UPR - Unstructured Grids Adapted to Geometric Objects
The module implements new methods for generating unstructured polyhedral grids that align to prescribed geometric objects. Control-point alignment of cell centroids is introduced to accurately represent horizontal and multilateral wells, but can also be used to create volumetric representations of fracture networks. Boundary alignment of cell faces is introduced to accurately preserve geological features such as layers, fractures, faults, and/or pinchouts. The module implements a new conflict-point handling scheme that creates conforming cells even at intersections between geometric objects in 2D. In 3D, the method honors control-point alignment of cell centroids and boundary alignment of cell faces away from object intersections.


The UPR module generates two types of grids in 2D:

  • composite grids that have Cartesian cell geometries away from the geometrical features one wants to adapt to and general polyhedral geometries close to lines that are either tracked by cell centers or faces
  • perpendicular bisector grids (also known as Voronoi grids) in which cell centers and/or cell faces adapt to prescribed lines

These grids can be extruded to 3D along straight lines, thereby giving 2.5D grids.

The module also implements routines for generating 3D Voronoi grids.

The following plots show some of the grids that are generated in the tutorial examples that accompany the module.




This module was initially written by Runar Lie Berge as part of his master thesis at NTNU (2015-2016), under supervision of Knut-Andreas Lie. The module has later been significantly improved and extended through a collaboration between Berge and Klemetsdal/Lie at SINTEF.


  1. R. L. Berge. Unstructured PEBI grids adapting to geological features in subsurface reservoirs. NTNU, 2016.
  2. Ø. S. Klemetsdal, R. L. Berge, K.-A. Lie, H. M. Nilsen, and O. Møyner. Unstructured gridding and consistent discretizations for reservoirs with faults and complex wells. SPE Reservoir Simulation Conference, Montgomery, Texas, USA, 20-22 February 2017. DOI: 10.2118/182666-MS
  3. R. L. Berge, Ø. S. Klemetsdal, and K.-A. Lie. Unstructured Voronoi grids conforming to lower-dimensional objects. Comput. Geosci., Vol. 23, Issue 1, pp 169-188 2019. DOI: 10.1007/s10596-018-9790-0. Springer Nature SharedIt
  4. R. L. Berge, Ø. S. Klemetsdal, and K.-A. Lie. Unstructured PEBI grids conforming to lower-dimensional objects. In "Advanced Modelling with the MATLAB Reservoir Simulation Toolbox (MRST)", K.-A. Lie and O. Møyner, eds., pp 3-40, Cambridge University Press. DOI: 10.1017/9781009019781.005.

Published December 8, 2016