- Knowledge of the MATLAB modelling platform, basic programming skills, independent user, able to write and run a script, generate numerical and graphical output.
- Recognize and able to solve Ordinary Differential Equations (ODE). Being familiar with most use methods in the Matlab Toolbox to solve ODEs and being able to apply these.
- Knowledge of numerical solution methods, finite difference, stability and truncation errors etc. Being able to apply this knowledge when solving (a set of) non-linear equations.
- Recognize and able to solve Partial Differential Equations (PDE’s) using tools available within Matlab and finite difference methods.
Transport phenomena are ubiquitous in science and technology, with a wide range of applications in different fields. Transport processes are usually described by a set of mathematical (differential) equations, which often can not be solved analytically. Consequently, a numerical approach is valuable and needed to understand the transport problems. This course will introduce the fundamentals of numerical computation, programming and solving of (differential) equations. A powerful software package, Matlab, will be used. The examples, problems and assignments used in this course will be closely related to the Transport Phenomena discussed elsewhere in the module.|
Objective of the course is (i) to obtain elemental knowledge on numerical modelling and programming; (ii) understand and being able to apply the basic programming language of Matlab; (iii) Able to solve ordinary differential equations and systems of linear equations; (iv) being able to solve partial differential equations related to heat, mass, and momentum transport.
The course will consist of lectures and hands-on exercise sessions. Via four different assignments, the competences for the aforementioned subjects will be tested. The numerical modelling skills are further an integrated part of the Project Transport Phenomena. A reader (lecture note) is available for the theory discussed.
The course part is divided in four sections, focussed on different competences:
- Competence 1 - Basic Programming in Matlab – starts with an introduction in the Matlab software package and basic programming. Focus is on becoming an independent user of Matlab and its elements. Students should be able to create a script file, define variables, use the help file, work with vectors and matrices, functions and function m-files, can use “if-else”, “for-while” loops, able to make plots, import- and export data, data analysis and code debugging. Competence 1 is finalized by completing, individually, a given set of exercises in an in-class exam.
- Competence 2 - ODE and Toolbox – focusses on solving Ordinary Differential Equations, using built-in tools in Matlab. With this, many time- and/or place dependent transport processes can be described. Attention will be given to validating the solution obtained. Competence 2 is finalized by solving, individually, assignments in an (in-class) exam.
- Competence 3 – Numerical Methods – aims to increase the understanding of the basics of numerical algorithms (iterative processes, truncation errors, extropolation), numerical solving (finite difference)- and minimization methods & tools, integration, stability criteria, and solving non-linear equations. Boundary condition problems, methods of Euler, Runge-Kutta etc. will be discussed. Competence 3 is completed by an individual (in-class) assignment where some of above elements are needed to solve the problem.
- Competence 4 – Solving PDEs – aims to introduce various methods and tools available in Matlab to solve Partial Differential Equations, commonly encountered in Transport Phenomena problems. Computational Fluid Dynamics principles will be illustrated and problems from heat, mass or momentum transfer will be discussed. Competence 4 is graded on basis of a dedicated assignment, related to the project work, in which a more complex Transport Phenomena situation will be described with PDEs and solved numerically.
|Open for students in an Engineering BSc programme.|
|Bachelor Scheikundige Technologie||Verplicht materiaal|