Mathematical Sciences

Lund University

  • Title: Modelling sedimentation of particles in a fluid with a PDE as an alternative to a particle-based model
  • Short description:

    The main part of the project is to calibrate a model of sedimentation written as a nonlinear partial differential equation (PDE) on conservation law form.

  • Long description:

    Sedimentation of particles in a liquid is a common separation process in chemical industry,
    wastewater treatment plants, mineral engineering and other applications. A particle-based model is
    a system of coupled ordinary differential equations (ODEs), each modelling a single particle. This is
    however not possible when the number of particles is very large. An alternative model for
    horizontally averaged concentrations is a one-dimensional continuum model of the process
    consisting of a nonlinear partial differential equation (PDE) on conservation law form. The tasks of
    the MSc project are to i) learn how to solve this type of equation with the method of characteristics;
    ii) learn how to obtain approximate numerical solutions; iii) implement the numerical algorithm for
    simulation with a general flux function of the model PDE and iv) calibrate the model to recently
    published simulations with a particle-based model. The aim is to investigate whether the simpler PDE
    model can provide usable averaged results.

    Prerequisites: Good grades in courses in mathematics (e.g., LTH courses including “Kontinuerliga
    system”) and numerical analysis.

  • Info: PDF
  • Contact: Stefan Diehl