MVEX01-21-05 Lattice Boltzmann simulations of droplet dynamics

​The lattice Boltzmann method is a fairly recent numerical method used mainly for solving transport equations like the Navier-Stokes equations for fluid flow or the advection-diffusion equation. It has the advantages of being comparatively easy to implement and easy to parallelize to run on multiple computer cores.
 
The Allen-Cahn equation is a reaction-diffusion equation, which can for example be used to describe the dynamics of for example droplets of water in air. Depending on the source term in the equation one can model different dynamics of the water-air interface.

This project is about implementing the lattice Boltzmann method to solve the Allen-Cahn ​equation in two dimensions and to study the effect of different types of dynamics. Depending on the preferences of the students, the project can be oriented more towards implementation and programming, in particular parallel programming for CPU and possibly GPU, or more towards theory of the lattice Boltzmann method, studying the effect of different model parameters.
Rapporten skrivs på svenska.
 
Projektkod MVEX01-21-05
Gruppstorlek 3-4 studenter
Målgrupp GU- och Chalmersstudenter. För GU-studenter räknas projektet som ett projekt i Tillämpad matematik (MMG900/MMG920). 
Projektspecifika förkunskapskrav Gärna någon kurs i PDE. Viss programmeringsvana, i C/C++ eller liknande, är nödvändigt.
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: må 26 okt 2020.