Consistent terminology: Modeling, DAE, ODE

Question

I am new to the subject "modeling of physical systems". I read some basic literature and did some tutorials in Modelica and Simulink/Simscape. I wanted to ask you, if I understand the following content correctly:

• Symbolic manipulation is the process of transforming a differential-algebraic system of equation (physical model: DAE) into a system of differential equations (ODE) that can be solved by standard solvers (Runge, Kutta, BDF, ...)
• There are also solver that can solve DAE's directly. But Modelica (openModelica, Dymola) and Simscape transfer the System into an ODE (why are this methods better compared to direct DAE solvers?)
• A "flat Modelica code" is the result ( = ODE) of the transformation.

Thank you very much for your answers.

Answer 1

Symbolic processing for Modelica includes:

• remove object oriented structure and obtain an hybrid DAE (flat Modelica)
• perform matching, index reduction, casualization to get an ODE
• perform optimization (tearing, common subexpression elimination, etc)
• generate code for a particular solver

OpenModelica can also solve the system in DAE mode without transforming it to ODE and I guess other Modelica tools can also do that.

A "flat Modelica code" is Modelica code where the object orientation is removed, connect equations are expanded to normal equations. The result is a hybrid DAE.

See Modelica Spec 3.3 for more info about all this (for example Appendix C): https://modelica.org/documents/ModelicaSpec33Revision1.pdf