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Merge pull request #288 from FourierFlows/ncc/docs-typo
Fixes in Docs
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Project.toml

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@@ -6,7 +6,7 @@ authors = ["Gregory L. Wagner <wagner.greg@gmail.com>", "Navid C. Constantinou <
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description = "Tools for building fast, hackable, pseudospectral partial differential equation solvers on periodic domains."
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documentation = "https://fourierflows.github.io/FourierFlowsDocumentation/stable/"
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repository = "https://github.com/FourierFlows/FourierFlows.jl"
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version = "0.7.0"
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version = "0.7.1"
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[deps]
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CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"

README.md

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@@ -102,7 +102,7 @@ and [Navid C. Constantinou][] (@navidcy).
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The code is citable via [zenodo](https://zenodo.org). Please cite as:
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> Navid C. Constantinou & Gregory L. Wagner. (2021). FourierFlows/FourierFlows.jl: FourierFlows v0.6.19 (Version v0.6.19). Zenodo. [http://doi.org/10.5281/zenodo.1161724](http://doi.org/10.5281/zenodo.1161724)
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> Navid C. Constantinou & Gregory L. Wagner. (2021). FourierFlows/FourierFlows.jl: FourierFlows v0.7.1 (Version v0.7.1). Zenodo. [http://doi.org/10.5281/zenodo.1161724](http://doi.org/10.5281/zenodo.1161724)
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docs/src/aliasing.md

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@@ -58,26 +58,26 @@ beyond what our grid can resolve anyway. In FourierFlows.jl, the former dealiasi
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implemented.
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!!! info "De-aliasing scheme"
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FourierFlows.jl curently implement dealiasing by zeroing out the top-`aliased_fraction`
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FourierFlows.jl curently implements dealiasing by zeroing out the highest-`aliased_fraction`
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wavenumber components on a `grid`.
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The number of wavenumber components that we need to zero-out to be sure the no aliasing errors
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infiltrate our solution depends on the order of the nonlinearities. For example, for quadratic
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nonlinearities, one expects that we need to discard the top-1/2 of the wavenumber components.
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nonlinearities, one expects that we need to discard the highest-1/2 of the wavenumber components.
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This way, when computing the product of two fields we won't have anything that projects onto
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harmonics with wavenumbers beyond those that our grid is able to resolve and, therefore, no
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aliasing errors.
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The above-mentioned 1/2-rule for dealiasing for quadratic nonlinearities is, however, not the
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most efficient. Orszag (1972) pointed out that for quadratic nonlirearities, simply only discarding
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the top-1/3 of wavenumber components is enough to save us from aliasing errors. To be fair,
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the highest-1/3 of wavenumber components is enough to save us from aliasing errors. To be fair,
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with Orszag's so-called 2/3-rule for dealiasing, still some aliasing errors occur, but those
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errors only occur to the higher-1/3 wavenumber components that will be zero-ed out next time
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we dealias our solution anyway.
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When constructing a `grid` we can specify the `aliased_fraction` parameter. By default, this is
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set to ``1/3``, appropriate for quadratic nonlinearities. Then `dealias!(fh, grid)` will zero-out
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the top-`aliased_fraction` wavenumber components of `fh`.
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the highest-`aliased_fraction` wavenumber components of `fh`.
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If we construct a grid with `aliased_fraction=0`, e.g.,
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docs/src/grids.md

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├── grid spacing dx: 0.09817477042468103
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├─────────── domain: x ∈ [-3.141592653589793, 3.0434178831651124]
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└─ aliased fraction: 0.3333333333333333
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```
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The grid domain is, by default, constructed symmetrically around ``x = 0``, but this
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can be altered using the `x0` keyword argument of `OneDGrid` constructor. The grid
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spacing is ``L_x / n_x``. Note that the last point of the domain is a grid-spacing
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before ``L_x / 2``. This is because periodicity implies that the values of any field
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at the end-points of the domain are equal and, therefore, grid-point values at
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both these end-points are reduntant.
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```
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The grid domain is, by default, constructed symmetrically around ``x = 0``, but this can be
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altered using the `x0` keyword argument of the `OneDGrid` constructor. The grid spacing
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is ``L_x / n_x``. Note that the last point of the domain is a grid-spacing before ``L_x / 2``.
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This is because periodicity implies that the values of any field at the end-points of the
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domain are equal and, therefore, grid-point values at both these end-points are reduntant.
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We can define an array `u` that contains the values of a function ``u(x)`` on this
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grid as

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