Initialization by static calculation: operation

Static initialization

To avoid this problem of “numeric transient”, initial conditions of the « Initialization by static calculation » type can be taken into account with Flux. The goal of this option is to initialize a time computation in order to avoid transient phenomena with no physical meaning.

These calculation conditions are presented in the following blocks.

Conditions of calculation

The initialization by static calculation is characterized by particular calculation conditions for the first time step: conditions, which permit to annul all the terms in d/dt at the step t = 0 s.

These conditions are summed up in the table below.

Element of the device Hypotheses / conditions of calculation at t = 0 s
in the finite elements domain in the electric circuit
Solid conductor Active (circuit coupling)

skin effects, proximity effects are not taken into consideration (= non magnetic conducting regions)

DC resistance (electric conduction resistance)

passive (no circuit coupling)

Induced currents are not taken into consideration (= non conducting magnetic region)

Coil conductor

Current in coil (=circuit current)

resistance (of coil conductor)

Element of the device in the electric circuit

Resistance (values of the Resistor component)


Inductance replaced by a resistor with small resistance


with initial voltage Uc

Capacitor replaced by a voltage source * (U = Uc)

without initial voltage

Capacitor replaced by an open circuit

Note: * Caution: for circuit with capacitor (with initial voltage) you must add a switch in the circuit (see “ Initialization by static calculation: particular cases”).

Example 1

Magnet placed at the center of the coil

Finite elements description: Circuit description:
Results without SI : Results with SI :

Example 2

Variable reluctance speed sensor as describe in the Generic Tutorial for Flux 3D

Finite elements description: Circuit description:

Results with and without SI: