CAREER: New Algorithms and Models for Turbulence in Incompressible Fluids

University Of Florida, Gainesville FL

Investigators

Abstract

Turbulence is ubiquitous in nature, and decisions that affect our life are made daily based on predictions of turbulent flows. Obtaining accurate predictions of turbulent flows is a central challenge in global change estimation, weather forecasting, freshwater supply, improving the energy efficiency of engines, controlling dispersal of contaminants, and designing biomedical devices. A turbulent flow is a highly irregular system, characterized by chaotic property changes involving a wide range of scales in nonlinear interaction with each other. These features yield a high computational complexity, which makes direct numerical simulations of turbulent flows that aim at resolving all features down to the smallest scales infeasible even with modern supercomputers. Instead, turbulence models are used for practical turbulence simulations to bypass the chaotic details and reduce the computational complexity. This project aims to develop a new family of ensemble averaged turbulence models and novel numerical methods for their solution, extending current applicability and computational limitations of effective turbulence simulations, which may have a great impact on numerous applications in aeronautics, hydraulics, chemical engineering, oceanography, meteorology, astrophysics, and geophysics, considering turbulence’s prominent influence in almost all geophysical and industrial flows. A comprehensive educational program will be developed to provide students with systematic training in computational fluid dynamics and bring them up to date on current research topics in this field. Turbulence modeling remains one of the most important scientific challenges. The fundamental approach for turbulence modeling is to seek to approximate suitable (ensemble, time, or spatial) averages of fluid velocity instead of pointwise velocity itself. Ensemble averaging is the most intuitive approach from the statistical theory for turbulence, but it is currently not in use for practical turbulence simulations of industrial flows due to the extremely high computational cost associated with ensemble simulations. This deadlock is recently broken with newly developed ensemble algorithms that give access to the full ensemble at every time step and thus open new and direct possibilities for developing turbulence models for the ensemble averaged Navier-Stokes equations. In this project the investigator will develop a new family of ensemble-based variational multiscale method (VMS) turbulence models and novel numerical methods under the new framework of ensemble averaging for practical turbulent flow simulations. New unconditionally stable ensemble algorithms will be developed for fast solution of the new ensemble-based VMS turbulence models and to effectively overcome the backflow instability for turbulent flows with open boundary conditions. This project will provide new avenues to turbulence modeling and simulations and build a new rigorous numerical analysis addressing how to make effective approximations in the face of Newtonian chaos. 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.