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Interfacial Gauge Methods for Incompressible Fluid Dynamics
Posted Mon June 13, 2016 @09:23AM
Resolving 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 is a difficult computational task.
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.
A jet of water impacts on a reservoir of water underneath, forming ripples just above the surface in the main jet. These ripples are caused by the surface tension of water. The video reveals a type of vortex shedding that occurs at the base of the ripples not previously seen in experiment. (Credit: Robert Saye/Berkeley Lab)
According to Saye, most existing methods for solving incompressible fluid flow problems coupled to moving boundaries and surfaces are “low-order” methods. Conversely, the interfacial gauge methods that Saye developed are “high-order” methods.
“High-order methods are in some sense more accurate. One interpretation is that, for fixed computing resources, a high-order method results in more digits of accuracy compared to a low-order method. On the other hand, it is often the case that you only need a handful of digits of accuracy in your simulation. In this case, a high-order method requires less computing power, sometimes significantly less,” Saye explains.
In addition, low-order methods for fluid interface dynamics tend to introduce “numerical boundary layers” into the calculated results. These lead to imperfections, a bit like film grain or noise in a photograph. It means you cannot closely examine and precisely analyze the fluid dynamics right next to the interface.
“What happens at the interface, such as the film of a soap bubble or the surface of a propeller, affects the large-scale dynamical structures in the surrounding environment,” says Saye. “Low-order methods work well when everything is smooth, but you need a high-order method when you have intricate dynamics, when things are moving very fast, or if there are small-scaled features in the interface.”
With cheaper computational models and increased resolution capabilities, researchers can study more complex phenomena, like how to optimize the shape of a propeller blade, the formation and destruction of foams, the resolution in modeling the boundary layers in blood flow in pumping hearts and the ejection of ink droplets in consumer inkjet printers.
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