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annotate src/SbpOperators/volumeops/derivatives/dissipation.jl @ 1326:e352630a0309 refactor/grids

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Fix a bunch of typos
author Jonatan Werpers <jonatan@werpers.com>
date Sun, 30 Apr 2023 22:33:13 +0200
parents 356ec6a72974
children e94ddef5e72f
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1 """
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2 undivided_skewed04(g::EquidistantGrid, p, direction)
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3
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4 Create undivided difference operators approximating the `p`th derivative. The
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5 operators do not satisfy any SBP-property and are meant to be used for
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6 building artificial dissipation terms.
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7
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8 The operators and how they are used to create accurate artifical dissipation
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9 is described in "K. Mattsson, M. Svärd, and J. Nordström, “Stable and Accurate
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10 Artificial Dissipation,” Journal of Scientific Computing, vol. 21, no. 1, pp.
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11 57–79, Aug. 2004"
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12 """
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13 function undivided_skewed04(g::TensorGrid, p, direction)
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14 op = undivided_skewed04(g.grids[direction], p)
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15 return LazyTensors.inflate(op, size(g), direction)
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16 end
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17
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18 function undivided_skewed04(g::EquidistantGrid, p)
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19 T = eltype(g)
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20 interior_weights = T.(dissipation_interior_weights(p))
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21
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22 D = StencilOperatorDistinctClosures(
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23 g,
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24 dissipation_interior_stencil(interior_weights),
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25 dissipation_lower_closure_stencils(interior_weights),
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26 dissipation_upper_closure_stencils(interior_weights),
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27 )
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28 Dᵀ = StencilOperatorDistinctClosures(
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29 g,
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30 dissipation_transpose_interior_stencil(interior_weights),
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31 dissipation_transpose_lower_closure_stencils(interior_weights),
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32 dissipation_transpose_upper_closure_stencils(interior_weights),
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33 )
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34
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35 return D, Dᵀ
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36 end
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37
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38 function dissipation_interior_weights(p)
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39 if p == 0
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40 return (1,)
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41 end
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42
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43 return (0, dissipation_interior_weights(p-1)...) .- (dissipation_interior_weights(p-1)..., 0)
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44 end
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45
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46 midpoint(weights) = length(weights)÷2 + 1
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47 midpoint_transpose(weights) = length(weights)+1 - midpoint(weights)
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48
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49 function dissipation_interior_stencil(weights)
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50 return Stencil(weights..., center=midpoint(weights))
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51 end
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52 function dissipation_transpose_interior_stencil(weights)
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53 if iseven(length(weights))
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54 weights = map(-, weights)
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55 end
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56
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57 return Stencil(weights..., center=midpoint_transpose(weights))
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58 end
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59
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60 dissipation_lower_closure_size(weights) = midpoint(weights) - 1
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61 dissipation_upper_closure_size(weights) = length(weights) - midpoint(weights)
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62
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63 function dissipation_lower_closure_stencils(interior_weights)
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64 stencil(i) = Stencil(interior_weights..., center=i)
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65 return ntuple(i->stencil(i), dissipation_lower_closure_size(interior_weights))
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66 end
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67
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68 function dissipation_upper_closure_stencils(interior_weights)
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69 center(i) = length(interior_weights) - dissipation_upper_closure_size(interior_weights) + i
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70 stencil(i) = Stencil(interior_weights..., center=center(i))
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71 return ntuple(i->stencil(i), dissipation_upper_closure_size(interior_weights))
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72 end
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73
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74 function dissipation_transpose_lower_closure_stencils(interior_weights)
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75 closure = ntuple(i->dissipation_transpose_lower_closure_stencil(interior_weights, i), length(interior_weights))
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76
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77 N = maximum(s->length(s.weights), closure)
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78 return right_pad.(closure, N)
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79 end
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80
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81 function dissipation_transpose_upper_closure_stencils(interior_weights)
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82 closure = reverse(ntuple(i->dissipation_transpose_upper_closure_stencil(interior_weights, i), length(interior_weights)))
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83
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84 N = maximum(s->length(s.weights), closure)
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85 return left_pad.(closure, N)
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86 end
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87
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88
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89 function dissipation_transpose_lower_closure_stencil(interior_weights, i)
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90 w = ntuple(k->interior_weights[i], dissipation_lower_closure_size(interior_weights))
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91
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92 for k ∈ i:-1:1
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93 w = (w..., interior_weights[k])
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94 end
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95
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96 return Stencil(w..., center = i)
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97 end
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98
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99 function dissipation_transpose_upper_closure_stencil(interior_weights, i)
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100 j = length(interior_weights)+1-i
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101 w = ntuple(k->interior_weights[j], dissipation_upper_closure_size(interior_weights))
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102
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103 for k ∈ j:1:length(interior_weights)
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104 w = (interior_weights[k], w...)
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105 end
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106
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107 return Stencil(w..., center = length(interior_weights)-midpoint(interior_weights)+1)
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108 end