplifies the γ, α, and β coefficients to be spatial vectors (length 3). The dependent variable can only be a tensor up to rank 1 (a vector), so use the weak form equation for dependent variables of higher ranks.
You also specify these coefficients for boundary conditions, which differs slightly from the General from PDE interface in the Model builder. It is straightforward to convert a Flux/Source boundary condition from this interface to an equivalent representation using only the f coefficient instead of the g coefficient.
Under this section you choose the dependent variable to use for the coefficient form equation. Similar to the dependent variable definition, you specify a reference to a dependent variable. In the Dependent variable reference list, you choose if you can use the physical quantity as the reference (choose Use physical quantity, which is the default), or if you have to append an unique tag (choose Use physical quantity + tag and enter a tag in the Unique tag field).
The options in the Selection list and Output entities list define the selection where this variable definition is valid. See Specifying Selections for more information.
Clear the Use volume factor in axial symmetry and for non-orthonormal systems check box if you want to skip any volume factors in the weak form integration. In axial symmetry this means that you do not get the factor 2πr. For more information on non-orthonormal systems.
If you want to use a different base vector system than the parent feature or property, you can choose a different system in the Base vector system list.
 |
|