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annotate src/SbpOperators/boundaryops/normal_derivative.jl @ 1656:89456aa6fa80 feature/sbp_operators/laplace_curvilinear

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Flesh out normal_derivative implementation some more.
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 27 Jun 2024 09:06:01 +0200
parents f4dc17cfafce
children 9c84e97de895
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1 """
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2 normal_derivative(g, stencil_set::StencilSet, boundary)
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3 normal_derivative(g::TensorGrid, stencil_set::StencilSet, boundary::TensorGridBoundary)
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4 normal_derivative(g::EquidistantGrid, stencil_set::StencilSet, boundary)
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5
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6 Creates the normal derivative boundary operator `d` as a `LazyTensor`
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7
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8 `d` computes the normal derivative at `boundary` of a grid function on `g` using the
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9 'd1' stencil in `stencil_set`. `d'` is the prolongation of the normal
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10 derivative of a grid function to the whole of `g` using the same stencil. On a
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11 one-dimensional grid, `d` is a `BoundaryOperator`. On a multi-dimensional
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12 grid, `d` is the inflation of a `BoundaryOperator`.
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14 See also: [`BoundaryOperator`](@ref), [`LazyTensors.inflate`](@ref).
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15 """
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16 function normal_derivative end
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18
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19 function normal_derivative(g::TensorGrid, stencil_set::StencilSet, boundary::TensorGridBoundary)
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20 op = normal_derivative(g.grids[grid_id(boundary)], stencil_set, boundary_id(boundary))
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21 return LazyTensors.inflate(op, size(g), grid_id(boundary))
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22 end
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23
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24 function normal_derivative(g::EquidistantGrid, stencil_set::StencilSet, boundary)
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25 closure_stencil = parse_stencil(stencil_set["d1"]["closure"])
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26 h_inv = inverse_spacing(g)
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28 scaled_stencil = scale(closure_stencil,h_inv)
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29 return BoundaryOperator(g, scaled_stencil, boundary)
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30 end
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32 function normal_derivative(g::MappedGrid, stencil_set::StencilSet, boundary)
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33 b_indices = boundary_indices(logicalgrid(g), boundary)
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34
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35 k = grid_id(boundary)
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38 # Compute the weights for the logival derivatives
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39 g⁻¹ = geometric_tensor_inverse(g)
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40 α = map(CartesianIndices(g⁻¹)[b_indices...]) do I # TODO: Fix iterator here
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41 gᵏⁱ = g⁻¹[I][k,:]
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42 gᵏᵏ = g⁻¹[I][k,k]
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43
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44 gᵏⁱ./sqrt(gᵏᵏ)
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45 end
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48 mapreduce(+,1:ndims(g)) do i
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49 if i == k
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50 ∂ξᵢ = normal_derivative(logicalgrid(g), stencil_set, boundary)
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51 else
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52 ∂ξᵢ = first_derivative(logicalgrid(g), stencil_set, i)
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53 end
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54
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55 αᵢ = componentview(α,i)
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56 DiagonalTensor(αᵢ) ∘ ∂ξᵢ
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57 end
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58 end