Time Discrete Solver
Use the 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.
General
Use the Defined by study step list to specify if the settings are synchronized with the corresponding study step.
Use the Times field to enter a vector of times that define the simulation’s time span.
The time step is specified in the Time step 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 Number of time discrete levels 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.
Use the Relative tolerance 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.
Absolute Tolerance
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 Global method 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:
Scaled to let the absolute tolerance be applied to scaled variables.
Unscaled to let the absolute tolerance be applied to unscaled variables.
Select a Tolerance method to specify how to enter and compute the absolute tolerance. Select:
Factor to specify a factor (default: 0.1) in the Tolerance factor 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.
Manual to specify a value for the absolute tolerance. In the Absolute tolerance 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 Variables list and modify the corresponding tolerance with the Method list. Select:
Scaled to apply the specified tolerance to scaled variables.
Unscaled to apply the specified tolerance to unscaled variables.
Use global (the default) to apply the tolerance specified for the global tolerance.
If you select Scaled or Unscaled, additional fields appear. Use the Tolerance field to modify the absolute tolerance for the selected variable.
Results while Solving
See Time-Dependent Solver for these settings.
Output
Use the Times to store list to control at what times the solver stores a solution. Select:
Specified times to store solutions at the times entered in the Times field in the General section.
Steps taken by solver to store solutions at the time steps taken by the solver.
When Specified times 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 Steps taken by solver.
Constants
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:
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 Add button () to add a constant and then define its name in the Constant name column and its value (a numerical value or parameter expression) in the Constant value column. By default, any defined parameters are first added as the constant names, but you can change the names to define other constants. Click Delete () to remove the selected constant from the list.
Log
This section, which is initially empty, contains a log from the time stepping. Select the Keep warnings in stored log check box as needed.