76 10 WinDali Simulation Interface

10.4 Dali solver

The default solver used by the simulation program, is a slightly modified version of the solver described in [1]. The solver has the following characteristics:

•Differential equation solver: 3 step, 3. order semi-implicit Runge Kutta (NT1 developed by Nørsett & Thomsen). Specially suited for stiff problems.

•Algebraic equation solver: Modified Newton iteration, which includes

oConvergence control (method for keeping the same Jacobian in several iterations)

oDivergence control (extrapolation method which extrapolates the variables into the convergence area at beginning divergence).

•Interpolation with 2. order splines, which is used for:

oGuessing static variables in next step (by extrapolation).

•The location of discontinuities is found using a secant-method.

The following parameters can be set for the solver:

Parameter	Meaning
Write	Select between the following
	• Start, End and Disc. points: writes the solution at Start, End and
	Discontinuity points.
	• All: writes the solution at all points.
	• Debug: writes Jacobians, information on iterations, etc. This
	generates very extensive information.
Max iterations	Maximum number of iterations in solution of static equations.
Max Jacobians	Maximum number of Jacobians the solver is allowed to calculate each time
	the static equation set is solved.
Relative error	Convergence criterion.
Max step size	The maximum step size the solver is allowed to use.
Min step size	The minimum step size the solver is allowed to use.
Max number of	How many times the solver is allowed to reject a step, change the step size
rejected steps	a try another step.
Use extern static	The build in static equation solver is fast, but can also cause problems.
solver	More stable (but also slower) solvers can be selected.

If you encounter problems solving the equations, a good idea is to try one or more of the following:

•Decrease the maximum step size

•Increase/decrease the Relative error

•Try an extern static equation solver

•Increase the number of iterations and/or the number of Jacobians.

When an extern static equation solver is used, the maximum number of iterations should be increased. The maximum number of Jacobians has no influence when an extern static equation solver is used.

WinDali

Morten Juel Skovrup