GPS-X Technical Reference

Miscellaneous 426
The trim parameters shown here refer to the output of the ACSL trim function. This is an
alternative steady-state solver, which uses the Jacobian matrix for accelerated searches. However,
this gradient type routine was not found to be very robust with the large models encountered
within GPS-X.
NUMERICAL CONTROL
The numerical issues discussed in this chapter are important because the success of a simulation
depends on the input data and the models and on the numerical solver used to do the calculations.
Any modeller using dynamic simulation should have an understanding of the underlying
numerical methods used to solve the equations to properly interpret the results. Understanding the
numerical methods used will help to identify problems that are numerical in nature.
The choice of which numerical solver to use is important. There are several numerical integration
methods available in GPS-X. The numerical solver can be set in the Simulation Control window
or can be saved into a scenario or the layout by setting it in
General Data > System > Input Parameters > Integration Control (Figure 15-11).
Generally the default integration method, Runge-Kutta-Fehlberg (2), works very well for most
models; however, there are situations where the solver may need to be changed. In general the
trade-off is between numerical accuracy and simulation speed. The fixed step algorithms
(i.e. Euler, Runge-Kutta (1), and Runge-Kutta (2)) are faster than the variable step algorithms
(i.e. Adams-Moulton, Runge-Kutta-Fehlberg (1), Runge-Kutta-Fehlberg (2), Gear's Stiff, and
Differential Algebraic Solver) but are not as accurate.
If the system is stiff then you may need to use the Gear's Stiff algorithm. A stiff system is one in
which there are processes occurring at very different time scales (e.g., a very fast process such as
the transfer of oxygen into a tank and a very slow reaction occurring at the same time).
In addition to the numerical solvers, the user can change some of the numerical parameters that
control the simulations. Changing the default parameters however requires extreme caution
because in some cases it may introduce errors in the results. The numerical parameters are
accessed by making the following selections:
General Data > System > Parameters > Numerical. The form is shown in Figure 15-12.
These parameters include bounds on flow, state variables, state derivatives, parameters,
exponentials, and volumes. The parameters for the implicit solver (IMPL - used for solving
implicit functions evaluated as residuals, where the residuals are reduced to zero) used in the
exact code option can be set here. Some of the parameters are discussed in more detail in the subsections
below.
GPS-X Technical Reference