# CartesianGrids.jl

a framework for working with spatial fields discretized on or immersed in Cartesian grids

The purpose of this package is to enable easy setup of and operations on spatial fields on 2-d uniform staggered Cartesian grids. Tools are provided for

• Constructing field data that lie in the different finite-dimensional spaces of the grid: the centers, corners, and edges of the cells
• Performing discretely-mimetic differential calculus operations on these data, such as div, grad, curl, etc. These operations are carried out in a manner that transforms them between the spaces.
• Solving Poisson's equation on infinite grids using the lattice Green's function
• Immersing data on co-dimension one and two entities (points, curves) into the grid
• Performing operations on these co-dimension data.

Many of the core aspects of the fluid-body interaction are based on the immersed boundary projection method, developed by Taira and Colonius [1].

## Installation

This package works on Julia 1.0 and higher and is registered in the general Julia registry. To install, type

]add CartesianGrids

Then type

julia> using CartesianGrids

The plots in this documentation are generated using Plots.jl. You might want to install that, too, to follow the examples.

## References

• 1Taira, K. and Colonius, T. (2007) "The immersed boundary method: a projection approach," J. Comput. Phys., 225, 2118–2137.