Electrical simulation methods have been developed extensively to simulate electrical and electronic circuits. It is commonly recognised that there are electrical analogs to mechanical components using mass, springs and dampers which can then be represented as capacitors, inductors and resistors, with these analogous circuit simulations it is then possible to determine the systems response to arbitrary user inputs, and perform frequency response sweeps, and to optimise component values to minimise overshoots and resonances, in many cases analogous circuit simulations can provide quick and elegant solutions to problems in other physical realms.
In my career as a research engineer (electrical) I've used electrically analogous systems several times but rarely come across other EE's doing the same.
There must be many other interesting practical applications of physical systems that are designed or analysed based on analogous electrical systems.
Background reading:
https://en.wikipedia.org/wiki/Mechanical%E2%80%93electrical_analogies
https://lpsa.swarthmore.edu/Analogs/ElectricalMechanicalAnalogs.html