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Mathematical and Numerical Modelling of Transport Processes

This is the study programme for 2019/2020. It is subject to change.

A central part of the course is to consider 1D models relevant for simulating single- and two-phase flow in porous media. Analytical solutions of these transport equations are discussed as well as principles for use of numerical methods.

Learning outcome

1) Nonlinear Conservation Law; 2) Two-phase transport models driven by diffusion and/or advective flow; 3) Analytical solutions and weak solutions; 4) Numerical discretization techniques for transport equations; 5) Modeling of chemical properties of surfactants, polymers, clay minerals, ion-exchange; 6) Single-phase advection-diffusion equation (linear advection and diffusion); 7) Single-phase advection-diffusion with adsorption; 8) Single-phase advection-diffusion with dissolution/precipitation of minerals.


Fundamental mathematical models for studying single-phase and two-phase behavior. Basic geochemical models relevant for transport-reaction in porous media are also discussed.

Required prerequisite knowledge


Recommended previous knowledge

Good knowledge in mathematics (calculus)


Weight Duration Marks Aid
Written exam1/14 hoursA - FStandard calculator.

Course teacher(s)

Course teacher
Pål Østebø Andersen , Tore Halsne Flåtten
Course coordinator
Steinar Evje

Method of work

Class room instruction, programming exercises, calculation exercises

Open to

Admission to Single Courses at the Faculty of Science and Technology
Computational Engineering, Master's Degree Programme
Petroleum Engineering - Master of Science Degree Programme
Petroleum Engineering - Master`s Degree programme in Petroleum Engineering, 5 years

Course assessment

Standard UiS procedure


Material published on Canvas, compedium, extracts from books
Some of the material is based on the books
"Finite Volume Methods for Hyperbolic Problems", R.J. LeVeque,
Cambridge Texts in Applied Mathematics, Berlin, 2002.
"Numerical Partial Differential Equations. Conservation laws and elliptic equations", J.W. Thomas,
Texts in Applied Mathematics 33, Springer, 1999.
"Geochemistry, groundwater and pollution", C.A.J. Appelo and D. Postma,
CRC Press, Taylor & Francis Group, 2005.

This is the study programme for 2019/2020. It is subject to change.

Sist oppdatert: 06.06.2020