Download Editorial This special issue is devoted to Numerical Modelling in

Editorial
This special issue is devoted to Numerical Modelling in Geomechanics and Geodynamics
with the aim to show complexity and computational demands of mathematical and numerical
models exploited in geotechnics and geophysics. More specifically, this special issue presents
papers that deal with selected challenging problems arising from the assessment of large
surface and underground constructions, mining technologies, geological repositories of
nuclear and other waste, as well as problems devoted to understanding of the Earth’s crust
movements, earthquakes and global phenomena.
The idea of this special issue arose already at the International Conference on
Computational Science in Amsterdam 2002, which was organized upon the chairmanship of
Prof. P. Sloot. We highly appreciate his invitation and thank the editors of the Elsevier’s
journal Future Generation Computer Systems for hosting this special issue.
What are the reasons for this special issue? Firstly, mathematical models in geomechanics,
geodynamics and in other fields of geophysics have many specific features such as large 3D
domains of interest, heterogeneity and multiscale aspects, modelling of complex nonlinear
material behaviour, coupled multiphysics investigation, assessment of reliability of the
models and influence of uncertainty in input data.
Secondly, there are of course also strong computational aspects of the described models. It
is generally recognized that the last decade was characterized by the development of high
performance computers and parallel computations have been introduced in all scientific
branches. The number of applications of parallel computations, as well as attention devoted to
the parallel computers, their programming and parallel algorithms have been increasing
tremendously making significant breakthroughs in many important fields. These new
possibilities give also a new breath to some problems in geomechanics and geodynamic since
they enable problem solving of a much higher complexity than before.
In this special issue, we attempt to show a sufficiently wide range of challenging problems,
which can be successfully solved by combination of knowledge and tools from the fields of
mathematical analysis, numerical methods, computer science, geomechanics, geodynamics,
seismology, etc. In this respect, we present seven papers covering the above mentioned goals.
The article Large Scale Parallel FEM Computations of Far / Near Stress Field Changes in
Rocks by R. Blaheta et al. describes large scale 3D modelling made possible by the use of
finite element method and problem decomposition techniques such as displacement
decomposition, overlapping domain decomposition and composite grids. These
decomposition techniques allow efficient parallel solutions on PC clusters and other parallel
computers.
P.J. Cleall, H.R. Thomas, T.A. Melhuish and D.H. Owen address the use of parallel
computing, iterative methods and visualisation techniques for the simulation of large scale
geoenvironmental problems in the paper Use of Parallel Computing and Visualisation
Techniques in the Simulation of Large Scale Geoenvironmental Engineering Problems. As an
example, they analyse of thermo-hydraulic phenomena for the prototype repository of spent
nuclear fuel in Äspö, Sweden.
The solutions to problems in geosciences need both parallel computing and assessment of
the influence of uncertainty in input data. These aspects are addressed in the paper Worst
Scenario and Domain Decomposition Methods in Geomechanics by I. Hlaváček, J. Nedoma
and J. Daněk. The uncertainty is evaluated by the so-called Worst Scenario Approach. The
domain decomposition is applied to the solution of problems of contact of deformable bodies.
The contact problems, which are important for modelling Earth’s mantle movements,
volcanic zones and plate tectonic effects, are also considered in the paper On a Solvability of
Contact Problems with Visco-Plastic Friction in the Thermo-Visco-Plastic Bingham Rheology
by J. Nedoma. This paper presents the mathematical analysis of these problems in case of
complex material behaviour.
G. Quillon and D. Sornette consider the Earth‘s crust as a medium with joints, cracks and
faults filled with fluid close to lithostatic pressures. This medium is modelled by an
asymmetric Hooke's law (threshold nonlinearity). The paper Long-range Static Directional
Stress Transfer in a Cracked, Nonlinear Elastic Crust then explores the main differences
between the stress fields generated by an earthquake (point source) in a nonlinear threshold
elastic medium in comparison to a standard linear elastic one.
Finite Element Approximation to Infinite Prandtl Number Boussinesq Equations with
Temperature-Dependent Coefficients - Thermal Convection Problems in a Spherical Shell by
M. Tabata numerically simulates the Earth’s mantle convection phenomenon by the
Boussinesq approximation with the infinite Prandtl number. The mantle geometry is
represented by a spherical shell and the investigation includes mantle viscosity strongly
dependent on the temperature. The paper also describes a stabilized version of the finite
element method and numerical experiments.
C. Wieners, M. Ammann and W. Ehlers elaborate a general concept of the parallel finite
element method in the paper Distributed Point Objects: A new concept for parallel finite
elements applied to a geomechanical problem. They apply this general methodology to a
demanding porous media stability problem. The results from a 3D nonlinear and time
dependent application show high parallel speed-up and efficiency gains with potential for
solving other demanding 3D nonlinear multiphysics problems.
We would like to thank all the authors for presenting the papers that hopefully reflect recent
advances and trends in challenging applications of mathematical modelling and computational
science in geotechnics and geophysics.
Radim Blaheta and Jiří Nedoma
(Inst. of Geonics and Inst. of Computer Science,
Academy of Sciences of the Czech Republic)