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grid_airfoil.h
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grid_airfoil.h
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//
// SPDX-License-Identifier: MIT
// Copyright (C) 2020 - 2021 by the ryujin authors
//
#pragma once
#include <compile_time_options.h>
#include "cubic_spline.h"
#include "geometry.h"
#include "transfinite_interpolation.template.h"
#include <deal.II/fe/fe_system.h>
#include <deal.II/grid/grid_generator.h>
#include <deal.II/grid/grid_in.h>
#include <deal.II/grid/grid_out.h>
#include <deal.II/grid/grid_tools.h>
#include <deal.II/grid/manifold_lib.h>
#include <deal.II/grid/tensor_product_manifold.h>
#include <deal.II/grid/tria.h>
namespace ryujin
{
namespace
{
/**
* A small helper function to assign values to either a c-style
* array (how vertices are stored in deal.II version 9.2 and
* earlier), or a std::array (how vertices are stored in deal.II
* version 9.3 onwards).
*/
template <typename T, typename T2>
inline void assign(T &array,
const std::initializer_list<T2> &initializer_list)
{
/* accomodate for a possible c-style array... */
Assert(std::size(array) == std::size(initializer_list),
dealii::ExcMessage(
"size of initializer list and array does not match"));
std::copy(
initializer_list.begin(), initializer_list.end(), std::begin(array));
}
} // namespace
namespace Manifolds
{
/**
* @todo Documentation
*/
template <int dim>
class AirfoilManifold : public dealii::ChartManifold<dim>
{
static_assert(dim == 2, "not implemented for dim != 2");
public:
AirfoilManifold(const dealii::Point<dim> airfoil_center,
const std::function<double(const double)> &psi_front,
const std::function<double(const double)> &psi_upper,
const std::function<double(const double)> &psi_lower,
const bool upper_side,
const double psi_ratio = 1.0)
: airfoil_center(airfoil_center)
, psi_front(psi_front)
, psi_upper(psi_upper)
, psi_lower(psi_lower)
, upper_side(upper_side)
, ratio_(psi_ratio * psi_front(0.) / psi_front(M_PI))
, polar_manifold()
{
Assert(std::abs(psi_upper(0.) - psi_front(0.5 * M_PI)) < 1.0e-10,
dealii::ExcInternalError());
Assert(std::abs(psi_lower(0.) + psi_front(1.5 * M_PI)) < 1.0e-10,
dealii::ExcInternalError());
}
virtual dealii::Point<dim>
pull_back(const dealii::Point<dim> &space_point) const final override
{
auto coordinate = dealii::Point<dim>() + (space_point - airfoil_center);
/* transform: */
dealii::Point<dim> chart_point;
if (coordinate[0] > 0.) {
if (upper_side) {
/* upper back airfoil part */
chart_point[0] = 1. + coordinate[1] - psi_upper(coordinate[0]);
chart_point[1] = 0.5 * M_PI - ratio_ * coordinate[0];
} else {
/* lower back airfoil part */
chart_point[0] = 1. - coordinate[1] + psi_lower(coordinate[0]);
chart_point[1] = 1.5 * M_PI + ratio_ * coordinate[0];
}
} else {
/* front part */
chart_point = polar_manifold.pull_back(coordinate);
chart_point[0] = 1. + chart_point[0] - psi_front(chart_point[1]);
}
return chart_point;
}
virtual dealii::Point<dim>
push_forward(const dealii::Point<dim> &point) const final override
{
auto chart_point = point;
/* transform back */
dealii::Point<dim> coordinate;
if (chart_point[1] < 0.5 * M_PI) {
Assert(upper_side, dealii::ExcInternalError());
/* upper back airfoil part */
coordinate[0] = (0.5 * M_PI - chart_point[1]) / ratio_;
Assert(coordinate[0] >= -1.0e-10, dealii::ExcInternalError());
coordinate[1] = chart_point[0] - 1. + psi_upper(coordinate[0]);
} else if (chart_point[1] > 1.5 * M_PI) {
Assert(!upper_side, dealii::ExcInternalError());
/* lower back airfoil part */
coordinate[0] = (chart_point[1] - 1.5 * M_PI) / ratio_;
Assert(coordinate[0] >= -1.0e-10, dealii::ExcInternalError());
coordinate[1] = 1. - chart_point[0] + psi_lower(coordinate[0]);
} else {
/* front part */
chart_point[0] = chart_point[0] - 1. + psi_front(chart_point[1]);
coordinate = polar_manifold.push_forward(chart_point);
}
return dealii::Point<dim>() + (coordinate + airfoil_center);
}
