Lattice Boltzmann Solver Total Energy Conservation
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Solution Overview
Problem
Current Lattice Boltzmann Method (LBM) solvers face challenges in conserving total energy and maintaining stability, especially in high-speed flows and complex boundary conditions, leading to inaccuracies in pressure convection and energy conservation.
Innovation Solution
The method involves simulating fluid flow using a LBM approach with a second distribution function for total energy, where specific total energy values are added to advected states and subtracted from non-advected states, ensuring energy conservation and stability by modifying state vectors and introducing a regularized collision operator for energy conservation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a single distribution function is used to solve mass, momentum and total energy, then the conservation of these quantities can be satisfied, but the lattice stencil size increases and more lattice velocities are required
Solution Approach 1:
The patent divides the single distribution function into two separate distribution functions: one for solving mass and momentum conservation, and another for solving total energy conservation. This segmentation allows each distribution function to use a smaller lattice stencil and fewer lattice velocities, reducing computational complexity while maintaining conservation properties.
Solution Approach 2:
The patent introduces an intermediary approach where the two distribution functions are coupled through a source term that ensures consistency between mass-momentum and energy conservation. This intermediary mechanism allows the separate functions to work together to achieve overall conservation without requiring a single complex distribution function.
2Productivity
If conventional LBM solvers are used, then computational efficiency is maintained, but total energy conservation and stability are compromised, especially in high-speed flows
Solution Approach 1:
The patent modifies the LBM formulation by changing the parameter representation from a single distribution function to two distribution functions with different lattice velocity sets. This parameter change enables the system to maintain computational efficiency while achieving better energy conservation and stability, particularly for high-speed flows where conventional solvers fail.
Solution Approach 2:
The patent introduces dynamic coupling between the two distribution functions through a source term that adjusts based on the flow conditions. This dynamic mechanism allows the solver to adapt to different flow regimes, maintaining stability and energy conservation in high-speed flows while preserving computational efficiency across various scenarios.
3Measurement precision
If the number of lattice velocities is increased to satisfy higher moment requirements, then conservation accuracy improves, but computational cost and stencil size increase
Solution Approach 1:
The patent segments the moment requirements between two distribution functions, allowing each function to use a smaller set of lattice velocities appropriate for its specific conservation role. This segmentation achieves the necessary conservation accuracy without requiring all particles to satisfy high-order moment requirements, thereby reducing computational cost.
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 enhances the stability range of the LBM solver, accurately conserving total energy and providing correct pressure gradients, even in high-speed flows and complex scenarios, improving the accuracy of fluid flow simulations.
Implementation Method 1
The advection process involves modeling movement of particles from one location to another according to the particles microscopic velocities
Implementation Method 2
The collision process involves interactions among particles obeying conservation laws
Data Source
AI summary
Techniques for simulating fluid flow using a lattice Boltzmann (LB) approach for solving scalar transport equations and solving for total energy are described. In addition to the lattice Boltzmann functions for fluid flow the techniques include modifying a set of state vectors of the particles by adding specific total energy to states of particles that will be advected and subtracting the specific total energy from states of particles that will not be advected over a time interval and performing advection of the particles according to the modified set of states.