Line data Source code
1 0 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : #pragma once
5 :
6 : #include <array>
7 : #include <cstddef>
8 : #include <optional>
9 :
10 : #include "DataStructures/Tensor/TypeAliases.hpp"
11 :
12 : /// \cond
13 : namespace PUP {
14 : class er;
15 : } // namespace PUP
16 : /// \endcond
17 :
18 : namespace domain::CoordinateMaps {
19 :
20 : /*!
21 : * \ingroup CoordinateMapsGroup
22 : *
23 : * \brief Maps a cylindrical shell block to a region bounded by an inner
24 : * right cylinder and an outer spherical surface.
25 : *
26 : * \image html CylindricalSphericalShell.png "The shaded region is the image."
27 : *
28 : * \details The logical coordinates are:
29 : * - radial \f$\xi \in [-1,1]\f$: interpolates between the inner right
30 : * cylinder and the outer sphere.
31 : * - angular \f$\eta \in (-\pi, \pi]\f$: azimuthal angle \f$\phi\f$ (S1
32 : * periodic direction). The inverse map returns
33 : * \f$\eta = \mathrm{atan2}(z, y)\f$, which lies in \f$(-\pi, \pi]\f$.
34 : * - axial \f$\zeta \in [-1,1]\f$: blends between the lower and upper ends
35 : * of the shell.
36 : *
37 : * The physical coordinates \f$(x, y, z)\f$ are computed as follows.
38 : * Let \f$\alpha = (\xi+1)/2\f$ and \f$\beta = (\zeta+1)/2\f$. Define
39 : *
40 : * \f{align}{
41 : * x_\mathrm{inner}(\beta) &= x^\mathrm{inner}_\mathrm{lower}
42 : * + \beta\,(x^\mathrm{inner}_\mathrm{upper}
43 : * - x^\mathrm{inner}_\mathrm{lower}), \\
44 : * x_\mathrm{outer}(\beta) &= x^\mathrm{outer}_\mathrm{lower}
45 : * + \beta\,(x^\mathrm{outer}_\mathrm{upper}
46 : * - x^\mathrm{outer}_\mathrm{lower}), \\
47 : * r_\mathrm{outer}(\beta) &= \sqrt{r_\mathrm{sphere}^2
48 : * - x_\mathrm{outer}(\beta)^2}.
49 : * \f}
50 : *
51 : * Then
52 : *
53 : * \f{align}{
54 : * x &= (1-\alpha)\,x_\mathrm{inner}(\beta)
55 : * + \alpha\,x_\mathrm{outer}(\beta), \\
56 : * r &= (1-\alpha)\,r_\mathrm{inner}
57 : * + \alpha\,r_\mathrm{outer}(\beta), \\
58 : * y &= r\cos\eta, \quad z = r\sin\eta.
59 : * \f}
60 : *
61 : * The six block faces have the following geometry:
62 : * - \f$\xi = -1\f$ (\f$\alpha=0\f$): the inner right cylinder at
63 : * \f$r = r_\mathrm{inner}\f$, extending in \f$x\f$ from
64 : * \f$x^\mathrm{inner}_\mathrm{lower}\f$ to
65 : * \f$x^\mathrm{inner}_\mathrm{upper}\f$.
66 : * - \f$\xi = +1\f$ (\f$\alpha=1\f$): a portion of the sphere
67 : * \f$r^2 + x^2 = r_\mathrm{sphere}^2\f$.
68 : * - \f$\zeta = \pm 1\f$: generically curved surfaces in Cartesian
69 : * coordinates (ruled surfaces that blend linearly in \f$(x,r)\f$ between
70 : * the inner cylinder edge and the outer sphere edge at the corresponding
71 : * axial end).
72 : * - \f$\eta\f$ direction: periodic (connected by the cylindrical_shell
73 : * topology).
