PDE Optimization for Problems in Theoretical and Computational Turbulence

Abstract: Turbulent flows occur in various fields and are a central, yet an extremely complex, topic in fluid dynamics. Understanding the behaviour of fluids is vital for multiple research areas including, but not limited to: biological models, weather prediction, and engineering design models for automobiles and aircraft. In this talk, we will introduce optimization techniques for systems described by partial differential equations, and frame a number of fundamental problems that arise in 2D turbulent flows using the Navier-Stokes system, such that they can be solved using computational methods. We utilize adjoint calculus to build the computational framework to be implemented in an iterative gradient flow procedure, using the "optimize-then-discretize" approach. The use of optimization methods together with computational mathematics provides an illuminating perspective on fluid mechanics, in particular the problems of the "zeroth law of turbulence" and the turbulence closure problem.

Bio: Pritpal 'Pip' Matharu is a postdoctoral fellow at The Royal Institute of Technology (KTH), in the Numerical Analysis Division with the Department of Mathematics. He is an applied mathematician with a background in numerical analysis, optimization, and scientific computing, which he utilizes in order to solve problems that arise in theoretical and computational fluid dynamics. This research covers problems ranging from viscous dominated flows, such as Stokes flow, to turbulent flows governed by the Navier-Stokes equations. He obtained his PhD in 2022 from McMaster University, where he used adjoint-based PDE optimization methods, high order approximation methods, and computational mathematics, to solve problems that arise in turbulent flows.