**
Fast and robust solution methods for the water quality equations
**

Adilson Morais

Supervisor: Kees Vuik

Site of the project:

Deltares

Rotterdamseweg 18

2629 HD Delft

start of the project: March 2011

In June 2012 the
Interim Thesis
and a
presentation has been given.

The Master project has been finished in March 2012
by the completion of the
Masters Thesis
and a final
presentation
has been given.

For working address etc. we refer to our
alumnipage.

**Summary of the master project:**

Deltares is the specialist in the field of water quality. The institute
is consulted by public authorities, engineering agencies or other companies for doing water quality research. Deltares models the water quality by means of partial differential equations. These so-called water quality equations are advection-diffusion-reaction equations for the concentration of the substances in water.
Two problems are considered.

In the first problem we consider methods which can be used to solve the
described partial differential equations. At this moment small timesteps are needed in order to solve the problems in a stable way. For explicit method one
has to satisfy the CFL inequality. This means that for small spacesteps one
has to use small timesteps, which the simulation very time consuming.
For this reason we are looking to find implicit methods such that large
timesteps are allowed where the accuracy is maintained.

Marsh before the coast of Lelystad

Another problem is the computation of the stationary solution of the water
quality model. In the sea there are many substances which are circulated over
a period of years. We assume that these substances are in steady state.
The current solution strategy is to use a time-stepping strategy. This implies
that many time steps are used before the solution is in steady state.
For this reason we are looking for a faster method to compute the steady state
solution.

Water quality in the North Sea

## Contact information:
Kees
Vuik

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