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view docs/src/grids_and_grid_functions.md @ 1996:d89f7a1a6f37 feature/grids/manifolds
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author | Jonatan Werpers <jonatan@werpers.com> |
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date | Wed, 23 Apr 2025 09:02:20 +0200 |
parents | ee3fc2d83c73 |
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# Grids and grid functions The submodule `Grids` aims to provide types and logic for all types of grids that are useful for implementing summation-by-parts difference methods. It provides an abstract top level type `Grid` which defines a broad interface for how a general grid is supposed to work. Currently only equidistant grids are supported, but the basic structure supports implementations of curvilinear grids, multi-block grids, periodic grids and much more. The module also has functionality for creating and working with grid functions. ## Interface for grids All grids are expected to work as a grid function for the coordinate function, and thus implements Julia's Indexing- and Iteration-interfaces. Notably they are *not* abstract arrays because that inteface is too restrictive for the types of grids we wish to implement. ## Plotting Plotting of grids and grid functions is supported through a package extension with Makie.jl. For grids we have: * `plot(::Grid{<:Any,2})` (same as `lines`) * `lines(::Grid{<:Any,2})` * `scatter(::Grid{<:Any,2})` For 1D grid functions we have: * `plot(::Grid{<:Any,1}, ::AbstractVector)` (same as `lines`) * `lines(::Grid{<:Any,1}, ::AbstractVector)` * `scatter(::Grid{<:Any,1}, ::AbstractVector)` For 2D grid functions we have: * `plot(::Grid{<:Any,2}, ::AbstractArray{<:Any,2})` (constructs a 2d mesh) * `surface(::Grid{<:Any,2}, ::AbstractArray{<:Any,2})` ## To write about <!-- # TODO: --> * Grid functions * Basic structure * Indexing * Curvilinear * Multiblock * Vector valued grid functions