Time-Explicit Solver
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.
Also see The Time-Explicit Solver Algorithms.
General
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.
For Runge-Kutta, select the order of the time-stepping scheme from the Order list.
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 (1e3 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.
In rare cases, when the PDE is nonlinear, you can adjust the Relative tolerance (default value: 0.01).
Results while Solving
See Time Dependent for these settings.
Output
See Time Discrete Solver for these settings.
Constants
See Time Discrete Solver for these settings.
Output
See Time Discrete Solver for these settings.