SSD - Berre Seminar
Prof. Dr. Inga Berre - Three-Dimensional Numerical Modelling of Hydraulic Stimulation of Geothermal Reservoirs: Permeability Enhancement and Induced Seismicity
Department of Mathematics, University of Bergen, Norway
Understanding the controlling mechanisms underlying injection‐induced seismicity is important for optimizing reservoir productivity and addressing seismicity‐related concerns related to hydraulic stimulation in Enhanced Geothermal Systems as well as other sub-surface engineering applications. Hydraulic stimulation enhances permeability through elevated pressures, which cause normal deformations and the shear slip of preexisting fractures.
The process involves strongly coupled physical processes, involving reactivation and deformation of fractures, deformation of surrounding rock, and fluid flow in the fractures and their surroundings. The talk presents an approach for modelling of the governing flow and mechanics, where fractures are modelled as surfaces with associated apertures in a three-dimensional domain. Considering both flow and deformation, processes in the fractures are coupled with processes in the surrounding rock. While flow is assumed to be governed by Darcy’s law both in the fractures and the matrix, the model for deformation is inherently different for the fractured and non-fractured parts of the domain. Fracture reactivation is based on a Mohr-Coulomb criterion, and the corresponding irreversible deformation is based on an empirical model for friction.
Furthermore, fractures may continuously deform in the normal direction according to a non-linear model accounting for the normal loading. For the rock surrounding the matrix, we assume a continuous elastic deformation. Numerical results are presented to show how the methodology can be applied to understand important mechanisms affecting permeability and induced seismicity. In particular, we show how normal closure of fractures enhances pressure propagation away from the injection region and significantly increases the potential for postinjection seismicity.
SSD - Kollmannsberger Seminar
Dr. Stefan Kollmannsberger - Simulation in Additive Manufacturing with Modern Discretizational Techniques
Chair of Computation in Engineer, Technical University of Munich, Germany
SSD - Banda Seminar
Prof. Dr. Mapundi Banda - A Lyapunov Approach to Boundary Feedback Stabilisation for Hyperbolic Balance Laws: a Numerical Perspective
Department for Mathematics and Applied Mathematics, University of Pretoria, South Africa
First-order systems of evolution models governed by time-dependent hyperbolic partial dierential equations will be considered. In this talk we will present a review of the Lyapunov approach for boundary feedback stabilisation for such dierential equations. The rst part of the presentation will give an overview of recent results in the mathematical analysis of stabilisation of hyperbolic balance laws. The second part will then discuss a numerical approach to discretise the balance laws. This will be followed by a numerical analysis for the discrete Lyapunov approach. A selection of examples will be discussed and the eectiveness of the numerical stabilisation will also be demonstrated.
EU Regional School - Holzapfel Seminar
Prof. Dr. Gerhard Holzapfel - Models for Fiber-Reinforced Elastic Solids with a Focus on Soft Biological Tissues
Institute of Biomechanics, Graz University of Technology, Austria
This short course provides a summary of models for fiber-reinforced elastic solids with distributed fiber orientations. As a motivation we start with a simple 1D problem which we then develop further to 3D considering a 3D isotropic fiber dispersion, perfectly aligned fibers, a rotationally symmetric dispersion and a non-rotationally symmetric dispersion. We review basic elements from the nonlinear theory of continuum mechanics that is required in the modeling of fiber-reinforced elastic solids. Of particular relevance are the structure tensors and related deformation invariants required to consider fibers and their dispersed directions in constitutive models. We also provide computational aspects needed for finite element implementation of the discussed models, and focus on an efficient formulation which avoids non-physical responses in the numerical analysis of anisotropic materials. The effect of the fiber structure on the material response is discussed on the basis of several examples. We discuss changes of the fiber structure in images obtained from cardiovascular tissues in health and disease using high-resolution optical microscopy. Related finite-element simulations highlight the need to incorporate the structural differences of soft biological (fibrous) tissues.
SSD - Hesthaven Seminar
Prof. Jan Hesthaven Ph.D.- New Directions in Reduced Order Modeling
Chair of Computational Mathematics and Simulation Science, Ecole Polytechnique Fédérale de Lausanne, Switzerland
The development of reduced order models for complex applications, offering the promise for rapid and accurate evaluation of the output of complex models under parameterized variation, remains a very active research area. Applications are found in problems which require many evaluations, sampled over a potentially large parameter space, such as in optimization, control, uncertainty quantification and applications where near real-time
response is needed. However, many challenges remain to secure the flexibility, robustness, and efficiency needed for general large-scale applications, in particular for nonlinear and/or timedependent problems. After giving a brief general introduction to reduced order models, we discuss developments in two different directions. In the first part, we discuss recent developments of reduced methods that conserve chosen invariants for nonlinear time-dependent problems. We pay particular attention to the development of reduced models for Hamiltonian problems and propose a greedy approach to build the basis. As we shall demonstrate, attention to the construction of the basis must be paid not only to ensure accuracy but also to ensure stability of the reduced model. As alternative approach we shall also, time permitting, discuss the importance of using a skew-symmetric form to ensure stability of the reduced models for more general conservation laws.
The second part of the talk discusses the combination of reduced order modeling for nonlinear problems with the use of neural networks to overcome known problems of online efficiency for general nonlinear problems. We discuss the general idea in which training of the neural network becomes part of the offline part and demonstrate its potential through a number of examples, including for the incompressible Navier-Stokes equations with geometric variations and a prototype combustion problem.
This work has been done with in collaboration with B.F. Afkram (EPFL, CH), N. Ripamonti EPFL, CH) and S. Ubbiali (USI, CH), Q. Wang (EPFL, CH).