Use the Time Explicit Solver (
) to find the solution to time-dependent problems (also called dynamic or unsteady problems) using the family of Runge–Kutta explicit time-stepping schemes or the Adams-Bashforth 3 solver. This solver is used with a
Time Dependent study. When adding a Time-Explicit Solver node,
Direct,
Advanced, and
Fully Coupled subnodes are added automatically. The Fully Coupled solver is meant to solve algebraic equations, and you can control it using the
Algebraic equations settings (see below) in models that use discontinuous Lagrange elements.
Use the Defined by study step list to specify if the settings are synchronized with the corresponding study step. You can also select
User defined to define all settings locally.
Use the Times field to enter a vector of times that define the time span for the simulation. Click the
Range button (
) to define a range using the
Range dialog box.
Use the Method list to specify the time-explicit method:
Adams-Bashforth 3,
Adams-Bashforth 3 (local) (available for the Wave Form PDE interface), or the classic
Runge-Kutta family.
From the Time stepping list, for Runge–Kutta and Adams–Bashforth 3, specify
Manual or time stepping
From expressions, where the latter is useful for the Wave Form PDE. When you use
From expression, a list of
Cell time scale expressions appear, where you can add such expressions to define the time stepping. For explicit methods, the largest stable time step can automatically be computed from an expression. Some physics interfaces (Wave Form PDE, for example) define such an expression in terms of an estimated maximum wave speed (defined by the interface) and the element size (
wahw.wtc). Here the element order is also taken into account. The expression should in general represent a local cell time scale. For wave problems, the expression should be proportional to the time it takes for the fastest wave to pass one mesh element. Each expression given is evaluated on all mesh elements. The smallest value (time scale), over all elements and all expressions, dictates the time step used. If you select
User defined from the
Defined by study step list, you can use the
Add button (
) and the
Delete button (
) to add or delete rows in the list.
The time step is specified in the Time step field when
Manual is selected from the
Time stepping list. Valid entries are a scalar, a vector of times, or an expression containing global expression variables. The default value is 0.001 s (1e
−3 s).
The Interpolate solution at end time check box is selected by default. The solver can then step past the last time in the
Output times list, leading to the end time being interpolated. If you clear this check box, the solver will not step past the last time in the
Output times list, so that the time stepping includes the last time and takes no steps past that time.
Use the Mass matrix solver list to select the linear solver to be used within the time-stepping scheme to invert the mass matrix. Available linear solvers appear in the model tree. The default is to use the
Direct linear solver. For cheap but approximate inversion of the mass matrix, use the
Lumped option.
From the Algebraic equations list, choose
Solve every Nth step (the default) and then enter a positive integer in the
N field (default: 1), or choose
Solve periodically and then enter the period (SI unit: s) in the
Period Δt field (default: 0) for solving algebraic equations. For more information, see
About the Wave Form PDE Interface.