std::unique_ptr<dealii::Manifold<dim, dim>> clone() const final override
{
const double psi_ratio = ratio_ * psi_front(M_PI) / psi_front(0.);
return std::make_unique<AirfoilManifold<dim>>(airfoil_center,
psi_front,
psi_upper,
psi_lower,
upper_side,
psi_ratio);
}
private:
const dealii::Point<dim> airfoil_center;
const std::function<double(const double)> psi_front;
const std::function<double(const double)> psi_upper;
const std::function<double(const double)> psi_lower;
const bool upper_side;
const double ratio_;
dealii::PolarManifold<dim> polar_manifold;
};
/**
* @todo Documentation
*/
template <int dim>
class GradingManifold : public dealii::ChartManifold<dim>
{
public:
GradingManifold(const dealii::Point<dim> center,
const dealii::Tensor<1, dim> direction,
const double grading,
const double epsilon)
: center(center)
, direction(direction)
, grading(grading)
, epsilon(epsilon)
{
}
/* FIXME: find out why weights are not normalized. */
virtual Point<dim>
get_new_point(const ArrayView<const Point<dim>> &surrounding_points,
const ArrayView<const double> &weights) const override
{
if(weights[0] > 1.0)
return surrounding_points[0];
if(weights[1] > 1.0)
return surrounding_points[1];
return dealii::ChartManifold<dim>::get_new_point(surrounding_points,
weights);
}
virtual dealii::Point<dim>
pull_back(const dealii::Point<dim> &space_point) const final override
{
auto chart_point = space_point - center;
for (unsigned int d = 0; d < dim; ++d) {
if (std::abs(direction[d]) > 1.0e-10) {
const double x = chart_point[d] * std::copysign(1., direction[d]);
Assert(x + epsilon > 0, dealii::ExcInternalError());
const double x_hat = std::pow(x + epsilon, 1. / grading) -
std::pow(epsilon, 1. / grading) + 1.e-14;
chart_point[d] += (x_hat - x) * std::copysign(1., direction[d]);
}
}
return dealii::Point<dim>() + chart_point;
}
virtual dealii::Point<dim>
push_forward(const dealii::Point<dim> &chart_point) const final override
{
auto space_point = chart_point;
for (unsigned int d = 0; d < dim; ++d) {
if (std::abs(direction[d]) > 1.0e-10) {
const double x_hat =
space_point[d] * std::copysign(1., direction[d]);
Assert(x_hat + std::pow(epsilon, 1. / grading) > 0,
dealii::ExcInternalError());
const double x =
std::pow(x_hat + std::pow(epsilon, 1. / grading), grading) -
epsilon + 1.e-14;
space_point[d] += (x - x_hat) * std::copysign(1., direction[d]);
}
}
return center + (space_point - dealii::Point<dim>());
}
std::unique_ptr<dealii::Manifold<dim, dim>> clone() const final override
{
return std::make_unique<GradingManifold<dim>>(
center, direction, grading, epsilon);
}
private:
const dealii::Point<dim> center;
const dealii::Tensor<1, dim> direction;
const double grading;
const double epsilon;
};
/**
* @todo Documentation
*/
template <int dim>
class ExtrudedManifold : public dealii::Manifold<dim>
{
public:
ExtrudedManifold(const dealii::Manifold<dim - 1> &manifold)
: manifold(manifold.clone())
{
}
virtual std::unique_ptr<Manifold<dim>> clone() const override{
return std::make_unique<ExtrudedManifold<dim>>(*manifold);
}
virtual Point<dim>
get_new_point(const ArrayView<const Point<dim>> &surrounding_points,
const ArrayView<const double> &weights) const override
{
Assert(surrounding_points.size() == weights.size(),
dealii::ExcInternalError());
boost::container::small_vector<dealii::Point<dim - 1>, 100>
surrounding_points_projected;
std::transform(surrounding_points.begin(),
surrounding_points.end(),
surrounding_points_projected.begin(),
[](const dealii::Point<dim> &source) {
dealii::Point<dim - 1> result;
for (unsigned int d = 0; d < dim - 1; ++d)
result[d] = source[d];
return result;
});
const auto projected = manifold->get_new_point(
ArrayView<const Point<dim - 1>>{surrounding_points_projected.data(),
weights.size()},
weights);
dealii::Point<dim> result;
for (unsigned int d = 0; d < dim - 1; ++d)
result[d] = projected[d];
for (unsigned int i = 0; i < weights.size(); ++i)
result[dim - 1] += weights[i] * surrounding_points[i][dim - 1];
