Lattice Boltzmann Fluid Simulation Using Tsallis Entropy
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Solution Overview
Problem
Conventional methods for simulating fluid flow, such as the Navier-Stokes and Boltzmann equations, face challenges in achieving efficient, accurate, and stable results, particularly when simulating fluid flows with high velocities or low viscosities, leading to unstable simulation outcomes.
Innovation Solution
The method employs Tsallis entropy and Rényi entropy to define a simulation space with lattices, determining space occupation and fluid states, and generates flow effects using collision rules that satisfy extremal values of Tsallis or Rényi divergence, ensuring stable and accurate fluid flow simulations across various conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional Navier-Stokes or Boltzmann equation methods are used to simulate fluid flow, then the simulation can be performed with standard equations, but the simulation becomes unstable when fluid velocity is high or viscosity is low
Solution Approach 1:
The patent changes the fundamental parameters of the simulation approach by switching from traditional Navier-Stokes or Boltzmann equations to a lattice Boltzmann method with Tsallis entropy. This parameter change in the mathematical framework allows the simulation to remain stable across a wider range of fluid conditions, particularly high velocity and low viscosity scenarios where conventional methods fail.
Solution Approach 2:
The patent substitutes the traditional mechanical continuum approach (Navier-Stokes) or standard kinetic theory (Boltzmann) with a statistical mechanics approach based on Tsallis entropy and lattice Boltzmann methods. This substitution replaces the conventional mechanical system with a statistical framework that better handles extreme flow conditions.
2Measurement precision
If conventional Boltzmann equation is used for fluid flow simulation, then the simulation can describe particle distribution, but it still lacks stability and accuracy for certain flow conditions
Solution Approach 1:
The patent modifies the Boltzmann equation approach by incorporating Tsallis entropy as the governing statistical measure instead of standard Boltzmann entropy. This parameter change in the entropy definition leads to improved accuracy in describing particle distribution while simultaneously enhancing simulation stability across various flow conditions.
3Productivity
If discrete lattice methods are used to simulate fluid flow, then the simulation can be computationally manageable, but achieving optimal parameter selection becomes difficult and may lead to simulation failure
Solution Approach 1:
The patent implements a self-service mechanism where the lattice Boltzmann method with Tsallis entropy automatically determines optimal simulation parameters through the inherent statistical mechanics framework. The method self-adjusts to maintain stability and accuracy without requiring extensive manual parameter tuning, thereby improving both computational efficiency and simulation success rate.
Data Source
AI summary
A method for optimally simulating fluid flow around a real object by (a) defining an initial state of a simulation space having a plurality of lattices with nodes; determining a space occupation state by objects, a fluid state, and a probability distribution state of a particle for respective nodes; generating a flow effect for the respective nodes using a collision rule which is a probability distribution of the particle with respect to the velocity thereof, obtained by satisfying a condition at which a Tsallis or a Rényi-divergence between the collision rule itself and a reference collision rule provides a simulated fluid flow result; and renewing the initial state and varying the space occupation state based on the simulated fluid flow result; and (b) based on step (a) modeling fluid flow around the real object.