Scalable algorithms for fully implicit ocean models

PhD ceremony: Mr. J. Thies, 13.15 uur, Academiegebouw, Broerstraat 5, Groningen

Title: Scalable algorithms for fully implicit ocean models

Promotor(s): prof. A.E.P. Veldman

Faculty: Mathematics and Natural Sciences

Climate research is one of the disciplines which rely most heavily on numerical simulations. Experiments are tedious because of the difficulty of scaling something as large as an ocean down to laboratory size. Observations are sporadic because research vessels are expensive and can only be at one location at a time. Satellites, on the other hand, are limited to observing the sea surface.

In this thesis we study innovative numerical techniques to make simulations of ocean flow easier. The focal point is the term ‘scalability’. We call an algorithm scalable if refining the computational grid leads to a linear increase of the required arithmetic operations. A computer program is called scalable if using more processors reduces the computing time accordingly.

The implicit approach that we propose is based on the solution of coupled systems of equations, whereas explicit models use simpler updates of the variables to get from one time step to the next. Our implicit approach can take unlimited time steps, which allows us to simulate much longer time intervals like ice ages -than explicit models can handle.

The ocean is a complex dynamical system which can be sensitive to small changes of parameters such as the temperature of the atmosphere. Traditional explicit models have to be restarted for each new scenario, whereas the implicit variant can step directly from one situation to the next, varying the parame¬ters slightly in every step (continuation). This leads to substantially increased efficiency if one wants to test many scenarios.