# Argyris Lecture

Einmal im Jahr zeichnen wir eine Persönlichkeit aus dem Bereich der **Simulationstechnologie** mit einer **Argyris Visiting Professorship **aus. Mit dieser Auszeichnung prämieren **wir international renommierte Wissenschaftlerinnen und Wissenschaftler** aus dem In- und Ausland, die als herausragende Repräsentanten ihres Fachs im Bereich der Simulationstechnologie tätig sind. Eine öffentliche *Argyris Lecture* zum Ende des Sommersemesters bietet der Gastprofessorin oder dem Gastprofessor die Gelegenheit, die eigenen wissenschaftlichen Arbeiten einem breiten Publikum vorzustellen.

**Prof. Dr. Peter Knabner**

Universität Erlangen-Nürnberg

*Micro-Macro Models for Reactive Flow and Transport Problems in Complex Media*

In porous media and other complex media with different length scales, (periodic) homogenization has been successfully applied for several decades to arrive at macroscopic, upscaled models, which only keep the microscopic information by means of a decoupled computation of “effective” parameters on a reference cell. The derivation of Darcy’s law for flow in porous media is a prominent example. Numerical methods for this kind of macroscopic models have been intensively discussed and in general are considered to be favourable compared to a direct microscale computation. On the other hand, if the interplay of processes becomes too complex, e.g. the scale seperation does not act in a proper way, the porous medium itself is evolving, ..., the upscaled models obtained may be micro-macro models in the sense, that the coupling of the macroscopic equations and the equations at the reference cell is both ways, i.e. at each macroscopic point a reference cell is attached and the solution in the reference cell depends on the macroscopic solution (at that point) and the macroscopic solution depends on the microscopic solutions in the reference cells. At the first glance such models seem to be numerically infeasible due to their enormous complexity ( in d+d spatial variables). If on the other hand this barrier can be overcome, micro-macro models are no longer a burden but a chance by allowing more general interaction of processes (evolving porous media, multiphase flow, general chemical reactions, ...), where the microscopic processes “compute” the constitutive laws, which need longer be assumed (similar to the concept of heterogeneous homogenization). We will discuss various examples and in particular numerical approaches to keep the numerical complexity in the range of pure macroscopic models.

**Prof. Ronaldo Borja**

Stanford University, USA

*Multiscale Poromechanics: Fluid flow, solid deformation, and anisotropic thermoplasticity*

Natural geomaterials often exhibit pore size distributions with two dominant porosity scales. Examples include fractured rocks where the dominant porosities are those of the fractures and rock matrix, and aggregated soils where the dominant porosities are those of the micropores and macropores. I will present a framework for this type of materials that covers both steady-state and transient fluid flow responses. The framework relies on a thermodynamically consistent effective stress previously developed for porous media with two dominant porosity scales. I will show that this effective stress is equivalent to the weighted sum of the individual effective stresses in the micropores and macropores, with the weighting done according to the pore fractions. Apart from this feature, some geomaterials such as shale exhibit pronounced anisotropy in their hydromechanical behavior due to the presence of distinct bedding planes. In this talk I will also present a thermo-plastic framework for transversely isotropic materials incorporating anisotropy and thermal effects in both elastic and plastic responses. Computational stress-point simulations under isothermal and adiabatic conditions reveal the importance of anisotropy and thermal effects on the inception of a deformation band. I will show that anisotropy promotes the formation of dilation band across a wide range of bedding plane orientations relative to the direction of loading.

**Dr. Dorival M. Pedroso**

University of Queensland, Australien

*Consistent Implementation of FEM **Solutions for the Theory of Porous Media*

The Theory of Porous Media (TPM) is a rational and convenient mathematical framework to represent the macroscopic behaviour of porous media including interactions between multiple constituents. The resulting system of equations is usually known as the hydro-mechanical problem and seldom possesses analytical solutions with few exceptions; however many successful applications take advantage of numerical solutions based on the finite element method (FEM).

A way to update primary and state variables in the FEM is to use implicit schemes that are unconditionally stable. These schemes nonetheless require a number of (consistent) derivatives for achieving (quadratic) convergence when using Newton’s method. Furthermore, all state variables must be initialised with consistent initial conditions. Therefore, overall consistency of the numerical solver must be followed in order to obtain accurate results under feasible computing times.

An additional challenge during the solution of the multiconstituent flow problem in porous media is the treatment of unilateral boundary conditions that arise when liquid may escape from the porous domain through a region prone to changes in saturation. These kind of boundary conditions greatly increases the difficulty especially in coupled simulations and hence requires a proper method to treat them. This presentation aims to clarify the aforementioned challenges and to suggest a couple of algorithms that were published in to their solution. Focus will be given to:

(a) the innovation around the derivation of all consistent operators and correct setting up of initial conditions;

(b) new method to handle unilateral boundary conditions;

(c) the concept of references and a hysteretic liquid retention model derived from it;

(d) computer implementation aspects and the convenient use

of the Go language to develop a general purpose FE solver with parallel computing capabilities (Gofem).

*06.07.2016*

**Prof. Dr. Michael Celia**Princeton University

*Modeling Approaches for CO2 Sequestration in Conventional and Unconventional Reservoirs*

Carbon capture and sequestration (CCS) is the only currently available technology that can significantly reduce atmospheric carbon emissions while allowing continued use of fossil fuels for electric power and industrial production. CCS involves capturing the CO2 before it is emitted to the atmosphere, and injecting it into deep subsurface formations, thereby keeping it out of the atmosphere for centuries to millennia or longer. While conventional, high-permeability formations have traditionally been considered as injection targets, recent proposals suggest possible injection of captured CO2 into unconventional reservoirs with low permeability, specifically depleted shale-gas reservoirs. Analysis of injection into both types of formations involves computational challenges, in part because of the need for comprehensive environmental risk assessments and associated analysis of possible leakage scenarios. A range of computational models can be developed to answer the most important practical questions associated with both of these injection options. In this presentation, different modeling approaches will be discussed and important practical questions related to injection of CO2 into both conventional and unconventional formations will be addressed.

08.07.2015

**Prof. Dr. René de Borst**University of Glasgow, UK

*Multi-scales, Multi-physics, and Evolving Discontinuities in Computational Mechanics*

Multi-scale methods are quickly becoming a new paradigm in many branching of science, including simulation-based engineering, where multi-scale approaches can further our understanding of the behaviour of man-made and natural materials. In multi-scale analyses a greater resolution is sought at ever smaller scales. In this manner it is possible to incorporate the physics more properly and therefore, to construct models that are more reliable and have a greater range of validity at the macroscale.

When resolving smaller and smaller scales, discontinuities become more and more prominent. In addition to cracks, faults and shear bands observed at the macroscopic scale, discontinuities like grain boundaries, solid-solid boundaries such as in phase transformations, and discrete dislocation movement now also come in consideration.

In this lecture, we will start by a concise classification of multi-scale computational methods. Next, we will focus on evolving discontinuities that arise at different scales, and discuss methods that can describe them. Examples will be given at the macroscopic scale, the mesoscopic scale, and within a multi-scale framework. Also, examples will be given of multi-scale analyses where coupling of evolving discontinuities is considered with non-mechanical fields.

*02.07.2014*