Time Accurate Prediction of Fluid Motion

Fluids transport and mix heat, chemical species, and contaminants. Accurate simulation of fluid velocities for low viscosity fluids and for longer times is essential for safety, critical prediction and design in engineering and science. Accurate flow predictions are key to limiting damage of hurricanes (estimated to be hundreds of billions of dollars in typical years) and to energy efficiency optimization (85% of US energy is generated by combustion for which accurate simulation of turbulent mixing is critical).

Fundamental barriers to accurate flow prediction will be addressed in this research. This research also develops expertise of PhD students who will contribute to the next generation of applied and computational mathematicians to address future challenges. This project will support six graduate students per year and one undergraduate per year for each of the three years of the project.

This project will develop time accurate methods in computational fluid dynamics. Time accurate prediction must improve current turbulence models because they are only satisfactory at statistical equilibrium. The proposed research will extend them to non-stationary turbulence, simplify the models and reduce the number of calibration parameters by aligning them more closely to the true energy flow between means and fluctuations.

Since fluid flow has complex dynamics, pushing out the limited predictability horizon requires reliable and efficient ensemble simulations. The research will develop algorithms allowing larger ensembles without sacrificing accuracy in realizations. Effective, adaptive time discretizations are under used in computational fluid dynamics.

This research will develop new time stepping methods of low computational, space and cognitive complexity that are stable, accurate and easily introduced into complex codes.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.