Multi-Scale Smoke Simulation Using Source and Doublet Panel Method

Solution Overview

Problem

Current methods for computer graphic simulation of incompressible gases face challenges in accurately modeling visual detail and handling boundary conditions, particularly with cup-shaped colliders and changing volume, where existing approaches either allow flow through or fail to account for volume changes.

Innovation Solution

A multi-scale method using the vorticity equation to derive dynamics, with Lagrangian particles and the source and doublet panel method for boundary modeling, combined with the fast multipole method for acceleration structure, allowing for non-uniform sampling and voxel-free resolution variation.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If source term only is used in panel method, then computational simplicity is improved, but flow passes through cup-shaped colliders incorrectly

Engineering Contradiction:

Improvecomputational simplicityVSAvoidboundary condition accuracy

Core Design Contradiction:

Ease of manufactureVSReliability

Solution Approach 1:

The panel method is segmented into two distinct components: source panels and doublet panels. Source panels handle volume generation/consumption while doublet panels handle flow direction and boundary adherence. This segmentation allows each component to specialize in its strength without compromise.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The source and doublet panel methods are merged into a unified boundary representation system. The combined approach uses both source strength (σ) and doublet strength (μ) parameters on the same boundary panels, allowing simultaneous satisfaction of volume conservation and no-flow-through conditions.

Inventive Principle:

Principle #5Merging (Combining)

2Reliability

If doublet term only is used in panel method, then cup-shaped collider handling is improved, but volume generation and consumption cannot be accounted for

Engineering Contradiction:

Improveboundary condition accuracyVSAvoidvolume change capability

Core Design Contradiction:

ReliabilityVSAdaptability or versatility

Solution Approach 1:

The panel method is segmented into two distinct components: source panels and doublet panels. Source panels handle volume generation/consumption while doublet panels handle flow direction and boundary adherence. This segmentation allows each component to specialize in its strength without compromise.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The source and doublet panel methods are merged into a unified boundary representation system. The combined approach uses both source strength (σ) and doublet strength (μ) parameters on the same boundary panels, allowing simultaneous satisfaction of volume conservation and no-flow-through conditions.

Inventive Principle:

Principle #5Merging (Combining)

3Stability of the object's composition

If uniform voxel grid is used, then numerical stability is improved, but resolution flexibility and performance are reduced

Engineering Contradiction:

Improvenumerical stabilityVSAvoidresolution flexibility

Core Design Contradiction:

Stability of the object's compositionVSAdaptability or versatility

Solution Approach 1:

The method transitions from static uniform grids to dynamic adaptive sampling. Voxel resolution is adjusted dynamically based on distance from the camera and region of importance, allowing high resolution where needed and low resolution where not needed, while maintaining numerical stability through the adaptive time step and sampling rate adjustments.

Inventive Principle:

Principle #15Dynamics

Solution Approach 2:

Different regions of the simulation domain are assigned different voxel resolutions based on their importance. Regions near the camera and regions of interest use fine resolution, while distant regions use coarse resolution. This local quality differentiation maintains visual fidelity where needed while improving overall performance.

Inventive Principle:

Principle #3Local quality

4Measurement precision

If high resolution sampling is used throughout, then visual detail accuracy is improved, but computational cost increases significantly

Engineering Contradiction:

Improvevisual detail accuracyVSAvoidcomputational efficiency

Core Design Contradiction:

Measurement precisionVSProductivity

Solution Approach 1:

Different regions of the simulation domain are assigned different voxel resolutions based on their importance. Regions near the camera and regions of interest use fine resolution, while distant regions use coarse resolution. This local quality differentiation maintains visual fidelity where needed while improving overall performance.

Inventive Principle:

Principle #3Local quality

Solution Approach 2:

The method transitions from static uniform grids to dynamic adaptive sampling. Voxel resolution is adjusted dynamically based on distance from the camera and region of importance, allowing high resolution where needed and low resolution where not needed, while maintaining numerical stability through the adaptive time step and sampling rate adjustments.

Inventive Principle:

Principle #15Dynamics

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 approach enables realistic simulation of incompressible gases in three dimensions with improved handling of boundaries and deformable object collisions, maintaining main shapes and timing while allowing flexible voxel resolution, thus enhancing the accuracy and efficiency of computer graphic simulations.

Implementation Method 1

Lagrangian particles may be created, modified and deleted in a manner that handles advection with buoyancy and viscosity

Methodology Applied

Scientific EffectAdvection: Advection

Implementation Method 2

Lagrangian particles may be created, modified and deleted in a manner that handles advection with buoyancy and viscosity

Methodology Applied

Scientific EffectBuoyancy: Archimedes' Principle (Buoyancy)

Implementation Method 3

Boundaries and deformable object collisions may be modeled with the source and doublet panel method

Methodology Applied

Scientific EffectPanel method:

Implementation Method 4

The acceleration structure may be based on the fast multipole method (FMM), but with a varying size to account for non-uniform sampling

Methodology Applied

Scientific EffectFast multipole method:

Implementation Method 5

A multi-scale method for computer graphic simulation of incompressible gases in three-dimensions... The dynamics may be derived from the vorticity equation

Methodology Applied

Scientific EffectVorticity:

Data Source

PatentUS10282885B2Computer graphic system and method of multi-scale simulation of smoke

Publication Date: 2019.05.07 PIXAR CORP

AI summary

A multi-scale method is provided for computer graphic simulation of incompressible gases in three-dimensions with resolution variation suitable for perspective cameras and regions of importance. The dynamics is derived from the vorticity equation. Lagrangian particles are created, modified and deleted in a manner that handles advection with buoyancy and viscosity. Boundaries and deformable object collisions are modeled with the source and doublet panel method. The acceleration structure is based on the fast multipole method (FMM), but with a varying size to account for non-uniform sampling.