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annotate src/SbpOperators/volumeops/derivatives/dissipation.jl @ 1347:08f06bfacd5c refactor/grids

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Fix typos and formatting of documentation
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 18 May 2023 22:53:31 +0200
parents 760a4a1ec4b7
children
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1 """
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2 undivided_skewed04(g::TensorGrid, p, direction)
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3 undivided_skewed04(g::EquidistantGrid, p)
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4
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5 Undivided difference operators approximating the `p`th derivative. The
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6 operators do not satisfy any SBP property and are meant to be used for
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7 building artificial dissipation terms.
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8
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9 The operators and how they are used to create accurate artificial dissipation
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10 is described in "K. Mattsson, M. Svärd, and J. Nordström, “Stable and Accurate
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11 Artificial Dissipation,” Journal of Scientific Computing, vol. 21, no. 1, pp.
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12 57–79, Aug. 2004"
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13 """
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14 function undivided_skewed04 end
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15
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16 function undivided_skewed04(g::TensorGrid, p, direction)
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17 D,Dᵀ = undivided_skewed04(g.grids[direction], p)
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18 return (
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19 LazyTensors.inflate(D, size(g), direction),
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20 LazyTensors.inflate(Dᵀ, size(g), direction),
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21 )
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22 end
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23
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24 function undivided_skewed04(g::EquidistantGrid, p)
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25 T = eltype(g)
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26 interior_weights = T.(dissipation_interior_weights(p))
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27
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28 D = StencilOperatorDistinctClosures(
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29 g,
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30 dissipation_interior_stencil(interior_weights),
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31 dissipation_lower_closure_stencils(interior_weights),
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32 dissipation_upper_closure_stencils(interior_weights),
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33 )
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34 Dᵀ = StencilOperatorDistinctClosures(
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35 g,
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36 dissipation_transpose_interior_stencil(interior_weights),
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37 dissipation_transpose_lower_closure_stencils(interior_weights),
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38 dissipation_transpose_upper_closure_stencils(interior_weights),
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39 )
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40
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41 return D, Dᵀ
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42 end
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43
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44 function dissipation_interior_weights(p)
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45 if p == 0
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46 return (1,)
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47 end
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48
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49 return (0, dissipation_interior_weights(p-1)...) .- (dissipation_interior_weights(p-1)..., 0)
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50 end
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51
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52 midpoint(weights) = length(weights)÷2 + 1
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53 midpoint_transpose(weights) = length(weights)+1 - midpoint(weights)
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54
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55 function dissipation_interior_stencil(weights)
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56 return Stencil(weights..., center=midpoint(weights))
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57 end
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58 function dissipation_transpose_interior_stencil(weights)
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59 if iseven(length(weights))
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60 weights = map(-, weights)
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61 end
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62
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63 return Stencil(weights..., center=midpoint_transpose(weights))
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64 end
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65
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66 dissipation_lower_closure_size(weights) = midpoint(weights) - 1
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67 dissipation_upper_closure_size(weights) = length(weights) - midpoint(weights)
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68
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69 function dissipation_lower_closure_stencils(interior_weights)
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70 stencil(i) = Stencil(interior_weights..., center=i)
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71 return ntuple(i->stencil(i), dissipation_lower_closure_size(interior_weights))
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72 end
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73
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74 function dissipation_upper_closure_stencils(interior_weights)
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75 center(i) = length(interior_weights) - dissipation_upper_closure_size(interior_weights) + i
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76 stencil(i) = Stencil(interior_weights..., center=center(i))
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77 return ntuple(i->stencil(i), dissipation_upper_closure_size(interior_weights))
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78 end
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79
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80 function dissipation_transpose_lower_closure_stencils(interior_weights)
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81 closure = ntuple(i->dissipation_transpose_lower_closure_stencil(interior_weights, i), length(interior_weights))
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82
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83 N = maximum(s->length(s.weights), closure)
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84 return right_pad.(closure, N)
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85 end
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86
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87 function dissipation_transpose_upper_closure_stencils(interior_weights)
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88 closure = reverse(ntuple(i->dissipation_transpose_upper_closure_stencil(interior_weights, i), length(interior_weights)))
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89
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90 N = maximum(s->length(s.weights), closure)
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91 return left_pad.(closure, N)
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92 end
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93
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94
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95 function dissipation_transpose_lower_closure_stencil(interior_weights, i)
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96 w = ntuple(k->interior_weights[i], dissipation_lower_closure_size(interior_weights))
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97
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98 for k ∈ i:-1:1
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99 w = (w..., interior_weights[k])
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100 end
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101
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102 return Stencil(w..., center = i)
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103 end
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104
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105 function dissipation_transpose_upper_closure_stencil(interior_weights, i)
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106 j = length(interior_weights)+1-i
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107 w = ntuple(k->interior_weights[j], dissipation_upper_closure_size(interior_weights))
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108
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109 for k ∈ j:1:length(interior_weights)
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110 w = (interior_weights[k], w...)
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111 end
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112
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113 return Stencil(w..., center = length(interior_weights)-midpoint(interior_weights)+1)
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114 end