Numerical Implementation of Hysteresis in Permafrost Modeling

• Main Author: Slugg, Nicholas
• Other Authors: Peszynska, Malgorzata, Thomann, Enrique, Faridani, Adel, Mathematics, Oregon State University. Honors College
• Format: Thesis
• Language: English; unknown
• Published: Oregon State University
• Subjects: permafrost
• Online Access: https://ir.library.oregonstate.edu/concern/honors_college_theses/5425kk78p

Hysteresis is a well known nonlinear phenomenon in which a system's response not only depends on its present state, but also on its history. This phenomenon is observed in phase changes occurring in permafrost, regions of soil which remain frozen for two years or longer, in which the unfrozen water content and temperature display hysteretic behavior. We configure a model for hysteresis in permafrost dynamics using the generalized play model for hysteresis. We first examine an ODE model where the constraint curves for hysteresis are lines, and then we examine a more general setting in which the constraint curves are nonlinear functions of temperature. We then couple this with a PDE to model the dynamics of heat. We discretize using nodal finite differences on space and implicit in time finite differences on the time component, and configure a semismooth framework for Newton's method to solve the nonlinear equations that arise. We prove well posedness of the discrete model, and give examples of solutions, analyzing the robustness of the solver. Key Words: Hysteresis, Permafrost, Finite Difference Method, Semismooth Newton