Lecture

Groundwater Flow: Laplace Equation and Boundary Conditions

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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 Laplace equation for groundwater flow, including the reminder of differential equations, harmonic potential, and boundary conditions. It also discusses the concept of velocity potential, harmonic potential, and the numerical resolution of Laplace's equation. The presentation emphasizes the conditions at boundaries, such as impermeable limits and equipotential surfaces, illustrated with examples like the flowerpot analogy and flow networks. The method of graphical flow networks is introduced as a tool to approximate solutions and determine flow characteristics. The lecture concludes with practical examples of groundwater flow in real-life scenarios.

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

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.

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