Upcoming Event: PhD Dissertation Defense

Simulation of a Partial Melting Mantle

Chenyu Tian, Ph.D. Candidate, Oden Institute

Abstract

This dissertation develops a multiphysics framework for modeling two-phase mantle dynamics with partial melting, emphasizing the handling of the degeneracy arising in no-melt regions and the relative movement between solid mantle and liquid magma. The model couples a degenerate Darcy–Stokes system describing static mechanics, a nonlinear transport system for chemical species and thermal energy, and a eutectic phase relation.

New mixed finite element spaces are introduced for the Darcy-Stokes system, including an H(div)-conforming finite element space for the Darcy flow and a modified Bernardi–Raugel finite element for the Stokes flow. Stability and approximation properties are established. The resulting saddle point system is solved by a modified Uzawa method. For nonlinear transport, we propose a new multilevel weighted essentially non-oscillatory (ML-WENO) reconstruction scheme. Coupling with the eutectic phase module links composition and enthalpy to porosity evolution, which closes the feedback loop between mechanical, transport, and phase processes. Numerical experiments validate the method. Simplified melting functions reproduce compaction-driven porosity waves, while fully coupled simulations capture phase transitions and porosity channel formation in upwelling columns, demonstrating both stability and accuracy of the approach.

 

Biography

Chenyu Tian is a CSEM Ph.D. candidate supervised by Prof. Todd Arbogast and Prof. Marc Hesse. His research includes the mixed finite element method, the finite volume method and the modeling of multiphse flow. Prior to joining CSEM, he earned a B.S. in Engineering Mechanics from University of Illinois at Urbana-Champaign.