Lecture

Numerical Groundwater Flow Resolution: Finite Elements

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

CIVIL-203: Soil mechanics and flow through porous media

The course introduces students to the fundamentals of the mechanics of soils and fluid-infiltrated porous media. The first part is devoted to the constitutive behavior of soils in dry conditions, while the second part accounts for the presence of pore wate ...

Description

This lecture covers the numerical resolution of groundwater flows using finite elements, including the discretization of differential equations, finite element shapes, and the interpolation functions used. It also discusses the resolution of transient flows, initial conditions, boundary conditions, and the assembly of elements to solve the differential equations. The lecture demonstrates the process step by step, emphasizing the importance of spatial and temporal discretization in solving groundwater flow problems.

Instructor

Laurent Vulliet

EDUCATION 2016 Board Member Certificate, Swiss Board School, Switzerland 2008 AMP (Advanced Management Program), INSEAD, Fontainebleau, France 1986 PhD (Dr sc. tech.), EPFL, Lausanne, Switzerland 1980 Ms, Civil Engineering (Dipl. Bauing. ETH), ETHZ, Zurich, Switzerland PROFESSIONAL ACTIVITIES 1994 - Present Professor, EPFL. Director of the Soil Mechanics Laboratory (1994-2008). Promoted from Associate to Full Professor in 1996. Part-time position since 2008 2008 - 2015 CEO, BG Consulting Engineers, Lausanne, Switzerland. 2001 - 2008 Dean, School of Architecture, Civil and Environmental Engineering (ENAC), Ecole polytechnique fédérale, Lausanne (EPFL) 1999 - 2001 Head, Civil Engineering Department, EPFL 1989 - 1993 Senior Engineer, De Cérenville Géotechnique SA, Ecublens, Switzerland 1987 - 1989 Lecturer, Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, USA 1986 Invited Researcher, Laboratoire central des ponts et chaussées (LCPC), Paris, France 1981 - 1986 Research assistant, and PhD student, Soil Mechanics Laboratory (LMS), EPFL. Thesis on the modeling of natural creeping slopes. Co-advisors Prof. E. Recordon (EPFL) and Prof. K. Hutter (TU Darmstadt) BOARDS / COUNCILS

Member of the Board of Directors, Implenia, Dietlikon, Switzerland (2016 - present)
Member of the Board of Directors, BG Consulting Engineers, Lausanne (2006 - 2015)
Vice-President, Swiss Society of Engineers and Architects (SIA). 2009-2013.
Member, Foundation Council, Foundation Les Bois Chamblard, financing research in Environmental Sciences at EPFL (focusing on bio-diversity). 2003-present
Member, Foundation Council of the Presses Polytechniques et Universitaires Romandes (PPUR), Lausanne. 1995-present
Member, Stiftungsrat der Präventionsstiftung der KGV (a Swiss foundation for the financing of applied research in the domain of natural risks from Cantonal Building Insurances). 2003-2008
Member of the Board of Directors, Stump Bohr AG, Nänikon. 1998 2001

PROFESSIONAL SOCIETIES

Swiss Society of Engineers and Architects (SIA)
American Society of Civil Engineers (ASCE)
International Association for Computer Meth. and Advances in Geomechanics (IACMAG)
International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE)
International Society for Rock Mechanics (ISRM)
Swiss Society for Soil and Rock Mechanics (SSMSR)
Swiss Society for Earthquake Engineering and Structural Dynamics (SGEB)

SCIENTIFIC COMMITTEES

Swiss National Science Foundation (NSF): member of the Foundation Council and of the Electoral Commission (1996-2003)
Extra-Parliamentary National Commission on Natural Disasters (PLANAT): member of the Commission 1997-2007 (member of the Executive Board from 1997 to 2000)
Natural Hazards Competence Centre CENAT (ETH Domain): founder member and member of the Board of Directors (1995-2007)
Alliance of European Research Laboratories (ALERT), member of the Board of Directors (1995-2009)
Beratende Kommission Swiss Federal Institute for Forest, Snow and Landscape Research (WSL): member (2000-2004)
Centro Stefano Franscini (CSF, Monte Verità): member of the Scientific Advisory Committee (1997-2007)
EPFL Press and Information Commission (CPI). Member 1994-94, President 1995-2000

EDITORIAL BOARDS

Adjunct Editor-in-Chief, Revue française de génie civil (Hermès); founder member (1996-Present). Cette revue est devenue "European Journal of Environmental and Civil Engineering"
Editorial Advisory Board, Int. J. Num. Analyt. Meth. in Geomech., John Wiley (1997-2009).
Editorial Board, Int. J. of Geomechanics (2000-2009).
Editorial Board, Computer & Geotechnics, Elsevier (2001-2009).
Editorial Board, Rivista Italiana di Geotecnica (1997-2009).

Official source

Related concepts (32)

Interpolation

In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable.

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .

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.

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.

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Related lectures (64)

Finite element methods MOOC: Sorption and transport in cementitious materials

Covers finite element methods for solving diffusion problems in porous media, including meshing, interpolation, and weighted residuals.

Distribution & Interpolation Spaces

Explores distribution and interpolation spaces, differential operators, Fourier transform, Schwartz space, fundamental solutions, Farrier transform, and uniform continuity.

Finite Difference Method: Approximating Derivatives and Equations

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Separation of Variables: Spatial Problems

Explores the method of separation of variables for solving spatial problems with second-order ODEs, emphasizing the significance of boundary conditions.

Vibratory Mechanics: Continuous Systems