Data Assimilation and Parameter Recovery for Convection

• Working with Jared Whitehead, Vincent Martinez

• August 2021 to present

• Masters thesis "Data Assimilation and Parameter Recovery for Rayleigh-Bénard Convection" published electronically at BYU Scholars Archive

Summary of Research 

• Found methods for simultaneous concurrent recovery of system state and Prandtl and Rayleigh numbers for Rayleigh-Bénard convection

• Used direct numerical simulation to analyze performance of various parameter update formulas

• Analyzed convergence analytically, and in one case obtained a proof of convergence

Talks 

• October 2022, AMS Western Sectional Meeting, Salt Lake City, Utah

• February 2022, BYU Student Research Conference (won "Best Presentation" in session)

GitHub Repository

https://github.com/jpw37/RB_parameters

Paper Abstract

Many problems in applied mathematics involve simulating the evolution of a system using differential equations with known initial conditions. But what if one records observations and seeks to determine the causal factors which produced them? This is known as an inverse problem. Some prominent inverse problems include data assimilation and parameter recovery, which use partial observations of a system of evolutionary, dissipative partial differential equations to estimate the state of the system and relevant physical parameters (respectively). Recently a set of procedures called nudging algorithms have shown promise in performing simultaneous data assimilation and parameter recovery for the Lorentz equations and the Kuramoto-Sivashinsky equation. This work applies these algorithms and extensions of them to the case of Rayleigh-Bénard convection, one of the most ubiquitous and commonly-studied examples of turbulent flow. The performance of various parameter update formulas is analyzed through direct numerical simulation. Under appropriate conditions and given the correct parameter update formulas, convergence is also established, and in one case, an analytical proof is obtained.