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Students have learned to perform modelling experiments derived from a science (physics, chemistry, hydrology or geology) problem context;
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Students have acquired basic skills in program development using the (modern) Fortran language. This includes analysis of relatively simple problems and corresponding program design and necessary basic knowledge of the Fortran syntax;
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Students have developed an elementary insight in numerical modelling and in the application of numerical methods such as interpolation, integration and solution of differential equations;
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Students have acquired a basic expertise in using the Linux operating system and in application of utilities, especially graphics programs and text-editors for the visualisation of scientific data and presentation of their work in several lab-reports.
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De cursus omvat 5 verschillende modulen. De eerste twee modulen (programmeren 1 en 2) zijn verplicht voor iedereen. Uit de overige modulen dient de student er 2 te kiezen.
Hieronder staan alle modulen nader beschreven.
Module 1:
Docent: C. Thieulot
Basiscursus computerprogrammeren waarin worden behandeld:
Enige basis kennis van computersystemen en vaardigheden in computergebruik; Inleiding computerprogrammeren in Fortran. In dit onderdeel worden de basis elementen van de taal Fortran behandeld en toegepast in een serie eenvoudige programmeeropdrachten. Fortran vindt veel toepassing in wetenschappelijk rekenwerk en vooral de modernere versies lenen zich uitstekend voor goed gestructureerde ontwikkeling van computerprogrammatuur. Fortran vindt veel toepassing in wetenschappelijk rekenwerk en vooral de modernere versies lenen zich uitstekend voor goed gestructureerde ontwikkeling van computerprogrammatuur.
Module 2:
Docent: C. Thieulot
Voortgezette cursus computerprogrammeren in Fortran waarin meer geavanceerde taalelementen aan de orde komen. Naast enkele tutorial oefeningen zal er een computerprogramma worden ontwikkeld voor het modelleren van verstoringen in het zwaartekrachtsveld van de aarde ten gevolge van aanwezige onregelmatigheden in de dichtheidsverdeling van de ondergrond.
Module 3:
Docent: A. Raoof
In this course module we consider heat transfer in porous media. The whole module has been designed in three steps.
Step1: We start with solving the pressure field in a two-dimensional medium for Dirichlet boundary conditions to calculate the Darcy flow in a porous medium. After calculation of Darcy flow the students compared the average hydraulic permeability calculated from the numerical model against the existing algebraic relations in the literature.
Step2: Heat diffusion in a porous medium (in absence of hydrodynamic forces) has been simulated using the explicit finite difference method. Two different boundary conditions for heat diffusion have been assigned. The numerical results are compared to the analytical results obtained using Fourier series.
Step3. Advection and diffusion of the equations are combined to simulate heat transfer in a homogenous porous medium. As the last exercise, the students try to simulate the heat transfer (advection + diffusion) in a heterogeneous porous medium where not only there is heterogeneity in hydraulic permeability but also in heat conductance of the porous medium. This module provides basic physical insights into the transport phenomena in porous media which are mostly modeled by advection diffusion equations. Characteristic time scales of these two components and the spatial and temporal temperature profiles are discussed.
Module 4:
Docent: P. Meijer
"Forward modelling of stratigraphy". To better understand the processes responsible for a given sedimentary sequence one can, also in this context, make great use of numerical modelling. In this exercise you will acquaint yourself with the application of the "cellular method" in the forward modelling of the 3D stratigraphic architecture of a fan delta. This model will be constructed step by step starting from a simple basic idea.
Module 5:
Docent: R. Schotting
In this course module we consider horizontal flow of groundwater in a phreatic (unconfined) aquifer. The main goal is to analyze the shape of the groundwater table under various hydro(geo)logical conditions, e.g. recharge (rainfall), permeability contrasts, etc. If we combine the continuity equation for the fluid and Darcy's Law and after some algebra, the resulting equation is a nonlinear diffusion equation in terms of the height of the water table. In this exercise we only consider stationary one-dimensional flow. In that case, the governing equation reduces to a linear Poison equation. The problems we are going to analyze numerically boil down to solving a two-point boundary-value problem on a bounded domain. Some linear algebra subroutines from the Numerical Recipes (Fortran) library will be provided, as well as the required structure of the main program. During the introductional lecture, the derivation of the governing equation for the position of the water table will be given. In addition, insight will be provided in the spatial finite-difference discretization, and in the numerical procedure to solve the resulting system of algebraic equations. The nice thing is that all problems that will be considered in this hydrogeological exercise have closed-form exact solutions. These solutions will be derived during the introductionallecture and will be used for verification purposes of the corresponding numerically obtained solutions.
Development of transferable skills:
2. Ability to work in a team: students work in pairs (programming and writing the report)
3. Written communication skills: Results are presented in reports.
4. Problem-solving skills: students receive a list of rather diverse assignments which they first have to conceptualize and then translate into computer code. The code is then refined and used to arrive at a results which will be analyzed in the report.
8. Analytical/quantitative skills: students learn how to make a computer model from a variety of mathematical and geophysical exercises.
10. Technical skills: students become familiar with the Linux operating system, learn the basics of programming and scientific plotting.
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