Thermodynamic Step Segmentation in Lattice Boltzmann Method
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Solution Overview
Problem
Current computational fluid dynamics methods, such as those using the Navier-Stokes equations, face challenges in efficiently simulating high Mach and high temperature fluid flows due to limitations in temperature coupling and stability, particularly in the Lattice Boltzmann Method (LBM), which restricts its applicability to low temperature and low Mach number applications.
Innovation Solution
Introducing a thermodynamic step that is separate and independent from the particle collision step in the LBM, allowing for temperature coupling during the advection process, which modifies the distribution function to include temperature variations and maintains stability across a wide range of temperatures and Mach numbers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If temperature coupling is integrated into the particle collision step in LBM, then the method can simulate thermal flows, but the stability and accuracy deteriorate at high temperatures and high Mach numbers
Solution Approach 1:
The patent segments the temperature coupling from the particle collision step and places it in the advection step. The distribution function evolution is divided into separate collision and advection processes, with temperature effects applied during advection rather than collision. This segmentation resolves the contradiction by allowing thermal effects to be incorporated without compromising collision-based stability.
Solution Approach 2:
The patent introduces an intermediary thermodynamic step that mediates between the particle collision process and the final distribution function. This intermediate step applies temperature coupling through a correction term that bridges the isothermal collision process and the thermal advection process, enabling high-temperature simulation stability.
2Ease of manufacture
If traditional temperature coupling methods are used in LBM, then the implementation is simple, but the method is restricted to low temperature and low Mach number applications
Solution Approach 1:
The patent makes the temperature coupling dynamic by applying it during the advection step where velocity and temperature variations are naturally handled. The thermodynamic correction term adapts to local flow conditions during advection, enabling the method to handle varying Mach numbers and temperatures while maintaining implementation feasibility through systematic modification of the standard LBM algorithm.
3Temperature
If the thermodynamic step is coupled with the particle collision step, then temperature effects are included, but the isotropic nature of the solver is compromised
Solution Approach 1:
By segmenting the thermodynamic step from the collision process and placing it in the advection step, the patent preserves the isotropic collision operator while introducing temperature effects through the advection correction. The collision step remains purely isotropic, and the anisotropic temperature effects are applied separately during advection, resolving the contradiction between temperature coupling and isotropy preservation.
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 the LBM to simulate high Mach and high temperature range applications with improved stability and accuracy, maintaining the isotropic nature of the solver and ensuring mass, momentum, and energy conservation, while avoiding the limitations of traditional temperature coupling methods.
Implementation Method 1
simulating an advection of the portion of the particles to the other location in the volume of fluid at a time t+Δt
Implementation Method 2
transport of particles in a volume of fluid, with the transport causing collision among the particles
Implementation Method 3
ensuring mass, momentum, and energy conservation
Implementation Method 4
ensuring mass, momentum, and energy conservation
Data Source
AI summary
A method includes simulating, in a lattice velocity set, transport of particles in a volume of fluid, with the transport causing collision among the particles; and generating a distribution function for transport of the particles, wherein the distribution function comprises a thermodynamic step and a particle collision step, and wherein the thermodynamic step is substantially independent of and separate from the particle collision step.