Time Discrete Solver

) to find the solution to time-dependent problems (dynamic or unsteady problems) that have already been discretized in time using, for example, the prev operator or the bdf operator. This solver is automatically used when a Time Discrete study is added to the model.

See About the Time Discrete Solver for background information.

Use the list to specify if the settings are synchronized with the corresponding study step. If you select (to override the settings defined in the corresponding study node), you can specify the , , and settings.

Use the list to choose a time unit that is suitable for the time span of the simulation. The default time unit is inherited from the corresponding setting in the study step.

Use the field to enter a vector of times that define the simulation’s time span.

The time step is specified in the field. Valid entries are a scalar, a vector of times, or an expression containing global expression variables.

Discretizing time derivatives using the prev operator or the bdf operator requires the solution at previous discrete times. How many previous time steps should be stored is specified in the field. If you, for example, use the first-order bdf operator (bdf(u,1)), the solution at one previous time step is required. Using the second-order bdf operator (bdf(u,2)) requires the solution at two previous time steps. The default value is 2.

From the list, choose one of the following options:

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Choose (the default) to store the output times using interpolation from the solver’s time steps.

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Choose to use the time steps from the solver that are closest to a given output time among all the steps that have passed this output time.

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Choose to store the actual time steps from the solver. Specify to store every Nth step in the field (default value: 1; that is, all time steps are stored).

Use the field to enter a positive number. This number controls how accurately the nonlinear system of equations is solved in each time step. In general, the desired relative error in the solution should be entered here.

Here you can specify an absolute tolerance that the nonlinear solver uses to control the absolute error. The tolerance specified here is applied to all variables unless modified per variable by selecting a method other than the global method for a variable.

Use the list to select how the specified absolute tolerance is to be interpreted for the variables that use the global method (by default, all variables use the global method). Select:

Select a to specify how to enter and compute the absolute tolerance. Select:

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to specify a factor (default: 0.1) in the field that makes the absolute tolerance proportional to the relative tolerance. With this method, the absolute error does not become dominating when you reduce the relative tolerance so that it is much smaller than the absolute tolerance.

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to specify a value for the absolute tolerance. In the field, enter a positive number that is applied to either scaled or unscaled variables.

To specify the absolute tolerance individually for a variable, select the variable from the list and modify the corresponding tolerance with the list. Select:

If you select or , additional fields appear. Use the field to modify the absolute tolerance for the selected variable.

See Time-Dependent Solver for these settings.

Use the list to control at what times the solver stores a solution. Select:

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to store solutions at the times entered in the field in the section.

When is selected, the solution to output is computed through interpolation. Therefore, the solution at previous time steps is not computed, which means that expressions with the prev and bdf operators cannot be used in analysis. Such expressions can only be used in analysis when you have selected .

In this section you can define constants that can be used as temporary constants in the solver. You can use the constants in the model or to define values for internal solver parameters. These constants overrule any previous definition (for example, from Global Definitions). Some examples of when it can be useful to define constants for a solver:

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When you want to define auxiliary parameters that are part of the equations like CFLCMP or niterCMP and where the solver does not define these parameters (niterCMP is defined by the nonlinear solvers).

Click the button (

) to add a constant and then define its name in the column and its value (a numerical value or parameter expression) in the column. By default, any defined parameters are first added as the constant names, but you can change the names to define other constants. Click (

) to remove the selected constant from the list.