Surface Algorithm for Lattice Boltzmann Fluid Simulation

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Solution Overview

Problem

The existing Lattice Boltzmann Method (LBM) simulations face limitations such as artificial noisiness in fluid quantities near walls, increased numerical dissipation, and a limited stability range, particularly for smooth and streamlined bodies and high-speed fluid flows due to the slip algorithm's volumetric representation and surface interactions.

Innovation Solution

A novel slip algorithm is introduced, where all surface elements interact with fluid domain particles, converting incoming distribution functions to outgoing functions to achieve zero tangential momentum flux, allowing for precise momentum flux addition, and using a different surface dynamics process to improve boundary condition accuracy.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If the volumetric representation with surface interactions is used, then mass conservation and momentum flux enforcement are achieved, but artificial noisiness and numerical dissipation increase

Engineering Contradiction:

Improvemass conservationVSAvoidartificial noisiness

Core Design Contradiction:

ReliabilityVSObject-generated harmful factors

Solution Approach 1:

The fluid domain is segmented into discrete lattice nodes, and the boundary surface is segmented into discrete surface elements. This segmentation allows for localized interaction operations between surface elements and fluid particles, enabling precise control of momentum flux at each boundary location while maintaining overall mass conservation, thereby reducing artificial noisiness compared to volumetric approaches.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Surface elements act as intermediaries between the fluid domain and the boundary conditions. The incoming distribution functions from the fluid are converted to outgoing distribution functions through the surface element interaction, which enforces boundary conditions on mass and momentum fluxes. This intermediary mechanism achieves exact mass conservation and precise momentum flux enforcement while maintaining numerical stability and reducing artificial dissipation.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Reliability

If the slip algorithm is used for boundary conditions, then mass and momentum fluxes are conserved, but stability range is limited for high-speed flows

Engineering Contradiction:

Improvemomentum flux conservationVSAvoidsimulation stability

Core Design Contradiction:

ReliabilityVSStability of the object's composition

Solution Approach 1:

The algorithm uses parameter changes in the distribution functions through the conversion process at surface elements. By adjusting the outgoing distribution functions based on incoming distributions and boundary conditions, the method adapts to different flow regimes including high-speed flows, expanding the stability range while maintaining momentum flux conservation.

Inventive Principle:

Principle #35Parameter changes

3Device complexity

If one-to-one dependence between incoming and outgoing distribution functions is used, then computational simplicity is maintained, but boundary condition accuracy decreases

Engineering Contradiction:

Improvealgorithm complexityVSAvoidboundary condition accuracy

Core Design Contradiction:

Device complexityVSMeasurement precision

Solution Approach 1:

Instead of using a simple one-to-one correspondence between incoming and outgoing distribution functions, the algorithm performs partial conversions where outgoing distribution functions are determined by converting from incoming distributions while enforcing boundary conditions. This excessive action of converting and re-enforcing boundary conditions improves accuracy without excessive computational complexity.

Inventive Principle:

Principle #16Partial or excessive action

Data Source

PatentUS20240160817A1Computer system for simulating physical processes using surface algorithm

Publication Date: 2024.05.16 DASSAULT SYSTEMS AMERICAS CORP

AI summary

Described are computer implemented techniques for simulating elements of a fluid flow. These techniques include storing in a memory state vectors for a plurality of voxels, the state vectors comprising a plurality of entries that correspond to particular momentum states of a plurality of possible momentum states at a voxel, storing in a memory a representation of at least one surface that is sized and oriented independently of the size and orientation of the voxels, perform interaction operations on the state vectors, the interaction operations modelling interactions between elements of different momentum states, perform surface interaction operations on the representation of the surface, the surface interaction operations modelling interactions between the surface and substantially all elements of voxels, and performing move operations on the state vectors to reflect movement of elements to new voxels.