KitBase.jl

KitBase.jl serves as a lightweight module of physical formulations in Kinetic.jl ecosystem. The package is interested in theoretical and numerical studies of many-particle systems of gases, photons, plasmas, neutrons, etc. It employs the finite volume method (FVM) to conduct 1-3 dimensional numerical simulations on CPUs and GPUs. Any advection-diffusion-type equation can be solved within the framework. Special attentions have been paid on Hilbert's sixth problem, i.e. to build the numerical passage between kinetic theory of gases, e.g. the Boltzmann equation

$\frac{\partial f}{\partial t}+\mathbf{v} \cdot \nabla_{\mathbf{x}} f = \int_{\mathbb R^3} \int_{\mathcal S^2} \mathcal B(\cos \beta, |\mathbf{v}-\mathbf{v_*}|) \left[ f(\mathbf v')f(\mathbf v_*')-f(\mathbf v)f(\mathbf v_*)\right] d\mathbf \Omega d\mathbf v_*$

and continuum mechanics, e.g. the Euler and Navier-Stokes equations

$\frac{\partial \mathbf W}{\partial t} + \nabla_\mathbf x \cdot \mathbf F = \mathbf S$

A partial list of current supported models and equations include

linear Boltzmann equation
nonlinear Boltzmann equation
multi-component Boltzmann equations
Fokker-Planck-Landau equation
direct simulation Monte Carlo
advection-diffusion equation
Burgers equation
Euler equations
Navier-Stokes equations
Extended hydrodynamical equations from gas kinetic expansion
Magnetohydrodynamical equations
Maxwell's equations

Documentation

For the detailed information on the implementation and usage of the package, please check the documentation.

Contributing

If you have further questions regarding KitBase.jl or have got an idea on improving it, please feel free to get in touch. Open an issue or pull request if you'd like to work on a new feature or even if you're new to open-source and want to find a cool little project or issue to work on that fits your interests. We're more than happy to help along the way.