Organizers: Marita Thomas, Timm John

Abstract Part B: 

Large-scale geodynamic behavior emerges from the interplay between deformation, rheology, and multiphase flow. This session addresses the modeling and mathematical methods with a focus on mechanical aspects of fluid-bearing rocks, including viscous, plastic, and brittle regimes of large scale deformations. This includes two-phase flow systems with dynamically evolving porosity-permeability relationships and feedbacks between compaction, dilation, and fluid pressure.

Speakers:

14:30h: Simon Boisserée (Johannes Gutenberg University Mainz)

Space-time adaptivity and preconditioning for porous media flow models

In models of porous media flows, the porosity of the solid matrix is often treated as a static quantity. However, under certain circumstances, such as in soft sedimentary rocks or in magma flows, the porosity of the solid material can evolve under the influence of fluid pressure which can lead to the formation of solitary porosity waves and of higher-porosity channels. We consider a system of nonlinear PDEs for porosity and effective pressure, based on a poroviscoelastic model, which describes such phenomena. We briefly recall well-posedness results for this PDE problem. Then we turn to results on an adaptive numerical method, which is based on a fixed-point scheme inspired by the analysis, combined with a space-time least-squares formulation. This yields an appropriate treatment of discontinuities and enables spatially varying time steps, which are required for efficient approximations of the strongly spatially and temporally localized features of solutions. We numerically also show its quasi optimality. Furthermore, we show first results on a preconditioner for the space-time least squares method to allow for efficient iterative solvers also in higher dimensions. Lastly, we indicate the potential of the space-time approach to solve related inverse problems since it allows to calculate the solution of (time-reversed) adjoint equations in a memory-efficient manner.

15:00h: Fan Cheng (FU Berlin)

Analysis of geodynamical viscoelastoplastic flows -- From porescale to macroscale

A model describing both viscoelastic and viscoplastic behavior in two-phase flows has been developed. This model is used in geodynamics, for example, to describe the evolution of fault systems in the lithosphere under the influence of fluid flow over geological time scales.

The system consists of a momentum balance, in which the Cauchy stress is constituted by a viscoelastic, Stokes-like term and a contribution from the internal stress, an evolution law for the internal deviatoric stress tensor, in which a Maxwell relation and a non-smooth viscoplastic dissipation term contribute, and a phase-separation law. Moreover, the phase-separation mechanism yields an additional capillary stress in the momentum balance. The evolution law for the internal stress features the Zaremba-Jaumann objective time derivative, The evolution of phase-separation is governed by a Cahn-Hilliard-type equation. Under an appropriate solution framework, global-in-time existence is established.

In addition, mathematical homogenization provides a systematic route for the upscaling from porescale rheology in heterogeneous media to macroscopic effective models. Depending on the microstructure and scaling, the macroscopic system features effective material parameters and generates an additional effective term.

This is joint work with Robert Lasarzik (WIAS Berlin), Marita Thomas (FU Berlin) and Piotr Wozniak (FU Berlin) within project B09 "Materials with discontinuities on many scales" and Project C09 "Dynamics of rock dehydration on multiple scales" of CRC 1114 "Scaling Cascades in Complex Systems" funded by the German Research Foundation.

15:30h: Javier García-Pintado (MARUM, University of Bremen)

Tectonic-scale patterns of viscoelastoplastic deformation subject to hydrothermal circulation

The movement of tectonic plates and the associated flow of asthenospheric mantle is related to the formation of sedimentary basins and submarine hydrothermal systems, as well as volcanic and earthquake activity beneath the ocean floor. Following continental rifting, spreading modes at mid-ocean ridges range from highly heterogeneous, ultramafic-dominated magmatic spreading to generally more homogeneous volcanic mafic systems. In this talk, I will summarise various tectonic-scale patterns identified in geodynamic simulations covering continental breakup and oceanic spreading. These will range from the life cycle of specific faults to approximately 10 million years of spreading. Rather than taking a mathematical approach, I will focus on describing various factors relevant to uncertainty and the upscaling of local deformation, as well as the sensitivity of the resulting patterns to selected parametrizations.