74 : *
75 : * ### Requirements
76 : * - \f$x^\mathrm{inner}_\mathrm{lower} < x^\mathrm{inner}_\mathrm{upper}\f$
77 : * - \f$x^\mathrm{outer}_\mathrm{lower} < x^\mathrm{outer}_\mathrm{upper}\f$
78 : * - \f$r_\mathrm{inner} > 0\f$
79 : * - \f$|x^\mathrm{outer}_\mathrm{lower}|,
80 : * |x^\mathrm{outer}_\mathrm{upper}| < r_\mathrm{sphere}\f$
81 : * - \f$r_\mathrm{inner} < r_\mathrm{outer}(\beta)\f$ for all
82 : * \f$\beta \in [0,1]\f$ (equivalently,
83 : * \f$r_\mathrm{inner} < \min(r_\mathrm{outer}(0), r_\mathrm{outer}(1))\f$).
84 : */
85 1 : class CylindricalSphericalShell {
86 : public:
87 0 : static constexpr size_t dim = 3;
88 :
89 : /*!
90 : * \brief Construct the map.
91 : *
92 : * \param x_inner_lower Axial coordinate \f$x\f$ at the lower end of the
93 : * inner cylinder (\f$\xi=-1, \zeta=-1\f$).
94 : * \param x_inner_upper Axial coordinate \f$x\f$ at the upper end of the
95 : * inner cylinder (\f$\xi=-1, \zeta=+1\f$).
96 : * \param x_outer_lower Axial coordinate \f$x\f$ at the lower end of the
97 : * outer spherical face (\f$\xi=+1, \zeta=-1\f$).
98 : * \param x_outer_upper Axial coordinate \f$x\f$ at the upper end of the
99 : * outer spherical face (\f$\xi=+1, \zeta=+1\f$).
100 : * \param r_inner Radius of the inner right cylinder.
101 : * \param r_sphere Radius of the outer bounding sphere (centered at the
102 : * origin).
103 : */
104 1 : CylindricalSphericalShell(double x_inner_lower, double x_inner_upper,
105 : double x_outer_lower, double x_outer_upper,
106 : double r_inner, double r_sphere);
107 :
108 0 : CylindricalSphericalShell() = default;
109 0 : ~CylindricalSphericalShell() = default;
110 0 : CylindricalSphericalShell(CylindricalSphericalShell&&) = default;
111 0 : CylindricalSphericalShell(const CylindricalSphericalShell&) = default;
112 0 : CylindricalSphericalShell& operator=(const CylindricalSphericalShell&) =
113 : default;
114 0 : CylindricalSphericalShell& operator=(CylindricalSphericalShell&&) = default;
115 :
116 : template <typename T>
117 0 : std::array<T, 3> operator()(const std::array<T, 3>& source_coords) const;
118 :
119 0 : std::optional<std::array<double, 3>> inverse(
120 : const std::array<double, 3>& target_coords) const;
121 :
122 : template <typename T>
123 0 : tnsr::Ij<T, 3, Frame::NoFrame> jacobian(
124 : const std::array<T, 3>& source_coords) const;
125 :
126 : template <typename T>
127 0 : tnsr::Ij<T, 3, Frame::NoFrame> inv_jacobian(
128 : const std::array<T, 3>& source_coords) const;
129 :
130 : // NOLINTNEXTLINE(google-runtime-references)
131 0 : void pup(PUP::er& p);
132 :
133 0 : static bool is_identity() { return false; }
134 :
135 0 : static constexpr bool supports_hessian{false};
136 :
137 : private:
138 0 : friend bool operator==(const CylindricalSphericalShell& lhs,
139 : const CylindricalSphericalShell& rhs);
140 0 : double x_inner_lower_{};
141 0 : double x_inner_upper_{};
142 0 : double x_outer_lower_{};
143 0 : double x_outer_upper_{};
144 0 : double r_inner_{};
145 0 : double r_sphere_{};
146 : };
147 :
148 0 : bool operator!=(const CylindricalSphericalShell& lhs,
149 : const CylindricalSphericalShell& rhs);
150 :
151 : } // namespace domain::CoordinateMaps
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