Department of applied mathematics and computational sciences

The project is aimed at strengthening the international cooperation and personal development of scientists from the Institute of Geonics of the CAS. The project implementation will enhance cooperation with major research organizations and their scientists. The realization of individual mobility stays will significantly contribute to the professional development of project participants and improvement of their workplaces. In addition, higher publishing activity and engagement of the IGN in international projects is expected at the same time.

The aim of the project is to support the professional development of young researcher as well as experienced researchers who will gain new skills and contacts at prestigious international workplaces. The final goal is the strengthening of the science and research in the Czech Republic. The fellowship will also contribute to the subsequent transfer of the acquired experiences to other IGN researchers during the return phase of the project.

The expected outputs are the participation and paper presentation at international conferences and the development of cooperation with foreign scientific institutions. An internal condition of the international mobility project is the preparation of a publication at a particular foreign workplace which will be published in a foreign journal of high impact.

The following 6 activities will be carried out: 3 working stays abroad for junior researchers and 3 working stays abroad for senior researchers - with the subsequent return phase.

The EURAD project (European Joint Program on Radioactive Waste Management) is a large-scale international project coordinated by the ANDRA (Agence Nationale pour La Gestion des Dechets Radioactifs). In total, 52 organizations from 23 European countries participate in this project. The IGN team is involved in the work package Development and Improvement Of Numerical methods and Tools for modelling coupled processes (DONUT).

The first research task Numerical methods for high-performance computing of coupled processes concerns the development of robust discretization methods for coupled (hydromechanical) processes - Finite element spaces for stable discretization, as well as the development of parallelizable preconditioners and iterative solvers for linear models (poroelasticity). This involves the development of both numerical methods and theory and medium-scale and large-scale testing. It also aims at hydromechanical models with nonlinearities, especially hydromechanical problems in the porous continuum with fractures (contact and non-penetration, conductivity changes due to changes in fracture apertures), and at the flow in partially saturated porous materials. The second research task Tools and methods to quantify/derive uncertainties induced by coupled processes aims at the construction of surrogate models and the use of the Bayesian approach in parameter identification problems.

By solving the project, the institute increases its competences in the field of deep geological disposal of highly radioactive wastes. The project enables the continuation of systematic research using previous experience with modeling of thermo-hydro-mechanical processes obtained through institutional support and participation in international projects, especially in several stages of the DECOVALEX project. The research includes processes in damaged porous continua with faults and fractures, which is a new area for the institute. It also involves new methods for the assessment and uncertainty quantification that are of extreme importance in the field of storage and disposal of spent nuclear fuel. The project leads to the creation of a modeling concept and methodology for the assessment of the properties of the excavation-damaged zone around the underground part of the planned deep radioactive waste repository in the Czech Republic.

The aim of this project is to develop efficient, reliable and theoretically supported computational techniques for geotechnical stability. The stability will be analyzed by methods based on limit analysis and incremental techniques. A particular interest will be devoted to the kinematic approach to limit analysis, combination of limit analysis and incremental methods, hydromechanical analysis of geotechnical structures, efficient implementation within in-house codes and solution of suitable benchmarks on geotechnical stability. These main research directions will be completed by some advanced techniques like uncertainty, finite element analysis, domain decomposition or mesh adaptivity.

The project focuses on the development of computational micromechanics methods (upscaling, inverse problems) for the analysis of micro-processes in the geological environment and their manifestations on a macroscopic scale. Knowledge of the geometry of rock microstructures is assumed; it is obtained by rock sample scanning using a high-resolution industrial CT scanner. The results contain solvers for numerical homogenization (upscaling), development of methods for the identification of local material parameters from the known macroscopic scale response, development of methods for the simulation of nonlinear behavior of geocomposites, and the simulation of composite damage under increasing load.

Within the project, IGN is fully responsible for solving the research program Numerical Methods in Engineering focused on the development, testing, and application of numerical methods for solving demanding and extensive physical-engineering problems. The research is mainly devoted to methods for the modeling of coupled processes (multiphysics) and processes in heterogeneous environments (multiscale) with special attention on the use of parallel algorithms and massively parallel supercomputers.

The research results include methods for demanding flow simulations in both porous media and open spaces, modeling of nonlinear processes in mechanics, and the development of new algorithms for uncertainty quantification and model calibration. Typical applications concern coupled thermo-hydro-mechanical processes related to the underground storage of spent nuclear fuel.

DECOVALEX is an international project which focus on the development of models of coupled processes in the field of nuclear waste disposal. The simulations and knowledge of such processes are necessary for the safety assessment and implementation of deep nuclear waste repositories. The project is funded by organizations responsible for the safe disposal of high-level radioactive waste in Europe (Germany, France, Belgium, Switzerland, Spain and more.), Asia (Japan, South Korea, China, and others), the USA, and Canada. The validation of the mathematical models is done using the data from in-situ experiments provided by these organizations and comparison with other teams. The involvement of Czech teams is managed by the Radioctive Waste Repository Authority (SURAO). The DECOVALEX project is running in four-year stages since 1992 and our team of the Department of Applied Mathematics was continuously involved in the project since 2008.

