Fluids algorithms from a High Performance Computing Perspective
Numerical approximations to Partial Differential Equations have provided diverse benefits to society over the years. Their applications in simulation codes have weathered a number of large changes in computing as well, from the original vector machines to task-based parallelism on scalar processors to the accelerators we now use. It seems each type of computing will favor a different type of numerical approximation, and this has changed over time. This presentation will cover common PDE discretization choices in fluid applications, what current High Performance Computing architectures are good at doing, how the two interact with one another in specific applications, and some potentially fruitful directions moving forward. Most of all, the goal is to present the major challenges we currently face and hopefully stoke creative ideas in applied mathematical approaches that will help the computational science community to achieve more ambitious and useful simulations in the future.