**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Computational Geomechanics: Week 4

Description

This lecture covers computational geomechanics topics related to transient flow in porous media. It discusses the governing equations, storage coefficient, diffusion equation, spatial discretization, and time integration schemes. The instructor explains the stability conditions for implicit and explicit schemes, boundary conditions, and the use of unstructured meshes. Various numerical methods and their applications in geomechanics are also explored.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

In course

Instructor

Related concepts (171)

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.

Numerical methods for partial differential equations

Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.

Finite difference method

In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.

Numerical methods for linear least squares

Numerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).

Fluid dynamics

In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

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.

Related lectures (456)

Turbulence: Numerical Flow SimulationME-474: Numerical flow simulation

Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.

Computational Geomechanics: Week 4CIVIL-423: Computational geomechanics

Explores boundary conditions, time variation in porous media, and storage coefficients in matrices.

Finite Difference GridsMATH-351: Advanced numerical analysis

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Numerical Methods: Boundary Value ProblemsChE-312: Numerical methods

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

Computational Geomechanics: Unconfined Flow AnalysisCIVIL-423: Computational geomechanics

Explores unconfined flow analysis in geomechanics, emphasizing iterative solution methods and boundary condition considerations.