One example from the science is 3D simulation of core-collapse supernova. Simulating the fluid dynamic, radiation transport, and magnetic field only in fully 3D requires at least sustained petaflops capable machine, meaning probably several tens or hundreds of real petaflops, not only theoretical peak speed (application that can run on 30% theoretical peak speed is considered great!).
Other applications are probably climate modeling, cosmology modeling, energy research, etc. There are a lot of scientific app that can use that kind of computing power. We are always limited by computational power, and therefore has to make a lot of approximation, simplification, and coarser resolution of modeling.
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One example from the science is 3D simulation of core-collapse supernova. Simulating the fluid dynamic, radiation transport, and magnetic field only in fully 3D requires at least sustained petaflops capable machine, meaning probably several tens or hundreds of real petaflops, not only theoretical peak speed (application that can run on 30% theoretical peak speed is considered great!). Other applications are probably climate modeling, cosmology modeling, energy research, etc. There are a lot of scientific app that can use that kind of computing power. We are always limited by computational power, and therefore has to make a lot of approximation, simplification, and coarser resolution of modeling.