In the DECOVALEX 2015 stage, the IGN team participated in the solution of Hydro-mechanical modeling of the performance of sealing elements in the SEALEX experiment, which used data of the SEALEX experiment carried out in Tournemire in France to develop a model of bentonite plug saturation and closing gaps arising from the construction of plug from bentonite blocks and technological gaps arising from placing the plug in the borehole. The multi-physical model developed by the IGN team included flow in a variably saturated environment, bentonite swelling, and deformation that affected the saturation curve and permeability.

Ultrascale computing in geosciences is a part of the COST Action IC1305 Network for Sustainable Ultrascale Computing (NESUS) project. The goals concern the solution of multiphysics problems (for example, poroelasticity with double porosity), effective iterative methods, micromechanics problems using CT scans, or the inverse problem of identification of material characteristics.

The results of the project are methods and software for computationally demanding simulations of individual and coupled physical processes using parallelization of Schwarz-type preconditioners. Another result is the analysis of the effectivity of these methods for the simulation of processes in the geological environment, especially the solution of poroelasticity and micromechanics problems, including inverse problems and problems with uncertainty in the input data.

A thorough evaluation of the stress and structural record in granitic environments is essential for evaluation of the long-term safety of deep nuclear waste repositories located in such environments. The international project “Large-Scale Monitoring” (LASMO) leaded by Nagra was aimed at determining a comprehensive way to describe stress changes in granitic rock caused by large-scale unloading/loading of the rock mass. The experimental phase of the project was being conducted at the underground laboratory of the Grimsel Test Site situated in the Swiss Alps. The measurements and the subsequent monitoring of strain changes, along with the analysis of stress-strain relations and special studies focusing on internal anisotropy of rock provide important characteristics of the overall stress evolution in the investigated region, influencing the stability of the rock mass. The above mentioned subproject LASMO belonged among SURAO supported activities within the LASMO international project. The Institute of Geonics CAS, the Czech Geological Survey and the Institute of Rock Structure and Mechanics CAS collaborated on this task.

Involvement in this international project provided with important information for the eventual construction of the 3D stress models required for a thorough evaluation of the safety of the future Czech underground repository. The main aim of this subproject was to determine the general characteristics of rock mass behavior as a result of loading and unloading processes under the larger scale conditions of the underground repository.

This part involves the study of models of continuous mechanics of damage and plasticity and their use in rock mechanics. At the same time, the effect on transport processes is also investigated.

During the project, we developed theoretically supported simulation tools for a general description of damage processes in quasi-brittle materials at low loads caused by mechanical and transport phenomena. Several damage mechanic models were analyzed and some of them were coupled with moisture transport and plasticity models. The combination of damage and transport processes was realized using an isotropic damage model and a simple model for moisture transport. Alternatively, this was also modeled using the Brinkman's flow model. The research also concerned suitable numerical methods for solving outcoming nonlinear systems. This involved the study and use of Newton's method and its variants. Furthermore, the arc-length method was improved and used. Many mathematical models and numerical methods have been analyzed in terms of the existence of the solution. Simulation tools have been successfully used to solve several real problems. Examples of such problems are the Aspo Pillar Stability Experiment, slope stability, damage to poroelastic rocks on a large time scale.

DECOVALEX is an international project which focus on the development of models of coupled processes in the field of nuclear waste disposal. The simulations and knowledge of such processes are necessary for the safety assessment and implementation of deep nuclear waste repositories. The project is funded by organizations responsible for the safe disposal of high-level radioactive waste in Europe (Germany, France, Belgium, Switzerland, Spain and more.), Asia (Japan, South Korea, China, and others), the USA, and Canada. The validation of the mathematical models is done using the data from in-situ experiments provided by these organizations and comparison with other teams. The involvement of Czech teams is managed by the Radioctive Waste Repository Authority (SURAO). The DECOVALEX project is running in four-year stages since 1992 and our team of the Department of Applied Mathematics was continuously involved in the project since 2008.

In the DECOVALEX 2019 stage, the IGN team was primarily involved in solving the task of modeling HM and THM Interactions in the Bentonite Engineered Barriers. These models use data from EB (Mont Terri) and FEBEX (Grimsel) experiments. The result of the task was the development and implementation of models describing the hydro-mechanical and thermo-hydro-mechanical processes in bentonite barriers. The model of the EB experiment describes a bentonite seal formed by a combination of bentonite blocks and pellets and studies the saturation and homogenization of this seal. The model of the FEBEX experiment also includes thermal effects affecting both saturation and deformation of the porous media. The contribution of the IGN team is also the enhancement of the models by the inclusion of saturation outside the classic pore space of the bentonite.

The scope of the project was to build a national supercomputer center in Ostrava and to support research in related areas of computer science and computational mathematics. The IGN team participates in the solution of two research programs, namely Numerical modelling and Library for parallel computations. The research follows up the long-term focus of the group of applied mathematics and the experience with parallel computing, which have been implemented here since the middle of the 1990s.