Fast and robust solver for the advection-diffusion equation

Paulien van Slingerland

Site of the project:
WL | Delft Hydraulics
Rotterdamseweg 185
2629 HD Delft

start of the project: September 2006

In December 2006 the Interim Thesis has been appeared and a presentation has been given.

The Master project has been finished in June 2007 by the completion of the Masters Thesis and a final presentation has been given. For working address etc. we refer to our alumnipage.

An article (Dutch) about the work of Paulien has been published in the Delta of March 13, 2007.

On March 27 2007, Paulien has given a presentation at the Second international conference on high order non-oscillatory methods for wave propagation, transport and flow problems' to be held at the University of Trento from March 26 to 30 2007.

Summary of the master project:
At present, plans are being made for the construction of Liquefied Natural Gas pipes in the sea bed off the coast of Hong Kong. To this end, dredging is necessary which causes plumes of silt in the water. The silt particles float in the water for a relatively long period of time, until, eventually, they settle on the sea bed. Unfortunately, both phenomena are in general harmful to coral reefs and Chinese white dolphins, two protected species that live in the sea near to Hong Kong. So, before the plans can be carried out, it is necessary to determine how much of the ocean may be affected by those plumes.


Fortunately, software is already available for this purpose. Delft3D-WAQ, a simulation program that has been developed by WL|Delft Hydraulics, is a useful tool in forecasting water quality. In particular, it is able to predict the size of silt plumes caused by dredging. Basically, the software approximates the solution of the advection diffusion equation by means of the finite volume method. Since it is often necessary to predict one or two years ahead, large time steps are prefered in order to have limited computing time.

However, there are two aspects that need improvement. First of all, the current schemes are either expensive explicit higher order schemes or inaccurate implicit first order schemes. Moreover, the convergence speed of the present solver for linear systems is unsatisfactory for diffusion dominated problems.

In this study, answers to the following questions will be sought:
  1. What are the possibilities for an accurate finite volume scheme for the advection diffusion equation on an unstructured three-dimensional grid that has a high upper bound for the time step?
  2. How can the convergence speed of the current linear solver be increased for systems resulting from diffusion dominated problems?
In other words: Can the eventual damage done to dolphins and coral reefs be estimated better and faster?

Click on the figure below to see the movement of the silt plumes due to the tidal effect.

WAQ's forecast of the silt plumes

Contact information: Kees Vuik

Back to the home page or the Master students page of Kees Vuik