LatticeBoltzmann.jl
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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