Continuous Simulation

Simulation of one time step executes according to the following steps. First causality is assigned to components in the acausal bond graph. (i) Fixed causality as enforced by sources and junctions that are OFF is propagated. (ii) Preferred causality of storage components is propagated. Fixed or preferred causality propagates in a depth first fashion. Causal analysis is aborted when a fixed causality conflict (i.e., between two sources) is detected. Derivative causality of storage components is handled but algebraic loops between resistances are not.

After causality is assigned to the energy related bond graph components, the execution order of all the components including the fixed causality block diagram components, is determined based on the availability of their input values at each moment during the propagation process. This execution order is determined by the following sequence of steps and stored in a central array, therefore, it only takes place once for each continuous mode:

1.

Clock components propagate time. This prevents time modulation from lagging one integration step, as is the case for other modulation types.

2.

Values of junctions that are OFF, values of sources, and values of storage elements that are in preferred causality are propagated.

3.

The effort and flow values of active bonds are propagated into the connected components.

4.

The block diagram model part is executed by propagating all component output values that can be calculated.

5.

Variables in finite state machine signal ports are conditionally updated. During continuous integration and when an individual state update takes place, both a priori and a posteriori are updated but during event iteration only a posteriori values are changed.

After events may have changed the state of one or more controlled junctions, causality is assigned and this execution order is compiled again.