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annotate src/SbpOperators/volumeops/derivatives/second_derivative.jl @ 1135:05b1d6fd6401 feature/boundary_conditions

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Add functions for constructing SATs
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Tue, 11 Oct 2022 18:15:47 +0200
parents 7fc8df5157a7
children 157a78959e5d
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1 """
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2 second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction)
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4 Creates the second-derivative operator `D2` as a `LazyTensor`
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6 `D2` approximates the second-derivative d²/dξ² on `grid` along the coordinate dimension specified by
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7 `direction`, using the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
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8 for the points in the closure regions.
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10 On a one-dimensional `grid`, `D2` is a `VolumeOperator`. On a multi-dimensional `grid`, `D2` is the outer product of the
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11 one-dimensional operator with the `IdentityTensor`s in orthogonal coordinate dirrections.
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13 See also: [`volume_operator`](@ref).
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14 """
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15 function second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction)
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16 h_inv = inverse_spacing(grid)[direction]
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17 return SbpOperators.volume_operator(grid, scale(inner_stencil,h_inv^2), scale.(closure_stencils,h_inv^2), even, direction)
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18 end
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21 """
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22 second_derivative(grid, inner_stencil, closure_stencils)
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24 Creates a `second_derivative` operator on a 1D `grid` given `inner_stencil` and `closure_stencils`.
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25 """
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26 second_derivative(grid::EquidistantGrid{1}, inner_stencil::Stencil, closure_stencils) = second_derivative(grid, inner_stencil, closure_stencils,1)
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29 """
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30 second_derivative(grid, stencil_set, direction)
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32 Creates a `second_derivative` operator on `grid` along coordinate dimension `direction` given a `stencil_set`.
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33 """
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34 function second_derivative(grid::EquidistantGrid, stencil_set::StencilSet, direction)
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35 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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36 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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37 second_derivative(grid,inner_stencil,closure_stencils,direction);
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38 end
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41 """
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42 second_derivative(grid, stencil_set)
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44 Creates a `second_derivative` operator on a 1D `grid` given a `stencil_set`.
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45 """
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46 second_derivative(grid::EquidistantGrid{1}, stencil_set::StencilSet) = second_derivative(grid, stencil_set, 1)