Toward Mixed-element Meshing based on Restricted Voronoi Diagrams

Pellerin, Jeanne; Lévy, Bruno; Caumon, Guillaume

doi:10.1016/j.proeng.2014.10.390

Cited by 11 publications

(4 citation statements)

References 26 publications

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“…(3) The model building and updating methods are simpler compared to the tetrahedron. The GTP model could be built by the Delaunay triangulation based on the coordinates of the top borehole orifice point (Pellerin et al, 2014), and then the TIN can be extended downward to obtain the GTP model. If there are new drilling exploration data, the model could only be updated by adding a new borehole using the TIN insertion method to update the model locally.…”

Section: The Gtp Voxelmentioning

confidence: 99%

Adaptive Interpolation Method for Generalized Triangular Prism (GTP) Geological Model Based on the Geometric Smoothness Rule

et al. 2022

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Three dimensional (3D) geological model is frequently used to represent the geological conditions of the subsurface. The generalized triangular prism (GTP) model designed for borehole sampling data is a spatial data model that could retain the internal connection between the three adjacent boreholes and distinguish between the bedding and cross-bedding directions, which is proper for accurate 3D geological modeling. The traditional building method cannot consider two factors: the borehole distance is usually longer than the stratigraphic thickness, and the top and the bottom surface have different accuracy at the same time. In this study, we describe the new interpolation method for the GTP 3D geological model to improve the model accuracy with sparse borehole data. Firstly, definition and calculation method of the GTP model smoothness are proposed to measure the model smoothness and accuracy degree, which are used to decide whether the GTP voxel requires interpolation. Secondly, the virtual borehole design and calculation method for the GTP voxel subdivision in terms of the GTP geometric smoothness are discussed in detail. Finally, the GTP adaptive interpolation can be performed through the GTP voxel subdivision and the geometric optimization rebuilding. This method could adaptively interpolate the existing GTP model by local updating without changing the GTP model structure, it has high efficiency compared to the classical method. In addition, the feasibility and accuracy of this method could be proven by the actual case. The study will provide a new and reliable interpolation method for the GTP model, and it is also conducive to economic geology related research.

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Section: The Gtp Voxelmentioning

confidence: 99%

Adaptive Interpolation Method for Generalized Triangular Prism (GTP) Geological Model Based on the Geometric Smoothness Rule

et al. 2022

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“…However, producing Voronoi diagrams that honour the internal interfaces represented by the fracture is not an easy task, particularly for complex 3D configurations. An attempt in that direction has been performed in [53] and [12].…”

Section: Voronoimentioning

confidence: 99%

Performances of the mixed virtual element method on complex grids for underground flow

Fumagalli¹,

Scotti²,

Formaggia³

2020

Preprint

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The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults, while the latter are connected to the properties of the rock matrix which might vary abruptly in space. The development of approximation schemes has recently focused on the overcoming of such difficulties with the objective of obtaining numerical schemes with good approximation properties. In this work we carry out a numerical study on the performances of the Mixed Virtual Element Method (MVEM) for the solution of a single-phase flow model in fractured porous media. This method is able to handle grid cells of polytopal type and treat hybrid dimensional problems. It has been proven to be robust with respect to the variation of the permeability field and of the shape of the elements. Our numerical experiments focus on two test cases that cover several of the aforementioned critical aspects.

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“…Dealing with more realistic geometries and sequential Boolean operations to reproduce the succession of geological events calls for further numerical and mathematical developments. Meanwhile, as statistical properties of random sets are not easily checked in practical cases, the numerical approach to relate objects to physics clearly remains an area of much interest (Botella et al 2016;Cacace and Blöcher 2015;Karimi-Fard and Durlofsky 2016;Merland et al 2014;Mustapha 2011;Pellerin et al 2014;Zehner et al 2015).…”

Section: Object Uncertaintymentioning

confidence: 99%

Geological Objects and Physical Parameter Fields in the Subsurface: A Review

Caumon

2018

Handbook of Mathematical Geosciences

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Geologists and geophysicists often approach the study of the Earth using different and complementary perspectives. To simplify, geologists like to define and study objects and make hypotheses about their origin, whereas geophysicists often see the earth as a large, mostly unknown multivariate parameter field controlling complex physical processes. This chapter discusses some strategies to combine both approaches. In particular, I review some practical and theoretical frameworks associating petrophysical heterogeneities to the geometry and the history of geological objects. These frameworks open interesting perspectives to define prior parameter space in geophysical inverse problems, which can be consequential in under-constrained cases.

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Toward Mixed-element Meshing based on Restricted Voronoi Diagrams

Cited by 11 publications

References 26 publications

Adaptive Interpolation Method for Generalized Triangular Prism (GTP) Geological Model Based on the Geometric Smoothness Rule

Adaptive Interpolation Method for Generalized Triangular Prism (GTP) Geological Model Based on the Geometric Smoothness Rule

Performances of the mixed virtual element method on complex grids for underground flow

Geological Objects and Physical Parameter Fields in the Subsurface: A Review

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