Event Detail

Event Type: 
Applied Mathematics and Computation Seminar
Friday, March 11, 2022 - 12:00 to 12:50

Speaker Info

Department of Mathematics, Oregon State University

We discuss numerical methods for models of heat conduction with phase change in heterogeneous media, i.e., the heterogeneous Stefan problem, with particular interest in modeling permafrost. The model features nonlinear and discontinuous constitutive relationships related to the presence of free boundaries and material interfaces, and provides many mathematical and computational challenges. We propose a monolithic discretization framework, well known for its conservative properties, based on the lowest order mixed finite elements which we call P0-P0 formulation. In the talk we first compare P0-P0 to other finite element models including P1-P1, P1-P0, Chernoff formula, and relaxation schemes. Then we apply the scheme at the porescale and upscale to obtain the so-called effective parameters governing the heat conduction in permafrost at Darcy scale; these can be compared to empirical models. Of particular interest is the temperature and enthalpy relationship of the upscaled values as well as hysteresis effects on the upscaling.
We follow with the study of robustness of our P0-P0 scheme at Darcy scale, with different scenarios pertaining to permafrost modeling. Further, we discuss extensions to the fully coupled THM model for the thermal-mechanical-hydrological coupled system. As part of this system we discuss our initial results on the hydrological-mechanical coupling within the Biot model. This is collaborative work of Lisa Bigler, Naren Vohra, and Malgorzata Peszynska.