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Published April 2011 | Published
Thesis Open

Understanding the Impact of Boundary and Initial Condition Errors on the Solution to a Thermal Diffusivity Inverse Problem


In this work, we consider simulation of heat flow in the shallow subsurface. As sunlight heats up the surface of soil, the thermal energy received dissipates downward into the ground. This process can be modeled using a partial differential equation known as the heat equation. The spatial distribution of soil thermal conductivities is a key factor in the modeling process. Prior to this study, temperature profiles were recorded at different depths at various times. This work is motivated by trying to match these temperature profiles using a simulation-based approach and analytic approaches in the context of an inverse problem. Specifically we determine soil thermal conductivities using derivative-free optimization to minimize the nonlinear-least square errors between simulation and data profile. Here, we conduct two sets of studies, assuming homogeneous and heterogeneous soil environments respectively. We also study how errors in the initial and boundary conditions propagate over time using both a numerical approach and an analytical method.

Additional Information

I would like to thank my advisor and mentor, Kathleen Fowler, for all the encouragement, trust, confidence, freedom, inspiration, honesty, understanding, knowledge, opportunities, emotional support and food that she provided in the past four years. My college would not have been so awesome without you. Thank you Brian Leventhal for spending all of those gorgeous summer days with me indoor at concrete cafe. Working on this project with you was pleasant! To Dr. Owen Eslinger, thank you for the data and project idea! I have never met you but this is not possible without your support! To Dr. Craig, Hayley Shen, Marcy and Clarkson Honors Program, thank you for the wise words, the deadlines and financial support. To Clarkson Department of Mathematics and Computer Science, thank you for being the right choice I made. And thanks to my parents, Ming Fu and Li Wan, for dealing with me not being home for 11 12 of the last four years. Finally big thanks to my fabulous friends, Akanksha, Allison, Devon, Gabbrielle, Hazelily, Phil, Qian, Ryan and Sam for helping me through the hardest time and for all the good times.

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August 19, 2023
October 20, 2023