Double-Sided Surfel Interface for Multi-Resolution Lattice Boltzmann

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Solution Overview

Problem

Conventional methods for connecting mesh regions with different resolutions in fluid flow simulations face challenges such as spatial uncertainty, misplacement of particles, and artificial wave reflections, particularly at scales near the lattice spacing, which affect the accuracy of fluid dynamic properties and their spatial propagation.

Innovation Solution

A surface-based approach using double-sided surfels (facets) is employed to connect mesh regions with different resolutions, where each surfel interfaces with one resolution on each side, allowing precise spatial location definitions and accurate propagation of particle distributions across resolution boundaries.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If volumetric overlap based VR methods are used to connect mesh regions, then computational cost is reduced and mass-momentum-energy conservation is achieved, but spatial uncertainty and particle misplacement occur leading to artificial wave reflections

Engineering Contradiction:

Improvecomputational costVSAvoidspatial accuracy

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The interface between coarse and fine regions is segmented into discrete surfel elements rather than using continuous volumetric overlap. Each surfel is a two-dimensional surface element that separates coarse and fine regions, allowing precise control over particle transfer at the interface without the spatial uncertainty inherent in volumetric methods.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The approach transitions from three-dimensional volumetric overlap to two-dimensional surface-based connection. By using surfels as interfaces, the method eliminates the third dimension of uncertainty in volumetric overlap while maintaining computational efficiency through surface-level particle transfer operations.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

2Ease of manufacture

If volumetric overlap is used to connect regions with different resolutions, then the geometric weight construction is simple, but it creates misplacement of particles in the stream-wise flow distribution

Engineering Contradiction:

Improvegeometric weight constructionVSAvoidparticle distribution accuracy

Core Design Contradiction:

Ease of manufactureVSManufacturing precision

Solution Approach 1:

Surfels act as intermediary elements between coarse and fine regions, mediating the particle transfer process. Instead of direct volumetric overlap causing misplacement, the surfel interface provides a controlled intermediate zone that preserves particle distribution accuracy while maintaining simple geometric weight construction through explicit surface-based transfer rules.

Inventive Principle:

Principle #24Intermediary (Mediator)

3Ease of operation

If overlapping volumetric domain is used, then the connection between regions is straightforward, but it creates artificial wave reflections that affect fluid dynamic properties near lattice spacing

Engineering Contradiction:

Improveregion connection simplicityVSAvoidfluid dynamic property accuracy

Core Design Contradiction:

Ease of operationVSReliability

Solution Approach 1:

The harmful volumetric overlap region is extracted and replaced with a surface-based surfel interface. This removes the source of artificial wave reflections while maintaining the simplicity of region connection. The surfel approach preserves fluid dynamic properties by providing precise particle transfer control at the interface.

Inventive Principle:

Principle #2Taking out (Extraction)

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

This method improves the accuracy of fluid flow simulations by reducing computational complexity, conserving mass and momentum, and enhancing the precision of fluid dynamic properties while maintaining exact flux definitions between regions with varying resolutions.

Implementation Method 1

Particle distributions are advected from neighboring voxels to the surface elements. Surface dynamics occur on the surface elements and particle distributions are propagated from the first side of the surface element to the second side of the surface element and vice versa.

Methodology Applied

Scientific EffectAdvection: Advection

Data Source

PatentUS20250378243A1Connecting two domains with different resolutions in lattice boltzmann method with double-sided surfels

Publication Date: 2025.12.11 DASSAULT SYSTEMS AMERICAS CORP

AI summary

Systems and methods include simulating, in a digital representation of a simulation space, a fluid flow across a boundary including double-sided facets abutting a first region and a second region by: determining first particle distributions for first facets of the double-sided facets based on particle distributions of first resolution voxels in the first region and second particle distributions for second facets of the double-sided facets based on particles of the second resolution voxels in the second region; performing surface interactions on the double-sided facets; combining particle distributions from the second facets to the first facets based on the surface interactions; determining particle distributions to be advected from the first facets to the second facets based on the surface interactions; and advecting particle distributions from the first facets to the first resolution voxels and from the second facets to the second resolution voxels.