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annotate src/Grids/mapped_grid.jl @ 1736:863385aae454 feature/grids/curvilinear

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author Jonatan Werpers <jonatan@werpers.com>
date Tue, 10 Sep 2024 21:59:10 +0200
parents 11640aa3e348
children 248304f88e49
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1 struct MappedGrid{T,D, GT<:Grid{<:Any,D}, CT<:AbstractArray{T,D}, JT<:AbstractArray{<:AbstractArray{<:Any, 2}, D}} <: Grid{T,D}
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2 logicalgrid::GT
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3 physicalcoordinates::CT
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4 jacobian::JT
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5 end
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6
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7 function Base.:(==)(a::MappedGrid, b::MappedGrid)
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8 same_logicalgrid = logicalgrid(a) == logicalgrid(b)
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9 same_coordinates = collect(a) == collect(b)
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10 same_jacobian = jacobian(a) == jacobian(b)
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11
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12 return same_logicalgrid && same_coordinates && same_jacobian
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13 end
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14
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15 jacobian(g::MappedGrid) = g.jacobian
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16 logicalgrid(g::MappedGrid) = g.logicalgrid
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17
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18
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19 # Indexing interface
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20 Base.getindex(g::MappedGrid, I::Vararg{Int}) = g.physicalcoordinates[I...]
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21 Base.eachindex(g::MappedGrid) = eachindex(g.logicalgrid)
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22
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23 Base.firstindex(g::MappedGrid, d) = firstindex(g.logicalgrid, d)
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24 Base.lastindex(g::MappedGrid, d) = lastindex(g.logicalgrid, d)
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25
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26 # Iteration interface
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27 Base.iterate(g::MappedGrid) = iterate(g.physicalcoordinates)
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28 Base.iterate(g::MappedGrid, state) = iterate(g.physicalcoordinates, state)
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29
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30 Base.IteratorSize(::Type{<:MappedGrid{<:Any, D}}) where D = Base.HasShape{D}()
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31 Base.length(g::MappedGrid) = length(g.logicalgrid)
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32 Base.size(g::MappedGrid) = size(g.logicalgrid)
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33 Base.size(g::MappedGrid, d) = size(g.logicalgrid, d)
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34
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35 boundary_identifiers(g::MappedGrid) = boundary_identifiers(g.logicalgrid)
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36 boundary_indices(g::MappedGrid, id::TensorGridBoundary) = boundary_indices(g.logicalgrid, id)
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37
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38 function boundary_grid(g::MappedGrid, id::TensorGridBoundary)
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39 b_indices = boundary_indices(g.logicalgrid, id)
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40
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41 # Calculate indices of needed jacobian components
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42 D = ndims(g)
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43 all_indices = SVector{D}(1:D)
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44 free_variable_indices = deleteat(all_indices, grid_id(id))
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45 jacobian_components = (:, free_variable_indices)
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46
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47 # Create grid function for boundary grid jacobian
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48 boundary_jacobian = componentview((@view g.jacobian[b_indices...]) , jacobian_components...)
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49 boundary_physicalcoordinates = @view g.physicalcoordinates[b_indices...]
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50
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51 return MappedGrid(
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52 boundary_grid(g.logicalgrid, id),
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53 boundary_physicalcoordinates,
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54 boundary_jacobian,
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55 )
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56 end
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57
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58 # TBD: refine and coarsen could be implemented once we have a simple manifold implementation.
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59 # Before we do, we should consider the overhead of including such a field in the mapped grid struct.
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60
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61 function mapped_grid(x, J, size::Vararg{Int})
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62 D = length(size)
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63 lg = equidistant_grid(ntuple(i->0., D), ntuple(i->1., D), size...)
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64 return mapped_grid(lg, x, J)
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65 end
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66
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67 function mapped_grid(lg::Grid, x, J)
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68 return MappedGrid(
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69 lg,
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70 map(x,lg),
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71 map(J,lg),
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72 )
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73 end
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74
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75 function jacobian_determinant(g::MappedGrid)
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76 return map(jacobian(g)) do ∂x∂ξ
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77 det(∂x∂ξ)
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78 end
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79 end
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80
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81 function metric_tensor(g::MappedGrid)
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82 return map(jacobian(g)) do ∂x∂ξ
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83 ∂x∂ξ'*∂x∂ξ
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84 end
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85 end
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86
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87 function metric_tensor_inverse(g::MappedGrid)
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88 return map(jacobian(g)) do ∂x∂ξ
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89 inv(∂x∂ξ'*∂x∂ξ)
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90 end
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91 end
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92
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93 function min_spacing(g::MappedGrid{T,1} where T)
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94 n, = size(g)
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95
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96 ms = Inf
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97 for i ∈ 1:n-1
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98 ms = min(ms, norm(g[i+1]-g[i]))
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99 end
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100
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101 return ms
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102 end
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103
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104 function min_spacing(g::MappedGrid{T,2} where T)
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105 n, m = size(g)
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106
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107 ms = Inf
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108 for i ∈ 1:n-1, j ∈ 1:m-1 # loop over each cell of the grid
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109
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110 ms = min(
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111 ms,
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112 norm(g[i+1,j]-g[i,j]),
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113 norm(g[i,j+1]-g[i,j]),
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114
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115 norm(g[i+1,j]-g[i+1,j+1]),
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116 norm(g[i,j+1]-g[i+1,j+1]),
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117
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118 norm(g[i+1,j+1]-g[i,j]),
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119 norm(g[i+1,j]-g[i,j+1]),
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120 )
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121 # NOTE: This could be optimized to avoid checking all interior edges twice.
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122 end
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123
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124 return ms
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125 end
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126
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127 """
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128 normal(g::MappedGrid, boundary)
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129
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130 The outward pointing normal as a grid function on the boundary
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131 """
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132 function normal(g::MappedGrid, boundary)
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133 b_indices = boundary_indices(g, boundary)
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134 σ =_boundary_sign(component_type(g), boundary)
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135 return map(jacobian(g)[b_indices...]) do ∂x∂ξ
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136 ∂ξ∂x = inv(∂x∂ξ)
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137 k = grid_id(boundary)
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138 σ*∂ξ∂x[k,:]/norm(∂ξ∂x[k,:])
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139 end
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140 end
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141
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142 function _boundary_sign(T, boundary)
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143 if boundary_id(boundary) == UpperBoundary()
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144 return one(T)
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145 elseif boundary_id(boundary) == LowerBoundary()
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146 return -one(T)
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147 else
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148 throw(ArgumentError("The boundary identifier must be either `LowerBoundary()` or `UpperBoundary()`"))
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149 end
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150 end