Gas bubbles in a glass of champagne, thin films rupturing into tiny liquid droplets, blood flowing through a pumping heart and crashing ocean waves -- although seemingly unrelated, these phenomena have something in common: they can all be mathematically modeled as interface dynamics coupled to the Navier-Stokes equations, a set of equations that predict how fluids flow.

Today, these equations are used everywhere from special effects in movies to industrial research and the frontiers of engineering. However, many computational methods for solving these complex equations cannot accurately resolve the often-intricate fluid dynamics taking place next to moving boundaries and surfaces, or how these tiny structures influence the motion of the surfaces and the surrounding environment.

This is where a new mathematical framework developed by Robert Saye, Lawrence Berkeley National Laboratory's (Berkeley Lab's) 2014 Luis Alvarez Fellow in Computing Sciences, comes in. By reformulating the incompressible Navier-Stokes equations to make them more amenable to numerical computation, the new algorithms are able to capture the small-scale features near evolving interfaces with unprecedented detail, as well as the impact that these tiny structures have on dynamics far away from the interface. A paper describing his work was published in the June 10 issue of Science Advances.

"These algorithms can accurately resolve the intricate structures near the surfaces attached to the fluid motion. As a result, you can learn all sorts of interesting things about how the motion of the interface affects the global dynamics, which ultimately allows you to design better materials or optimize geometry for better efficiency," says Saye, who is also a member of the Mathematics Group at Berkeley Lab.