Curved Surface Elements for Accurate Lattice Boltzmann Simulation
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Solution Overview
Problem
Existing lattice Boltzmann methods (LBMs) using planar surface elements for simulating fluid flow around complex geometries with high curvature suffer from increased computational cost and noise, particularly in simulations involving automotive underhood and airfoil geometries, without providing accuracy benefits.
Innovation Solution
The use of curved surface elements, such as facets, to represent complex geometries, allowing for reduced computational complexity and improved accuracy by combining multiple planar elements into curved ones, preserving exact mass and momentum conservation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If piecewise planar surface elements are used to represent complex geometries, then the geometry can be discretized and processed, but computational cost increases and surface noise is introduced without accuracy benefits
Solution Approach 1:
Multiple adjacent planar surface elements are merged into a single curved surface element that represents the underlying curved geometry. This merging reduces the total number of surface elements interacting with voxels, thereby decreasing computational cost while maintaining geometric accuracy through the curved representation.
Solution Approach 2:
The patent introduces curved surface elements that explicitly represent curved geometries rather than approximating them with multiple planar elements. This curvature representation reduces surface noise in simulations and maintains accuracy without requiring the fine discretization that planar elements would need, thus reducing computational complexity.
2Manufacturing precision
If multiple planar surface elements are used to represent high curvature geometries, then geometric representation is achieved, but surface noise increases and computational efficiency decreases
Solution Approach 1:
Curved surface elements are used to represent high curvature geometries directly, which eliminates the surface noise artifacts that arise from using multiple small planar elements. The curved representation naturally captures the geometry's curvature properties, providing accurate geometric representation without the harmful surface noise effect.
Solution Approach 2:
By merging multiple planar elements into curved surface elements, the patent reduces the number of discrete interactions between surface elements and voxels. This merging maintains geometric accuracy while eliminating the surface noise that would otherwise be introduced by numerous small planar elements.
3Ease of operation
If planar surface elements are used for boundary conditions, then the lattice structure can be processed, but flux definitions become approximate and mass/momentum conservation is not exact
Solution Approach 1:
Curved surface elements enable precise definition of boundary locations and exact flux calculations by accurately representing the curved geometry's orientation and area. This curvature representation allows for exact mass and momentum conservation through proper integration over the curved surface, improving flux definition precision while maintaining lattice processing capability.
Data Source
AI summary
Systems and methods for digitally simulating a physical process in a three-dimensional CAD model of a simulation space include receiving a digital representation of a simulation space, the digital representation including a three-dimensional CAD model of the simulation space including a lattice structure represented as a plurality of voxels including particles, the simulation space including one or more surfaces sized and oriented independently of the voxels. A plurality of planar facets are determined to represent the one or more surfaces of the simulation space in the lattice structure. One or more curved facets are determined based on the plurality of planar facets; and a physical process is simulated by performing surface interactions between the one or more curved facets and the particles in one or more voxels adjacent the one or more curved facets.