Theory and practice of efficient modeling with the Boundary Element
Method Modeling
Modélisation efficace par la méthode des éléments frontières : théorie,
pratique et exemples applications en géosciences.
Par Gabriele Morra,
Maitre de Conférences invité à Université de Lorraine - ENSG / Géoressources,
Seoul National University et Lafayette University.
Module de 20h d'enseignement, du 2 au 5 Juillet 2013, ENSG.
Motivation: The study of three-dimensional coupled processes in the subsurface of
the Earth raises a number of theoretical and practical challenges, which call for very
efficient numerical techniques. This class will present a numerical technique which
has been applied to model coupled physical and geodynamical processes such as
diverse as those controlling plate tectonics, exhumation and erosion, geothermal
systems, or bubble behavior in magma chambers.
The goal of this summer class is to present the theoretical basis of the Boundary
Element Method and make the students familiar with recent optimizations which
make this method applicable on complex physical problems in 3D. Application
examples will be provided in geosciences.
Modeling bubble dynamics (Morra et al., Procedia Computer Science 2011).
Outline:
Part 1 (theory):
- Introduction to the Boundary Element Method (BEM). Advantages and
disadvantages respect to Finite Differences and Finite Element approaches.
- What is Fast Multipole Method (FEM). Most common implementations. How to use
it to accelerate BEM simulations.
- Parallelization of the FMM-BEM: practical techniques and limitations. Future
perspectives for petascale super-computers.
- Stokes flow: Stokeslet, Stresslet, analytical integration of singular functions.
Benchmarks for a spherical mesh.
- Elasticity: analogies and differences to Stokes flow.
Part 2 (application):
- Modeling two phase flow: bubbles, internal and external flow, interactions of many
bubbles.
- Handling large deformations, surface remeshing. Use of the particle-level-set
method. Example: plume development and head morphology
- Other applications in geodynamics: plate tectonics, Earth sphericity, coupling with a
Finite Element mechanical code.
- Open issues: surface contact, conservation of the volume, limitations of a low order
implementation.
- Perspectives for porous media: flow in a porous matrix. Generation of a synthetic
porous system. Coupling with an elastic matrix.
- Stresses in a faulted crust. Ideas and early applications.
Mechanical interaction between faults and subduction (Morra et al, Acta Geotechnica 2008).
Part 3 (hands-on):
- Learn how to use an existing BEM software
- Setup a run with a Python script. Visualize your results with Paraview.
- Test random configurations of two-phase flow. Become familiar with the software.
- Create and solve your own problem (requires Python scripting for setting it up, and
possibly C-coding for modifying the software client).