Piecewise
A Piecewise function () is created by splicing together several functions, each defined on one interval. Define the argument, extrapolation and smoothing methods, and the functions and their intervals. The piecewise function is a function of one variable with different definitions on different intervals, which must not overlap or have any holes between them. The default Function name is pw1.
The Analytic, Interpolation, and Piecewise functions can also be added to Materials. See Using Functions in Materials.
Definition
Enter a name for the argument to the piecewise function in the Argument field.
Select an Extrapolation method to control what happens when the function is evaluated in a point that does not belong to any interval: Constant (the default), None, Nearest function, Specific value, or Periodic.
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Constant. Uses the function value from the endpoint of the closest interval. Uses the value from the starting point of the first and the endpoint of the last interval on the corresponding sides.
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None. Evaluation fails outside of the intervals where it is defined. Trying to evaluate the function generates an error and evaluates to NaN (Not-a-Number).
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Nearest function. Evaluate the function from the closest interval. The function at the first or last interval (depending of the side) is used to evaluate at the actual point where a value is requested.
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Specific value. Also enter a value in the Value outside range field. If selecting the specific-number method, assign a single value (usually zero or NaN) to all points outside the intervals.
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Periodic. The function becomes periodic by repeating its values in the interval where it is defined in regular intervals of the same size.
Select a Smoothing: No smoothing (the default), Continuous function (to make the function continuous but not its derivatives), Continuous first derivative, or Continuous second derivative. For any selection (except No smoothing), enter a value in the Size of transition zone field (dimensionless). The default is 0.1. Using the Transition zone list you can select if the size should be relative or absolute. Relative size (the default) means that the size is relative in relation to the size of the intervals on both sides of the border. Absolute size gives smoothing on an interval that is symmetric around the border. If you have chosen to use smoothing and the Extrapolation is Constant, Specific value, or Periodic, a Smooth at endpoints check box appears. Select that check box if you want to smooth at the endpoints — that is, the left endpoint of the leftmost interval and the right endpoint of rightmost interval.
The functions in contiguous intervals need not evaluate to the same value where the intervals meet. If the values differ the function has a discontinuity, and it is recommended that you apply smoothing to make the piecewise function more well-behaved numerically. Functions from neighboring intervals are then blended close to where the intervals meet.
For each cell in the Intervals table, enter Start and End interval limits. The intervals must not overlap, and there cannot be any holes between intervals. Enter an expression defining the Function. You can move rows up and down in the table, insert a row above the selected rows, remove a row from the table, and clear the table using the buttons underneath the table or by right-clicking in the table.
The intervals must be contiguous.
A plot group for a piecewise function contains three connected line graphs: a line graph of the piecewise function and two line graphs using dashed red lines, Left Extrapolation and Right Extrapolation, that show how the selected extrapolation extends the piecewise function on both sides.
See Common Settings for the Function Nodes for information about the Units section.
With the Heat Transfer Module, see Radiative Heat Transfer in a Utility Boiler: Application Library path Heat_Transfer_Module/Thermal_Radiation/boiler.