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annotate src/SbpOperators/volumeops/derivatives/dissipation.jl @ 1203:254934aac3f8 feature/dissipation_operators

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Change name and clarify docs
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 03 Feb 2023 10:05:52 +0100
parents 9f0121e465a5
children 99df343c7f61
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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 operator do not satisfy any SBP-property and are meant to be used for
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5 building artificial dissipation terms.
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6
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7 The operators and how they are used to create accurate artifical dissipation is described in
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8 "K. Mattsson, M. Svärd, and J. Nordström, “Stable and Accurate Artificial Dissipation,” Journal of Scientific Computing, vol. 21, no. 1, pp. 57–79, Aug. 2004"
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9 """
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10 function undivided_skewed04(g::EquidistantGrid, p, direction)
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11 T = eltype(g)
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12 interior_weights = T.(dissipation_interior_weights(p))
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13
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14 D = stencil_operator_distinct_closures(
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15 g,
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16 dissipation_interior_stencil(interior_weights),
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17 dissipation_lower_closure_stencils(interior_weights),
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18 dissipation_upper_closure_stencils(interior_weights),
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19 direction,
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20 )
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21 Dᵀ = stencil_operator_distinct_closures(
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22 g,
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23 dissipation_transpose_interior_stencil(interior_weights),
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24 dissipation_transpose_lower_closure_stencils(interior_weights),
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25 dissipation_transpose_upper_closure_stencils(interior_weights),
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26 direction,
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27 )
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28
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29 return D, Dᵀ
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30 end
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31
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32 undivided_skewed04(g::EquidistantGrid{1}, p) = undivided_skewed04(g, p, 1)
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33
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34 function dissipation_interior_weights(p)
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35 if p == 0
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36 return (1,)
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37 end
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38
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39 return (0, dissipation_interior_weights(p-1)...) .- (dissipation_interior_weights(p-1)..., 0)
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40 end
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41
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42 midpoint(weights) = length(weights)÷2 + 1
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43 midpoint_transpose(weights) = length(weights)+1 - midpoint(weights)
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44
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45 function dissipation_interior_stencil(weights)
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46 return Stencil(weights..., center=midpoint(weights))
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47 end
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48 function dissipation_transpose_interior_stencil(weights)
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49 if iseven(length(weights))
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50 weights = map(-, weights)
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51 end
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52
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53 return Stencil(weights..., center=midpoint_transpose(weights))
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54 end
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55
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56 dissipation_lower_closure_size(weights) = midpoint(weights) - 1
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57 dissipation_upper_closure_size(weights) = length(weights) - midpoint(weights)
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58
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59 dissipation_lower_closure_stencils(interior_weights) = ntuple(i->Stencil(interior_weights..., center=i ), dissipation_lower_closure_size(interior_weights))
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60 dissipation_upper_closure_stencils(interior_weights) = ntuple(i->Stencil(interior_weights..., center=length(interior_weights)-dissipation_upper_closure_size(interior_weights)+i), dissipation_upper_closure_size(interior_weights))
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61
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62 function dissipation_transpose_lower_closure_stencils(interior_weights)
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63 closure = ntuple(i->dissipation_transpose_lower_closure_stencil(interior_weights, i), length(interior_weights))
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64
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65 N = maximum(s->length(s.weights), closure)
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66 return right_pad.(closure, N)
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67 end
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68
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69 function dissipation_transpose_upper_closure_stencils(interior_weights)
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70 closure = reverse(ntuple(i->dissipation_transpose_upper_closure_stencil(interior_weights, i), length(interior_weights)))
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71
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72 N = maximum(s->length(s.weights), closure)
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73 return left_pad.(closure, N)
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74 end
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75
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76
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77 function dissipation_transpose_lower_closure_stencil(interior_weights, i)
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78 w = ntuple(k->interior_weights[i], dissipation_lower_closure_size(interior_weights))
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79
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80 for k ∈ i:-1:1
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81 w = (w..., interior_weights[k])
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82 end
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83
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84 return Stencil(w..., center = i)
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85 end
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86
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87 function dissipation_transpose_upper_closure_stencil(interior_weights, i)
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88 j = length(interior_weights)+1-i
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89 w = ntuple(k->interior_weights[j], dissipation_upper_closure_size(interior_weights))
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90
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91 for k ∈ j:1:length(interior_weights)
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92 w = (interior_weights[k], w...)
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93 end
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94
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95 return Stencil(w..., center = length(interior_weights)-midpoint(interior_weights)+1)
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96 end