Mathematical modeling in the environment

- Know the role of mathematical models in the study of environmental sciences.
- Know some models related to the description of biological communities.
- Know some models related to the spread of pollution.

Topic 1: Introduction.
1.1. Modeling process.
1.2. Mathematical model.
1.3. Numerical simulation.
1.4. Types of models

Topic 2: The first steps: Models of biological communities.
2.1. Communities of one specie.
2.2. Communities of two species.
2.3. Population dynamics models structured by age.

Topic 3: Mathematical models in geophysics: introduction to fluids.
3.1 Basic concepts. The Euler and Navier-Stokes equations.
3.2 Adimensional numbers.
3.3 Incompressible flows. Boussinesq approximation for natural convection problemes.
3.4 Selection of models and numerical methods.

Topic 4: Transport and diffusion models. Polution.
4.1 Transport and diffusion.
4.2 Phenomena involved in polution studies.
4.3 Some control polution problems.

Topic 5: Shallow water models.
5.1 Gravitational flow with free surface.
5.2 The Saint-Venant equations.
5.3 Erosion and sediment transport.

Topic 6: Water polution.
6.1 Adsorption and absortion.
6.2 Simplified polution models.

Topic 7: Alternative shallow water models.
7.1 Models for dispersive flows.
7.2 Multilayer models.

Topic 8: Further mathematical models in environmental engineering.
8.1 Subsurface flows. Richards equation.
8.2 GPR model for continuum mechanics.

Basic:

C.R. Hadlock, Mathematical modeling in the environment, Mathematical Association of America, 1998.

N. Hritonenko – Y. Yatsenko, Mathematical modeling in economics, ecology and the environment, Kluwer Academic Publishers, 1999.

J. Pedlosky, Geophysical fluid dynamics, Springer Verlag, 1987.

Complementary:

S.C. Chapra, Surface water-quality modelling, WCB/McGraw Hill, 1997.

P.L. Lions, Mathematical topics in fluid mechanics. Vol. 2: Compressible models, Clarendon Press, 1998.

G.I. Marchuk, Mathematical models in environmental problems, North-Holland, 1986.

J. D. Murray, Mathematical Biology. Springer-Verlag, 1993.

J.C. Nihoul, Modelling of marine systems, Elsevier, 1975.

L. Tartar, Partial differential equation models in oceanography, Carnegie Mellon Univ., 1999.

R.K. Zeytounian, Meteorological fluid dynamics, Springer Verlag, 1991.

Basic:

CG4: To have the ability to communicate the findings to specialist and non-specialist
audiences in a clear and unambiguous way.

CG5: To have the appropriate learning skills to enable them to continue studying in a
way that will be largely self-directed or autonomous, and also to be able to
successfully undertake doctoral studies.

Specific:
CE1: To acquire a basic knowledge in an area of Engineering / Applied Science, as a
starting point for an adequate mathematical modelling, using well-established
contexts or in new or unfamiliar environments within broader and multidisciplinary
contexts.

CE4: To be able to select a set of numerical techniques, languages and computer tools,
suitable for solving a mathematical model.

CE7: To know how to model complex elements and systems or in poorly established
fields, which lead to well-posed/formulated problems.

The class is a combination of master sessions (where the teacher will present the
theoretical contents of the subject) and problems and/or exercises solving sessions (in these
hours the teacher will solve problems for the different topics and will introduce new
mathematical approaches from a practical point of view).
The copetences related to this teaching methodology are: CG4, CG5, CE1, CE4, CE7

The student will also be asked to solve some problems proposed by the teacher in order to apply the acquired knowledge.
The copetences related to this teaching methodology are: CE1, CE4, CE7.

CRITERIA FOR THE 1ST EVALUATION OPPORTUNITY:

1-Problem solving and / or exercises (50% of the grade):

a) Attendance and active participation in class.
b) Exercises and / or works that will be proposed in the classroom.

2-Final exam of the course (50% of the grade).

CRITERIA FOR THE 2nd EVALUATION OPPORTUNITY:

The same as for the 1st evaluation opportunity

Problem solving: 28 HP 45 HNP 73 T

Master sessions: 28 HP 45 HNP 73 T

Final exam: 4 HP 0 HNP 4 T

The student is recommended to use online tutoring for any doubt related to this subject.

UNIVERSITIES FROM WHICH IT IS TAUGHT: Universidade de Santiago, Universidade da Coruña
CREDITS: 6 ECTS credits
TEACHER / COORDINATOR: José Manuel Rodríguez Seijo (jose.rodriguez.seijo@udc.es)
TEACHER: Saray Busto Ulloa (saray.busto.ulloa@usc.es)