Simulations are cool, but running simulations on supercomputers is even cooler. Although, you may want to make sure you are using the hardware optimally, before you decide you need a bigger computer to get the job done fast enough.
A parallel solver for a 2D heat equation
A conjugate gradient solver for a 2D heat equation, parallelized with OpenMP for a shared-memory machine with several ccNUMA domains and benchmarked on the Fritz cluster at NHR@FAU. I wrote it together with Shreyas Balumurali as a course project for "Programming Techniques for Supercomputers" at FAU.
Dielectric antenna simulations in MATLAB
For a bachelor's course "Antennas & Wireless Systems" I wrote a finite-difference time-domain simulator (in one and two dimensions) to simulate how an array of dielectric rods with particular alignment can actually behave as a pretty efficient antenna.