we all know the military applications, so some civilian applications:
1. Computational chemistry and solid state physics - for better solar cells, medicine, processes, etc. that require detailed knowledge of the behavior of millions of molecules at once (which is still a tiny nanometer sized piece of the material or device) over timescales that are not directly observable in experiments such as femtoseconds or centuries.
2. Weather forecasting - did you know that merely 50 years ago, all of mankind was at the mercy of the weather and nobody knew what would happen even within 12 hours? Without supercomputers, weather forecasts will not exist.
3. Fluid dynamics - for the design of everything that moves through fluid mediums, ranging from swimsuits to aircraft.
4. Finance - the markets are extremely complicated and many highly volatile markets require supercomputer models to predict trends. In fact, algorithmic trading is already a thing and many traders actually rent supercomputer processors to do exactly this.
5. Astrophysics - astrophysics is extremely computationally intensive because of a thing called multiscale dynamics. For example, in chemistry and solid state physics, everything that matters happens at the nanometer range. That's a single size scale. In fluid dynamics, everything that matters happens at a meter scale. That's also a single size scale. But in astrophysics, there's things that happen at at the atomic level, but which have effects that manifest at the stellar scale (millions of years and across millions of miles), which makes it so that only supercomputers can handle the code.
