Numerical modeling (geology)

Summary

In geology, numerical modeling is a widely applied technique to tackle complex geological problems by computational simulation of geological scenarios. Numerical modeling uses mathematical models to describe the physical conditions of geological scenarios using numbers and equations. Nevertheless, some of their equations are difficult to solve directly, such as partial differential equations. With numerical models, geologists can use methods, such as finite difference methods, to approximate the solutions of these equations. Numerical experiments can then be performed in these models, yielding the results that can be interpreted in the context of geological process. Both qualitative and quantitative understanding of a variety of geological processes can be developed via these experiments. Numerical modelling has been used to assist in the study of rock mechanics, thermal history of rocks, movements of tectonic plates and the Earth's mantle. Flo

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Fracture analysis of plain concrete and rock numerical modelling using a smeared crack approach

EPFL1995

Consolidation œdométrique d’argile Champlain. Détermination directe et indirecte de la conductivité hydraulique en fonction de l’indice des vides.

Nicolas Berner

Conventional laboratory odometer tests were performed to determine the consolidation behaviour of Champlain Sea clays. Odometer permeability tests were also completed for each sample between two of the consolidation steps. The tests lasted 20 to 24 days. The goal of this project was to design and implement a numerical modelling approach to reduce the number of laboratory permeability tests required for each sample, thereby reducing the test duration to 12-14 days.

2008

Multilevel preconditioners for elliptic problems with multiple scales

Klaus Sapelza

The purpose of this thesis is to investigate methods for the solution of multiscale problems both from the mathematical and numerical point of view, with a particular concern on applications to flows through heterogeneous porous media. After an overview of the recent developments in this vast field, a study of two representative multiscale techniques is carried out. The multiscale finite element method and a conjugate gradient iterative method preconditioned with an overlapping Schwarz domain decomposition preconditioner are compared in the one-dimensional case. Both methods are well suited for parallel environments and have comparable performance and accuracy. Then, we focus our attention on an aggregation-based two-level overlapping Schwarz domain decomposition preconditioner. We study its theoretical properties and show its robustness to mesh refinement as well as to strong variations in the multiscale coefficients of our model problem. We carry out a convergence analysis to give upper bounds for the condition number of the preconditioned linear system arising from the finite element discretization of the problem at hand. We make explicit the relation between the multiscale coefficient and the coarse space basis functions and show that the condition number can be bounded independently of the ratio of the values of the multiscale coefficient even when the discontinuities in the coefficient are not resolved by the coarse mesh. A new aggregation algorithm is proposed according to the suggestions issuing from the theory which builds a coarse space able to cope with the multiscale coefficient. Numerical experiments on various configurations show that the bounds are sharp and that the method is robust with respect to strong variations. Finally, an application of this preconditioning technique to a two-phase flow problem is presented in order to investigate its performance.

EPFL2007