Hierarchical Grid Search for Discrete Element Contact Detection
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Solution Overview
Problem
Existing Discrete Element Method (DEM) simulations face significant computational challenges in contact detection, particularly for large simulations with varying particle sizes, leading to inefficient contact detection algorithms and increased computational costs.
Innovation Solution
A multiple grid search method, specifically a hierarchical grid search, is employed to efficiently detect contacts between particles and boundary elements by allocating entities to cells based on size and searching across multiple grid levels, thereby reducing the number of unnecessary pair checks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a neighbour list approach is used to reduce contact detection cost to order N, then computational efficiency is improved, but collision detection reliability deteriorates because entities moving faster than the validity period allows may overlap without contact being detected
Solution Approach 1:
The neighbour list validity period is made dynamic by adjusting it based on the maximum speed of entities in the system. When entity speeds increase, the validity period is reduced accordingly, ensuring that even fast-moving entities cannot travel far enough to cause undetected collisions within the list's validity window. This dynamic adjustment maintains collision detection reliability while preserving computational efficiency.
Solution Approach 2:
The minimum separation distance parameter is adjusted based on entity speeds and the neighbour list validity period. By changing this parameter dynamically, the system ensures that the neighbour list includes all entities that could possibly collide within the validity window, thereby maintaining reliable collision detection while optimizing the list size for computational efficiency.
2Ease of manufacture
If a single uniform grid is used for contact detection, then the algorithm is simple to implement, but computational cost increases for simulations with highly varying particle sizes due to excessive pair checks
Solution Approach 1:
The simulation space is divided into multiple grid levels with different cell sizes, each optimized for detecting contacts among particles of specific size ranges. This segmentation allows the algorithm to efficiently handle particles of varying sizes by routing them to appropriate grid levels, reducing unnecessary pair checks while maintaining implementation feasibility through a structured hierarchical approach.
Solution Approach 2:
Different regions of the simulation space are assigned different grid resolutions based on the local particle size distribution. Areas with small particles use finer grids, while areas with large particles use coarser grids. This local adaptation optimizes contact detection efficiency for each region's specific characteristics while keeping the overall algorithm manageable through localized adjustments.
Data Source
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AI summary
A discrete element method for modelling granular or particulate material, the method including a multiple grid search method wherein the multiple grid search method is a hierarchical grid search method, and wherein entities, such as particles and boundary elements, are allocated to cells of respective grids based on size. The search method further includes: (a) performing a search of cells in a first of the grid levels to determine pairs of entities which satisfy predetermined criteria to be included in a neighbour list for which both entities belong to the first grid level; (b) mapping each nonempty cell in the first grid level to each of the other grid levels, determining neighbouring cells in each of the other grid levels and determining all pairs of entities belonging to a pair of levels that satisfy the predetermined criteria for inclusion in the neighbour list; and (c) repeating (a) and (b) for all grid levels.