Pseudo-Incompressible LBM for Stable High-Density Flow Simulation
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Solution Overview
Problem
Existing methods fail to accurately simulate fluid flows, particularly multiphase flows with high density ratios, leading to truncation errors and instability in digital simulations.
Innovation Solution
Implementing a Lattice Boltzmann Method (LBM) that accounts for pseudo-incompressible fluid flows by defining the first and zeroth moments of the distribution function to be independent of local density, reducing truncation errors and improving Galilean invariance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the standard Lattice Boltzmann Method is used for simulating incompressible fluid flows, then the simulation can be performed, but truncation errors occur leading to unphysical results and reduced accuracy
Solution Approach 1:
The patent modifies the LBM equations by introducing a pseudo-compressibility parameter and adjusting the equation of state to allow density variations that compensate for truncation errors. This parameter change enables the simulation to maintain physical correctness while preserving computational efficiency.
Solution Approach 2:
The patent separates the density calculation into two components: a reference density component and a perturbation component. This segmentation allows the simulation to handle incompressible flows by focusing on pressure-driven velocity fields while using density perturbations only to correct truncation errors, rather than treating full compressibility.
2Adaptability or versatility
If the standard Lattice Boltzmann Method is used, then computational operations can be performed, but Galilean invariance is not maintained leading to frame-dependent results
Solution Approach 1:
The patent performs a preliminary transformation of the distribution function to a Galilean-invariant form before performing collision operations. This preliminary action ensures that the subsequent simulation steps automatically maintain frame independence, eliminating the need for post-processing corrections.
3Quantity of substance
If high density ratios are used in multiphase fluid flow simulation, then phase differentiation is achieved, but truncation errors increase causing unphysical results
Solution Approach 1:
The patent introduces a pseudo-compressibility intermediary that mediates between the high density ratio requirement for phase differentiation and the truncation error problem. This intermediary allows density to play a corrective role without requiring full compressibility, thus maintaining accuracy while enabling multiphase simulation.
Data Source
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AI summary
Systems and methods for digitally simulating a fluid flow in a three-dimensional computer-aided design (CAD) model of a simulation space include digitally simulating movement of one or more digital particles representing the fluid from one or more first voxels in a mesh to one or more second voxels in the mesh, performing one or more interaction operations on the one or more digital particles at the one or more second voxels to determine a distribution of the one or more digital particles. A first quantity represented by the distribution of the one or more digital particles is based on a temperature and a pressure at the one or more second voxels and a reference fluid density. A second quantity represented by the distribution of the one or more digital particles is based on the reference fluid density, velocities of the one or more digital particles, and a mean fluid velocity.