/
nabla_formulae.hpp
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/
nabla_formulae.hpp
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/** @file
* @copyright University of Warsaw
* @section LICENSE
* GPLv3+ (see the COPYING file or http://www.gnu.org/licenses/)
*/
#pragma once
#include <libmpdata++/blitz.hpp>
#include <libmpdata++/formulae/idxperm.hpp>
#include <libmpdata++/formulae/arakawa_c.hpp>
namespace libmpdataxx
{
namespace formulae
{
namespace nabla
{
using idxperm::pi;
using arakawa_c::h;
template <class arg_t, typename real_t>
inline auto grad(
const arg_t &x,
const rng_t &i,
const real_t dx
)
{
return blitz::safeToReturn(
(
x(i+1) -
x(i-1)
) / dx / 2
);
}
// 2D version
template <int d, class arg_t, typename real_t>
inline auto grad(
const arg_t &x,
const rng_t &i,
const rng_t &j,
const real_t dx
)
{
return blitz::safeToReturn(
(
x(pi<d>(i+1, j)) -
x(pi<d>(i-1, j))
) / dx / 2
);
}
// 3D version
template <int d, class arg_t, typename real_t>
inline auto grad(
const arg_t &x,
const rng_t &i,
const rng_t &j,
const rng_t &k,
const real_t dx
)
{
return blitz::safeToReturn(
(
x(pi<d>(i+1, j, k)) -
x(pi<d>(i-1, j, k))
) / dx / 2
);
}
template <class arg_t, typename real_t>
inline auto grad_cmpct(
const arg_t &x,
const rng_t &i,
const real_t dx
)
{
return blitz::safeToReturn(
(
x(i+1) -
x(i)
) / dx
);
}
// 2D version
template <int d, class arg_t, typename real_t>
inline auto grad_cmpct(
const arg_t &x,
const rng_t &i,
const rng_t &j,
const real_t dx
)
{
return blitz::safeToReturn(
(
x(pi<d>(i+1, j)) -
x(pi<d>(i , j))
) / dx
);
}
// 3D version
template <int d, class arg_t, typename real_t>
inline auto grad_cmpct(
const arg_t &x,
const rng_t &i,
const rng_t &j,
const rng_t &k,
const real_t dx
)
{
return blitz::safeToReturn(
(
x(pi<d>(i+1, j, k)) -
x(pi<d>(i, j, k))
) / dx
);
}
// helper function to calculate gradient components of a scalar field
// 1D version
template <int nd, class arrvec_t, class arr_t, class ijk_t, class dijk_t>
inline void calc_grad(arrvec_t v, arr_t a, ijk_t ijk, dijk_t dijk, typename std::enable_if<nd == 1>::type* = 0)
{
v[0](ijk) = formulae::nabla::grad<0>(a, ijk[0], dijk[0]);
}
// 2D version
template <int nd, class arrvec_t, class arr_t, class ijk_t, class dijk_t>
inline void calc_grad(arrvec_t v, arr_t a, ijk_t ijk, dijk_t dijk, typename std::enable_if<nd == 2>::type* = 0)
{
v[0](ijk) = formulae::nabla::grad<0>(a, ijk[0], ijk[1], dijk[0]);
v[1](ijk) = formulae::nabla::grad<1>(a, ijk[1], ijk[0], dijk[1]);
}
// 3D version
template <int nd, class arrvec_t, class arr_t, class ijk_t, class dijk_t>
inline void calc_grad(arrvec_t v, arr_t a, ijk_t ijk, dijk_t dijk, typename std::enable_if<nd == 3>::type* = 0)
{
v[0](ijk) = formulae::nabla::grad<0>(a, ijk[0], ijk[1], ijk[2], dijk[0]);
v[1](ijk) = formulae::nabla::grad<1>(a, ijk[1], ijk[2], ijk[0], dijk[1]);
v[2](ijk) = formulae::nabla::grad<2>(a, ijk[2], ijk[0], ijk[1], dijk[2]);
}
// 2D version
template <int nd, class arrvec_t, class arr_t, class ijk_t, class ijkm_t, class dijk_t>
inline void calc_grad_cmpct(arrvec_t v, arr_t a, ijk_t ijk, ijkm_t ijkm, dijk_t dijk, typename std::enable_if<nd == 2>::type* = 0)
{
v[0](ijkm[0] + h, ijk[1]) = formulae::nabla::grad_cmpct<0>(a, ijkm[0], ijk[1], dijk[0]);
v[1](ijk[0], ijkm[1] + h) = formulae::nabla::grad_cmpct<1>(a, ijkm[1], ijk[0], dijk[1]);
}
// 3D version
template <int nd, class arrvec_t, class arr_t, class ijk_t, class ijkm_t, class dijk_t>
inline void calc_grad_cmpct(arrvec_t v, arr_t a, ijk_t ijk, ijkm_t ijkm, dijk_t dijk, typename std::enable_if<nd == 3>::type* = 0)
{
v[0](ijkm[0] + h, ijk[1], ijk[2]) = formulae::nabla::grad_cmpct<0>(a, ijkm[0], ijk[1], ijk[2], dijk[0]);
v[1](ijk[0], ijkm[1] + h, ijk[2]) = formulae::nabla::grad_cmpct<1>(a, ijkm[1], ijk[2], ijk[0], dijk[1]);
v[2](ijk[0], ijk[1], ijkm[2] + h) = formulae::nabla::grad_cmpct<2>(a, ijkm[2], ijk[0], ijk[1], dijk[2]);
}
// divergence
// 2D version
template <int nd, class arrvec_t, class ijk_t, class dijk_t>
inline auto div(
const arrvec_t &v, // vector field
const ijk_t &ijk,
const dijk_t dijk,
typename std::enable_if<nd == 2>::type* = 0
)
{
return blitz::safeToReturn(
(v[0](ijk[0]+1, ijk[1]) - v[0](ijk[0]-1, ijk[1])) / dijk[0] / 2
+
(v[1](ijk[0], ijk[1]+1) - v[1](ijk[0], ijk[1]-1)) / dijk[1] / 2
);
}
// 3D version
template <int nd, class arrvec_t, class ijk_t, class dijk_t>
inline auto div(
const arrvec_t &v, // vector field
const ijk_t &ijk,
const dijk_t dijk,
typename std::enable_if<nd == 3>::type* = 0
)
{
return blitz::safeToReturn(
(v[0](ijk[0]+1, ijk[1], ijk[2]) - v[0](ijk[0]-1, ijk[1], ijk[2])) / dijk[0] / 2
+
(v[1](ijk[0], ijk[1]+1, ijk[2]) - v[1](ijk[0], ijk[1]-1, ijk[2])) / dijk[1] / 2
+
(v[2](ijk[0], ijk[1], ijk[2]+1) - v[2](ijk[0], ijk[1], ijk[2]-1)) / dijk[2] / 2
);
}
} // namespace nabla_op
} // namespace formulae
} // namespace libmpdataxx