Reservoir simulation:

• The GeoScale project portfolio

Modern methods for modelling and characterisation of reservoirs are leading industry to routinely build detailed reservoir models that are much larger than what can be handled by industry-standard reservoir simulators. In a series of projects funded in part by the Research Council of Norway and in part by industry, we seekt to develop a numerical technology that facilitates desktop simulation of fluid flow directly on high-resolution geomodels of highly heterogeneous and fractured reservoirs.

• Geological Storage of CO₂: Mathematical Modelling and Risk Analysis

is a strategic research project  (2007-2011) funded in part by the Climit programme at the Research Council of Norway and in part by StatoilHydro and Shell. The project aims to develop analytical and numerical tools to be used in risk assessment analysis of geological storage of CO₂.

Image processing:

• PDE-based image processing: 

As part of the strategic inter-departmental research at SINTEF ICT, we have implemented, applied, and compared various PDE-methods for image processing. In particular, we have studied PDE-methods for  image registration, segmentation, enhancement, and anisotropic smoothing.

Ocean wave simulations:

• UNDA: 

From 1993 to 2002 we developed the UNDA computer simulator for calculations of fully nonlinear waves around marine structires. UNDA is based on a novel spline-collocation method.

• Nonlinear ocean wave simulations: 

Simulations of bichromatic waves demonstrate how weakly nonlinear self-interaction can affect the evolution of a wave train on deep water.

• Simulation of surface waves at Hasvik harbour: 

The Hasvik harbour is carrying a lot of traffic and has always been very sensitive to weather conditions. A new breakwater was constructed in 1996 to make the harbour more stable. However, during a storm on October 31, 1997, the breakwater was destroyed by waves. In this project, we study the focusing effect that banks and underwater slopes has on incoming waves. The simulated wave height indicates strong reflection from, and thus heavy load on the breakwaters, and this probably accounts for the damage during the storm of October 31.

• Wave power plant: 

For many years the TAPCHAN ocean wave power plant at Toftestallen produced the most power among all operating wave-powered generators. The TAPCHAN generator was based on research from SINTEF (SI). 

Miscellaneous:

• Winter schools:

Since 2001 we have organized a yearly winter school in computational mathematics at Dr. Holms Geilo. The Geilo winter schools have become quite popular, having between 70-80 participants the last two years.

• Nonlinear partial differential equations of evolution type - theory and numerics

Not all our research is driven by the needs of an industrial customer. In this four year project (2000-2003), we performed pure academic research by developing new high-resolution methods for hyperbolic conservation laws and studying convergence and error estimates for operator splitting methods for degenerate convection-diffusion equations.