Go with the flow

Mathematician models complex flows of oil, air and ocean currents

For most of us, learning to solve math problems was an end unto itself. But University of South Carolina mathematics professor Zhu Wang uses math to solve real-world problems.

His work has helped improve the process of simulating turbulent flows, such as in an oil pipeline, to better control the actual process.

“Understanding complex flows is vital to numerous industrial and engineering applications, such as designing oil transport in pipelines, flow through pumps and turbines, and airflow around aircraft wings,” fellow mathematics professor Lili Ju says. “However, the big hurdle for optimally controlling such flows is the dramatically large computational cost required for repeatedly simulating them.”

Wang has designed physics-based methods to model the flows and has created new algorithms to decrease the computational costs. “Because of Professor Wang’s innovations, we can now successfully simulate turbulent flows both quickly and reliably. Before, it would have been unlikely to do those two things simultaneously,” Ju says.

I will face new challenges caused by integrating more components in the model, and tackle them using my mathematical knowledge.

Zhu Wang, mathematics

For Wang, each new breakthrough is just one more piece in the complex puzzle of understanding the world around us. “When I was young, I was very interested in mathematics, both applied and computational,” Wang says. “It really can solve real-world engineering problems.”

His next math problem? Creating, with Ju, improved computer models for simulating oceanic flows. “We developed a novel numerical scheme [that] outperforms the current state-of-the-art numerical algorithms in computational efficiency and makes it possible to implement coastal modeling in long-term simulations,” Ju says.

The work is significant, Wang says, because ocean currents are a key determinant in global climate and concerns about coastal flooding. His work is helping the U.S. Department of Energy with its modeling, simulation and prediction of ocean flows.

“In particular, we developed a conservative, local time-stepping algorithm to speed up the numerical simulations of ocean models with multiscale,” Wang says.

Though for many of us, math problems have a single, finite answer, Wang keeps searching for new ways to perfect his models. “I will face new challenges caused by integrating more components in the model, and tackle them using my mathematical knowledge,” Wang says.

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