Here is an example simulation, showing the steady-state thermal response of a 2-D system. A wire heater is pattered on a silicon-dioxide membrane, as might be manufactured with a silicon-on-insulator process. For example, this may be used in a flow sensor. An advection term is used in the PDE so that the flow of water, or air, can be considered.
-src
pdeSim.py - code for solving the PDE
models.py - contains the model geometry
materials.csv - thermal properties of materials, referenced by models.py
-scripts
membrane_heater.ipynb - runs the overall simulation, performs data analysis
-data
membrane_heater.hdf5 - the simulation data, including the input parameters, as attributes
-figures
*.png - snapshots of the simulation results
The PDE is written as a sparse matrix equation and directly solved using the scipy.sparse.linalg.spsolve method. At a larger matrix size, an iterative solved would have been used but, here, the run time of the direct solver is acceptable.