MVEX01-20-19 Collocation methods for solution of nonlinear transport equations

​In many real world applications, the transport of liquids and molecules through porous materials is of fundamental importance. Some examples include controlling release of pharmaceuticals from tablets, membranes for energy production through osmosis and liquid-absorbing hygiene products.  In general, the equations that describe these processes are flow equations and advection-diffusion equations, which are partial differential equations.  Additionally, when molecules are reacting or being adsorbed to surfaces, the partial differential equations that describe the transport may become non-linear and the coefficients depend on the solution itself.

In such cases, the numerical solution of the equations may be simplified by using so called collocation methods, which assume that the equation is satisfied exactly at certain locations - collocation points. This is in contrast to e.g. finite element methods, which are based on integrating the equation against test functions.

In this project, you will investigate the properties of collocation methods numerically and theoretically, using different types of basis functions (polynomials, B-splines, ...). The results will be applied to problems derived from real-world applications and will be compared to finite difference and/or finite element methods.

 
Projektkod MVEX01-20-19
Gruppstorlek 3-4 studenter
Målgrupp GU- och Chalmersstudenter. Mest intressant för studenter med någon fysik/kemi-bakgrund, eller intresserade av numeriska metoder.
För GU-studenter räknas projektet som ett projekt i Tillämpad matematik (MMG900/MMG920).
Projektspecifika förkunskapskrav Gärna någon kurs i PDE.
Se respektive kursplan för allmänna förkunskapskrav. Utöver de allmänna förkunskapskraven i MVEX01 ska Chalmersstudenter ha avklarat kurser i en- och flervariabelanalys samt linjär algebra.
Handledare Tobias Gebäck
Examinator Maria Roginskaya, Ulla Dinger
Institution Matematiska vetenskaper 

Publicerad: to 31 okt 2019.