Keywords
There are a number of ways of simulating and executing various aspects of Systems Modeling Language v1 (SysML®), and they are not just novelties! They also really help your models become more robust, logical, and organised.
There is "internal" tool simulation of Activities and StateMachines based on fUML (or variations of it).
The Magic Model Analyst® (Cameo Simulation Toolkit®) for MagicDraw/Cameo currently supports most of fUML-1.3/1.4 and adds on lots of additional simulation capabilities, including sending signals via Ports on Block usages via Behaviors.
There is also the ability to perform constraint maths calculations using SysML Parametrics. The SysML Parametrics approach is very powerful and intuitive, and definitely useable on real world projects. It can also be used for Trade Off Studies.
The MagicDraw/Cameo tools support most basic mathematics using an internal maths engine, but one can also connect to external engines such as Mathematica, Maple, or MATLAB with the results being fed back live into the tool.
Then there's the SysML Extension for Physical Interaction and Signal Flow Simulation (SysPhS), which enables one to develop Block models representing signal flows and physical interactions (together with SysML Parametrics) and export them to Modelica or Simulink/Simscape/Stateflow to perform time-dependent system simulation and calculations (integrate systems over time). There's even the ability in MagicDraw/Cameo to view the results of OpenModelica directly in the tool.
To learn about the combinations of tools and plugins you may need visit:
Did you know?
SysMLv2 is being designed with simulation in mind from the very start! But don't let anyway tell you that you have to wait for SysMLv2 to do industrial strength simulation and execution work with SysML, there's already a lot you can on real world projects.
Some example UML/SysML1.x slide trails and screencast videos on this site involving simulation, execution, and calculations: