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Gridding and discretization

Gridding and discretization form the backbone of numerical simulation, transforming continuous mathematical models into finite sets of discrete quantities that can be solved for on a computer. Research on new methods is essential to develop more accurate, efficient, and robust simulations.

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Proficiency in gridding and discretization is generally broad and can be applied to different fields. Nevertheless, the intricacies in formulating and implementing advanced techniques vary significantly from one application to another. Developing new and highly effective methods therefore requires a thorough understanding of the challenges and requirements unique to each specific field.

What do we do?

We are proficient in a wide spectrum of both standard and more advanced gridding and discretization methods. Our expertise, however, centers around the following topics:

Enhancing grids for underground fluid flow applications

In industrial applications involving underground fluid flow, the design of computational grids becomes a critical endeavor. These grids must accurately capture the intricate geology of subsurface formations and their impact on fluid flow behavior. While various grid formats exist, they typically exhibit some level of unstructured topology and complex polytopal cell geometries. Overcoming the challenges posed by such grids—illustrated in Figure 1—has provided us with extensive expertise in both gridding and discretization methods. Figure 2 showcases two contemporary grid types specifically tailored to improve the representation of intricate rock formations.

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Figure 1: Illustration of typical grid geometries seen in 3D grid models of hydrocarbon-bearing rock formations and the challenges they pose: degenerate and twisted cell geometries, internal gaps, multiple neighboring connections, large aspect ratios and variations in cell thickness, internal gaps, non-matching cell interfaces, etc.
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Figure 2: Two examples of modern grid types in subsurface applications. The left image shows a cut-cell grid in which a regular background grid is truncated against curved surfaces generating polytopal cells locally. The right image shows a Voronoi grid, also called a perpendicular bisector (PEBI) grid, that adapts to well paths and fault surfaces generated with the UPR module from our open-source MRST software.

Advancing grid generation techniques

Our group boasts expertise in a range of grid generation methods and the effective utilization of grid generation software. Among these approaches, tetrahedral grids stand out as a highly versatile choice for approximating complex computational domains. Notably, we have extensive experience with Gmsh, a powerful tool for creating tetrahedral grids.

Furthermore, we recognize the value of tree-based grids in adaptive simulations. These grids prove particularly useful when the computational domain undergoes dynamic changes over time or during optimization processes related to shape and topology.

By leveraging these advanced grid generation techniques, we enhance our ability to model and simulate fluid dynamics, structural mechanics, and other complex phenomena in various industrial applications.

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Figure 3: Illustration of multimesh approaches from Johansson et al. The top plot shows a mesh of a propellar immersed into a static background grid. The lower plot shows a set of solid bodies described by individual meshes that that move and intersect freely relative to each other and a fixed background mesh.