Lattice Boltzmann Entropy Solver for High Speed Flow Stability
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional Lattice Boltzmann methods face instability and inaccuracies in simulating high-speed flows due to the presence of second-order velocity terms, particularly at high Mach numbers, leading to numerical artifacts and mesh dependencies.
Innovation Solution
A Lattice Boltzmann entropy solver is developed, using an additional set of lattice vectors to represent specific entropy, which avoids second-order velocity terms by employing a regularized collision operator that only considers first-order non-equilibrium effects, stabilizing the simulation for high-speed applications.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional Lattice Boltzmann methods are used to simulate high-speed flows, then the simulation can be performed, but instability and inaccuracies occur due to second-order velocity terms at high Mach numbers
Solution Approach 1:
The patent extracts and removes the problematic second-order velocity terms from the collision operator by using a regularized collision operator that only includes first-order non-equilibrium effects. This extraction eliminates the source of instability while preserving the essential physics of the flow simulation.
Solution Approach 2:
The patent changes the mathematical structure of the collision operator by introducing a regularization parameter that controls the inclusion of higher-order terms. By adjusting this parameter to exclude second-order velocity terms, the method achieves stability at high Mach numbers while maintaining accuracy through controlled approximation.
2Adaptability or versatility
If second-order velocity terms are included in the collision operator, then more physical effects are captured, but numerical artifacts and mesh dependencies increase
Solution Approach 1:
The patent converts the potential harm of truncated expansions into a benefit by using the regularization technique to systematically control which terms are included. The regularized collision operator deliberately excludes problematic second-order terms while maintaining sufficient physical accuracy, turning a limitation into an advantage for high-speed flow simulations.
3Measurement precision
If the collision operator includes all non-equilibrium effects, then accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent applies partial action by including only the essential first-order non-equilibrium effects in the regularized collision operator, rather than all possible higher-order effects. This partial inclusion provides sufficient accuracy for high-speed flows while significantly reducing computational complexity and avoiding the numerical instability associated with complete expansions.
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
The solver provides stable and accurate transient results for high-speed flows with compressibility effects, enhancing stability and reducing numerical noise, especially in complex geometries and high temperature ratio scenarios.
Implementation Method 1
Instead of solving the Navier-Stokes equations, the discrete Boltzmann equation is solved to simulate the flow of a Newtonian fluid with collision models such as Bhatnagar-Gross-Krook (BGK). By simulating streaming and collision processes across a limited number of particles, the intrinsic particle interactions evince a microcosm of viscous flow behavior applicable across the greater mass.
Implementation Method 2
simulating a time evolution of entropy of the flow by collecting incoming set of distributions from neighboring mesh locations for the collision operation, calculating by the computer scalar values in each location, determining outgoing distributions as a product of the collision operation and addition of a heat source
Implementation Method 3
modifying the flow by the computer performing for a time interval, an advection of the particles to subsequent mesh locations
Implementation Method 4
calculating by the computer, the effect of heating by fluid viscosity and heating by fluid conduction
Implementation Method 5
calculating by the computer, the effect of heating by fluid viscosity and heating by fluid conduction
Implementation Method 6
calculating by the computer, the entropy diffusion and removing this from the additional heat source term
Data Source
AI summary
Techniques for simulating fluid flow on a computer that involve a stable entropy solver are described. The techniques include simulating activity of a fluid across a mesh, the activity of the fluid being simulated so as to model movement of particles across the mesh, storing, in a computer accessible memory, a set of state vectors for each mesh location in the mesh, each of the state vectors comprising a plurality of entries that correspond to particular momentum states of possible momentum states at a corresponding mesh location, simulating a time evolution of entropy of the flow by collecting incoming set of distributions from neighboring mesh locations for the collision operation, calculating by the computer scalar values in each location, determining outgoing distributions as a product of the collision operation and addition of a heat source, and modifying the flow by the computer performing for a time interval, an advection of the particles to subsequent mesh locations.