LatticeBoltzmann.jl

Build Status	Documentation

This package was developed for my thesis A Theoretical & Practical Framework for Lattice Boltzmann Models. Currently the documentation is a work in progress.

The notebooks contain reproducible examples of results that I've used in my thesis. I've focused on four problems:

• Shear wave decay: shows we solve initial value problems and can obtain steady state solutions with quadratic convergence.
• Taylor Green Vortex: Shows we can obtain quadratic convergence for the velocity and stress components. It also shows the effect the initialization strategy of a Lattice Boltzmann Method can have on its accuracy (in particular it shows that having an inconsistent pressure can lead to larger errors).
• Couette flow: Shows that the D2Q9 quadrature can find an exact solution of the Couette flow. The other quadratures are only second or first order accurate due to an inexact boundary condition.
• Poiseuille: shows how we can find a solution to the 2D poiseuille flow and how its accuracy depends on the relaxation time.

Quadratures

• D2Q4
• D2Q5
• D2Q9
• D2Q13
• D2Q17
• D2Q21
• D2Q37

Collision models

• SRT (+ Force)
• TRT (+ Force)
• Regularized (projected) MRT (slow) (+ Force)

Initial conditions

• Velocity (equilibrium w. constant density)
• Velocity + stress (offequilibrium)
• Velocity + pressure (analytical equilibrium)
• Velocity + pressure + stress (analytical equilibrium + offequilibrium)
• Iterative (Mei et al)

Boundary conditions

• Periodic (default)
• Bounce back
• Moving wall

Test problems

• Shear wave (decay / steady state)
• Taylor Green Vortex (decay / steady state)
• Couette
• Poiseuille

TODO

Project

• Add documentation & doctests
• Improve code coverage
• Try mutation testing

Features

• Add abstraction for simulation parameters (Δx, Δy, Re)
• Double Distribution Functions for temperature
• Double Distribution Functions for multicomponent and multiphase flows
• Improve plotting and process managers (the ugly code)
• Allow using different equilibrium functions
• Implement 1D and 3D features

Boundary conditions

Boundary conditions should be rewritten so that they can be applied to a node at a location not necessarily at the boundary, so that we can have second order bounce back boundary conditions.

• Pressure difference
• Temperature
• Multispeed boundary conditions

Performance / infrastructure

• Improve benchmarks
• Refactor to use StaticArrays
• Refactor collision models to use kernel methods (will make it easier to allow distributed computing)
• Add instructions for Docker and Singularity