WaterLily: A fast differentiable CPU/GPU flow simulator in Julia

Integrating computational fluid dynamics (CFD) software into optimization and machine-learning frameworks is hampered by the rigidity of classic computational languages and the slow performance of more flexible high-level languages. WaterLily is an open-source incompressible viscous flow solver written in the Julia language. The small code base is multi-dimensional, multi-platform and backend-agnostic (serial CPU, multi-threaded, & GPU execution). The simulator is differentiable and uses automatic-differentiation internally to immerse solid geometries and optimize the pressure solver. The computational time per time step scales linearly with the number of degrees of freedom on CPUs, and we see up to a 182x speed-up using CUDA kernels. This leads to comparable performance with Fortran solvers on many research-scale problems opening up exciting possible future applications on the cutting edge of fluid mechancis and machine-learning research.