Lecture

Computational Geomechanics: Week 4

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In course

CIVIL-423: Computational geomechanics

The goal of this course is to introduce the student to modern numerical methods for the solution of coupled & non-linear problems arising in geo-mechanics / geotechnical engineering. ...

Description

This lecture covers the study of boundary conditions, sources of time variation in porous media, and the specific storage coefficient in incompressible porous matrices. It also delves into the derivation of finite volume discretization for diffusion equations and time integration schemes. The course emphasizes reverse teaching, with weekly lectures, quizzes, and exercise sessions to enhance understanding.

Instructor

Brice Tanguy Alphonse Lecampion

I am currently an assistant Professor and the head of the Geo-Energy Lab - Gaznat Chair on GeoEnergy at Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland. Prior to joining EPFL, I have worked for Schlumberger in research and development from 2006 until May 2015 - serving in a variety of roles ranging from project manager to principal scientist in both Europe and the United States. I received my PhD in mechanics from Ecole Polytechnique, France in 2002 and worked as a research scientist in the hydraulic fracturing research group of CSIRO division of Petroleum resources (Melbourne, Australia) from 2003 to 2006. During my time in Schlumberger R&D, I have worked on problems related to the integrity of deep wells, large scale monitoring of reservoir deformation and more specifically on the stimulation of oil and gas wells by hydraulic fracturing. My current research interests cover hydraulic fracture mechanics, mechanics of porous media and dense suspensions flow.

Official source

Ontological neighbourhood

Mathematics

Discrete mathematics: Discrete exterior calculus

Related concepts (32)

Dirichlet boundary condition

In the mathematical study of differential equations, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Peter Gustav Lejeune Dirichlet (1805–1859). When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take along the boundary of the domain. In finite element method (FEM) analysis, essential or Dirichlet boundary condition is defined by weighted-integral form of a differential equation.

Robin boundary condition

In mathematics, the Robin boundary condition (ˈrɒbɪn; properly ʁɔbɛ̃), or third type boundary condition, is a type of boundary condition, named after Victor Gustave Robin (1855–1897). When imposed on an ordinary or a partial differential equation, it is a specification of a linear combination of the values of a function and the values of its derivative on the boundary of the domain. Other equivalent names in use are Fourier-type condition and radiation condition.

Boundary value problem

In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.

Neumann boundary condition

In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative applied at the boundary of the domain. It is possible to describe the problem using other boundary conditions: a Dirichlet boundary condition specifies the values of the solution itself (as opposed to its derivative) on the boundary, whereas the Cauchy boundary condition, mixed boundary condition and Robin boundary condition are all different types of combinations of the Neumann and Dirichlet boundary conditions.

Cauchy boundary condition

In mathematics, a Cauchy (koʃi) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary condition. It is named after the prolific 19th-century French mathematical analyst Augustin-Louis Cauchy.

Related lectures (64)

Computational Geomechanics: Week 4

Explores transient flow in porous media, covering governing equations, stability conditions, and numerical methods.

Numerical Methods: Boundary Value Problems

Explores numerical methods for boundary value problems, including heat diffusion and fluid flow, using finite difference methods.

Computational Geomechanics: Unconfined Flow

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Heat Equation: Modeling and Numerical Methods

Covers the heat equation, its physical interpretation, and numerical methods for solving it.

Finite Difference Method: Approximating Derivatives and Equations