# Numerical technology

### NURBS representation of geology

IC-FERST uses a surface-based geological modelling (SBGM) workflow that uses NURBS (Non-Uniform Rational B-Splines) surfaces to represent geological heterogeneities without reference to a pre-defined grid. The NURBS surfaces represent a broad range of heterogeneity. The geological model is constructed using the NURBS surfaces and a mesh created only when required for flow simulation or other calculations. Surface interactions, such as erosion, stacking or conforming, are enforced to ensure geological relationships are preserved and the boundary representation is watertight. See Jackson et al. 2015 and Jacquemyn et al. 2016 for more details.

### Unstructure dynamic mesh optimisation

Dynamic mesh optimisation employs the surfaces that define the boundaries of the geologic domains with contrasting material properties. The surfaces that define geologic heterogeneity are preserved during adaptivity. The mesh is adapted to provide high resolution to certain fields, for porous media simulations this is normally the pressure and the saturation field. See Jackson et al. 2015 and Salinas et al. 2015 for more details.

### Stable with high Courant numbers

IC-FERST has a new method to admit large Courant numbers. The governing equations are discretized in time using an adaptive theta-method. However, the use of implicit discretizations does not guarantee convergence of the nonlinear solver for large Courant numbers. IC-FERST uses a double-fixed point iteration method with backtracking, which improves both convergence and convergence rate. See Salinas et al. 2016 for more information.

### High order methods

IC-FERST is based on a control volume finite element mixed formulation and new force-balanced finite element pairs. The novelty of the method lies in (i) permitting both continuous and discontinuous description of pressure and saturation between elements; (ii) the use of arbitrarily high-order polynomial representation for pressure and velocity and (iii) the use of high-order flux-limited methods in space and time to avoid introducing non-physical oscillations while achieving high-order accuracy where and when possible. See Gomes et al. 2016 for more details.

### High order mesh to mesh interpolation

IC-FERST implements a higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations. See Adam et al. 2016 for a better explanation.

### Solid fluid coupling

IC-FERST can couple with Solidity and model the interaction between rock mechanics and fluids. See Yang et al. 2016 for a better explanation.