A default Global Equations node (
) is added to
The Global ODEs and DAEs Interface. To add additional
Global Equations nodes, either right-click and select it from the context menu or click
Global Equations in the toolbar.
You can enter a suitable name for the global equations in the Name field. The default name (for the first
Global Equations node) is
ODE1. The name must be a valid variable name and is used to set the field name attribute on the ODE model entity created by the
Global Equations node. This name is used as an identifier for the corresponding solver feature under
Dependent Variables (
comp1.ODE1, for example).
with the initial conditions u(t0) = u0 and
ut(t0) = ut,0 (where the subscript
t indicates the time derivative). Several equations can be added and the equation can be coupled.
The first time derivative of u is written
ut, and the second time derivative of
u is
utt. With time derivatives, this equation is an ODE (ordinary differential equation). With no time derivatives, the equation is an algebraic equation or a transcendental equation. If some equations include time derivatives and others do not, the system is a DAE (differential-algebraic equation).
In the Global Equations table, each row corresponds to a named equation; that is, it defines a single degree of freedom and one equation.
The software then adds this global equation to the system of equations. When solving the model, the value of the dependent variable u is adapted in such a way that the associated global equation is satisfied. All dependent variables and their time derivatives can be used as well as any parameters, global variables, and coupling operators with a scalar output and global domain of definition in the
f(u,ut,utt,t) column. The variables can be functions of the dependent variables in the global equations. Setting an equation for a dependent variable is optional. The default value of
0 means that the software does not add any additional condition to the model.
Save the definitions of the global equations to a text file by clicking the Save to file button (
) and using the
Save to File dialog box that appears. To load a text file with global equation definitions, use the
Load from File button (
) and the
Load dialog box that appears. You can also click the downward arrow beside the
Load from File button and choose
Load From (
) to open the fullscreen
Select File window. Data must be separated by spaces or tabs (or be in a Microsoft Excel Workbook spreadsheet if the license includes LiveLink™
for Excel®).
The Discretization section for
Global Equations is used to specify the
Value type (
Real or
Complex) of the variables. The
Split complex variables in real and imaginary parts setting is activated in the
Compile Equations node of any solver sequence. The default for the split complex variables setting is to be not active and in that case you do not need to specify the value type for global equations variables (the value type specified would be ignored in such cases). The value type (complex or real) for all the variables defined by this
Global Equations node is selected in the
Value type when using splitting of complex variables selection. The default value type is
Complex.
Select the Dependent variable quantity that defines the unit for the dependent variable
u. The default is
Dimensionless (with
1 in the
Unit column). Click the
Select Dependent Variable Quantity button (
) to open the
Physical Quantity dialog box to browse to find a physical quantity to use. You can also type a search string in the text field at the top of the dialog box and then click the
Filter button (
) to filter the list of physical quantities. For example, type
potential and click the
Filter button to only list physical quantities that represent some kind of potential. Alternatively, click the
Define Dependent Variable Unit button (
) to edit the unit directly in the
Unit column, typing a unit to define the dependent variable quantity. The quantity column then contains
Custom unit.
Select the Source term quantity that defines the unit for the source term
f (the unit for the right — and left — side of the global equation). The default is
Dimensionless (with
1 in the
Unit column). Click the
Select Source Term Quantity button (
) to open the
Physical Quantity dialog box to browse to find a physical quantity to use. You can also type a search string in the text field at the top of the dialog box and then click the
Filter button (
) to filter the list of physical quantities. For example, type
potential and click the
Filter button to only list physical quantities that represent some kind of potential. Alternatively, click the
Define Source Term Unit button (
) to edit the unit directly in the
Unit column, typing a unit (for example,
W/m^3 or
A/m^3) to define the dependent variable quantity. The quantity column then contains
Custom unit.