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annotate src/SbpOperators/volumeops/derivatives/dissipation.jl @ 1034:ed19c549c506 feature/dissipation_operators

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Implement undevided dissipation operators
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 22 Mar 2022 12:33:58 +0100
parents 0cb4c6b15d8e
children ceda69b8f27a
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1034
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1 function undevided_dissipation(g::EquidistantGrid, p, direction)
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2 T = eltype(g)
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3 interior_weights = T.(dissipation_interior_weights(p))
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4
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5 D = stencil_operator_distinct_closures(
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6 g,
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7 dissipation_interior_stencil(interior_weights),
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8 dissipation_lower_closure_stencils(interior_weights),
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9 dissipation_upper_closure_stencils(interior_weights),
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10 direction,
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11 )
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12 Dᵀ = stencil_operator_distinct_closures(
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13 g,
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14 dissipation_transpose_interior_stencil(interior_weights),
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15 dissipation_transpose_lower_closure_stencils(interior_weights),
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16 dissipation_transpose_upper_closure_stencils(interior_weights),
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17 direction,
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18 )
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19
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20 return D, Dᵀ
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21 end
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22
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23 undevided_dissipation(g::EquidistantGrid{1}, p) = undevided_dissipation(g, p, 1)
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24
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25 function dissipation_interior_weights(p)
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26 if p == 0
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27 return (1,)
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28 end
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29
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30 return (0, dissipation_interior_weights(p-1)...) .- (dissipation_interior_weights(p-1)..., 0)
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31 end
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32
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33 midpoint(weights) = length(weights)÷2 + 1
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34 midpoint_transpose(weights) = length(weights)+1 - midpoint(weights)
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35
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36 dissipation_interior_stencil(weights) = Stencil(weights..., center=midpoint(weights))
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37 dissipation_transpose_interior_stencil(weights) = Stencil(weights..., center=midpoint_transpose(weights))
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38
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39 dissipation_lower_closure_size(weights) = midpoint(weights) - 1
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40 dissipation_upper_closure_size(weights) = length(weights) - midpoint(weights)
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41
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42 dissipation_lower_closure_stencils(interior_weights) = ntuple(i->Stencil(interior_weights..., center=i ), dissipation_lower_closure_size(interior_weights))
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43 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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44
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45 function dissipation_transpose_lower_closure_stencils(interior_weights)
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46 closure = ntuple(i->dissipation_transpose_lower_closure_stencil(interior_weights, i), length(interior_weights))
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47
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48 N = maximum(s->length(s.weights), closure)
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49 return right_pad.(closure, N)
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50 end
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51
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52 function dissipation_transpose_upper_closure_stencils(interior_weights)
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53 closure = reverse(ntuple(i->dissipation_transpose_upper_closure_stencil(interior_weights, i), length(interior_weights)))
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54
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55 N = maximum(s->length(s.weights), closure)
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56 return left_pad.(closure, N)
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57 end
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58
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59
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60 function dissipation_transpose_lower_closure_stencil(interior_weights, i)
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61 w = ntuple(k->interior_weights[i], dissipation_lower_closure_size(interior_weights))
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62
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63 for k ∈ i:-1:1
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64 w = (w..., interior_weights[k])
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65 end
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66
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67 return Stencil(w..., center = i)
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68 end
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69
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70 function dissipation_transpose_upper_closure_stencil(interior_weights, i)
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71 j = length(interior_weights)+1-i
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72 w = ntuple(k->interior_weights[j], dissipation_upper_closure_size(interior_weights))
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73
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74 for k ∈ j:1:length(interior_weights)
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75 w = (interior_weights[k], w...)
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76 end
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77
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78 return Stencil(w..., center = length(interior_weights)-midpoint(interior_weights)+1)
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79 end