Mimetic methods are promising discretizations on complex grids consisting of (almost) arbitrary polyhedral cells. A mimetic method can be considered as a special kind of mixed finite-element method or as a special multipoint finite-volume method. A particular advantage of mimetic methods is that the implementation is generic and compact for large classes of grids and hence suitable for discretizations on geological models with complex geology. Connected to our work on these methods, there are two topics that are suitable for students:

• Mimetic vs MPFA - In this project you will study two different approaches for reducing grid-orientation effects and, in particular, focus on advantages and disadvantages for real reservoir geometries.
• Cells with curved faces - Many geological models contain cells with curved faces. The flow over non-planar faces can be discretized by either introducing extra degrees of freedom over curved faces or by subdividing each curved faces into triangular patches. In the project, you will implement these two approaches (e.g., in MRST) and compare their accuracy, efficiency, and simplicity of use.

We offer supervision at NTNU and at the universities of Bergen and Oslo. For all the projects listed above, you must work in close collaboration with the GeoScale team and we expect you to do quite a bit of programming. 

Contact: Knut-Andreas Lie