The complexity and beauty of the movement of liquids and gases might not be obvious to everyone, but the scientific field of fluid dynamics is the source of some of the biggest unsolved problems in mathematics and physics. Further, its visually pleasing movements and surprising effects are just fascinating. Nicole Sharp’s successful science blog “Fuck Yeah Fluid Dynamics” presents a great mixture of novel scientific discoveries, explanations for everyday phenomena and artistic views of fluid dynamics.
I usually focus on computational fluid dynamics (CFD), that is, the numerical solution of the equations of motion of fluids. Sometimes for testing novel computational methods, for optimizing computational performance or just for the visual result. Here, I show some pictures that solving the following, incompressible Navier-Stokes equations can give you:
\begin{align}\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla) \mathbf{u} &= -\nabla \tilde{p} + \nu \nabla^2 \mathbf{u} + \mathbf{g}, \\ \nabla \cdot \mathbf{u} &= 0.\end{align}Very different solution methods were used: classical finite difference methods, pseudospectral methods and entropic Lattice Boltzmann methods.
