Modeling Discontinuities in Heterogeneous Structures Using Substacks
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Solution Overview
Problem
Existing methods for modeling multidimensional heterogeneous structures, such as geological formations, face challenges in accurately representing discontinuities due to cell deformation and the resulting artifacts, leading to inaccurate modeling and increased computational time.
Innovation Solution
Dividing stacks into substacks along discontinuities with separating surfaces, allowing for accurate representation of discontinuities without cell deformation, and storing the composition and position of substacks in memory, enabling efficient processing and storage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a tetrahedral grid is used to model continuous three-dimensional space, then flexibility and adaptability to any space or structure are improved, but the amount of information to be stored increases and processing time becomes relatively long
Solution Approach 1:
The patent divides the three-dimensional space into a regular grid of cubic cells with fixed dimensions, segmenting the continuous space into discrete, manageable units. This segmentation allows the use of simple integer coordinates (i, j, k) to identify each cell, dramatically reducing the information storage requirements compared to arbitrary tetrahedral grids while maintaining sufficient modeling capability for heterogeneous structures.
2Measurement precision
If the resolution of the three-dimensional grid is increased to model discontinuities accurately, then modeling precision is improved, but the amount of information increases and processing time becomes longer
Solution Approach 1:
The patent applies local quality by allowing different physical properties to be assigned to different cells in the grid, enabling accurate representation of discontinuities and heterogeneous structures. Each cell can have its own property values (e.g., material type, porosity, permeability), allowing high modeling precision for discontinuities without requiring increased grid resolution, thus avoiding the computational burden of finer grids.
3Manufacturing precision
If stacks are arranged along a discontinuity to improve geometry approximation, then geometric accuracy is improved, but cells with strongly deviating shapes and small volume are formed at transitions, leading to modeling artifacts
Solution Approach 1:
The patent uses a regular cubic grid structure that copies the same cell geometry throughout the domain, avoiding the need to create cells with strongly deviating shapes. This uniform copying of cell geometry prevents the formation of degenerate cells at discontinuity transitions, eliminating modeling artifacts while maintaining geometric accuracy through the regular grid's ability to represent interfaces between cells with different properties.
Data Source
AI summary
Method, apparatus, computer program and data carrier for modeling a multidimensional, heterogeneous structure using a digital processing unit, by means of a grid built up of stacks of multidimensional cells. A cell is bounded by boundary surfaces and represents at least one property of the structure. The composition of a stack, the position of the stacks in the grid and the properties represented by cells are stored in memory means by the processing unit. For modeling a discontinuity, a respective stack is divided into two or more substacks separated by separating surfaces. The composition and the position of the substacks in a respective stack are stored in the memory means. The modeling method enables an accurate and fast computation of properties of the modeled structure or space.