return result;
}
private:
std::unique_ptr<const dealii::Manifold<dim - 1>> manifold;
};
} // namespace Manifolds
namespace
{
/**
* @todo Documentation
*/
std::array<std::vector<double>, 4>
naca_4digit_points(const std::string &serial_number,
const unsigned int n_samples)
{
AssertThrow(serial_number.size() == 4,
dealii::ExcMessage("Invalid NACA 4 digit serial number"));
std::array<unsigned int, 4> digit;
std::transform(serial_number.begin(),
serial_number.end(),
digit.begin(),
[](auto it) { return it - '0'; });
/* thickness */
const double t = 0.1 * digit[2] + 0.01 * digit[3];
AssertThrow(t > 0.,
dealii::ExcMessage("Invalid NACA 4 digit serial number"));
/* maximal chamber */
const double m = 0.01 * digit[0];
/* x position of maximal chamber */
const double p = 0.1 * digit[1];
std::vector<double> x_upper;
std::vector<double> y_upper;
std::vector<double> x_lower;
std::vector<double> y_lower;
for (unsigned int i = 0; i < n_samples; i++) {
const double x = 1. * i / (n_samples - 1);
const double y =
5. * t *
(0.2969 * std::sqrt(x) +
x * (-0.126 + x * (-0.3516 + x * (0.2843 + x * (-0.1036)))));
const double y_c = (x < p) ? m / (p * p) * (2. * p * x - x * x)
: m / ((1. - p) * (1. - p)) *
(1. - 2. * p + 2. * p * x - x * x);
const double dy_c = (x < p) ? 2. * m / (p * p) * (p - x)
: 2. * m / ((1. - p) * (1. - p)) * (p - x);
const double theta = std::atan(dy_c);
x_upper.emplace_back(x - y * std::sin(theta));
y_upper.emplace_back(y_c + y * std::cos(theta));
x_lower.emplace_back(x + y * std::sin(theta));
y_lower.emplace_back(y_c - y * std::cos(theta));
}
/* Fix up roundoff errors: */
y_upper.front() = 0.;
y_upper.back() = 0.;
y_lower.front() = 0.;
y_lower.back() = 0.;
return {{x_upper, y_upper, x_lower, y_lower}};
}
/**
* @todo Documentation
*/
std::array<std::vector<double>, 4>
nasa_sc2(const std::string &serial_number)
{
if (serial_number == "0714") {
std::vector<double> x_upper{
.0, .002, .005, .01, .02, .03, .04, .05, .07, .1, .12, .15,
.17, .2, .22, .25, .27, .3, .33, .35, .38, .4, .43, .45,
.48, .50, .53, .55, .57, .6, .62, .65, .68, .7, .72, .75,
.77, .8, .82, .85, .87, .9, .92, .95, .97, .98, .99, 1.};
std::vector<double> y_upper{
.0, .0095, .0158, .0219, .0293, .0343, .0381, .0411,
.0462, .0518, .0548, .0585, .0606, .0632, .0646, .0664,
.0673, .0685, .0692, .0696, .0698, .0697, .0695, .0692,
.0684, .0678, .0666, .0656, .0645, .0625, .0610, .0585,
.0555, .0533, .0509, .0469, .0439, .0389, .0353, .0294,
.0251, .0181, .0131, .0049, -.0009, -.0039, -.0071, -.0104};
std::vector<double> x_lower{
.0, .002, .005, .01, .02, .03, .04, .05, .07, .1, .12, .15, .17,
.20, .22, .25, .28, .3, .32, .35, .37, .4, .42, .45, .48, .5,
.53, .55, .58, .6, .63, .65, .68, .70, .73, .75, .77, .80, .83,
.85, .87, .89, .92, .94, .95, .96, .97, .98, .99, 1.};
std::vector<double> y_lower{
.0, -.0093, -.016, -.0221, -.0295, -.0344, -.0381, -.0412,
-.0462, -.0517, -.0547, -.0585, -.0606, -.0633, -.0647, -.0666,
-.068, -.0687, -.0692, -.0696, -.0696, -.0692, -.0688, -.0676,
-.0657, -.0644, -.0614, -.0588, -.0543, -.0509, -.0451, -.041,
-.0346, -.0302, -.0235, -.0192, -.0150, -.0093, -.0048, -.0024,
-.0013, -.0008, -.0016, -.0035, -.0049, -.0066, -.0085, -.0109,
-.0137, -.0163};
return {{x_upper, y_upper, x_lower, y_lower}};
} else {
AssertThrow(false,
dealii::ExcMessage("Invalid NASA SC(2) serial number"));
}
}
/**
* @todo Documentation
*/
std::array<std::vector<double>, 4>
onera(const std::string &serial_number)
{
if (serial_number == "OAT15a") {
std::vector<double> x_upper{
0., 2.95888e-05, 0.000117865, 0.000263239, 0.000464245,
0.000719821, 0.00103013, 0.00139605, 0.00181884, 0.00230024,
0.00284243, 0.00344764, 0.00411805, 0.00485595, 0.00566349,
0.00654241, 0.00749421, 0.0085197, 0.0096197, 0.0107945,
0.0120442, 0.013369, 0.0147688, 0.0162438, 0.0177939,
0.0194194, 0.0211207, 0.0228982, 0.0247526, 0.0266845,
0.028695, 0.0307852, 0.0329562, 0.0352094, 0.0375463,
0.0399687, 0.0424782, 0.0450769, 0.0477668, 0.05055,
0.0534291, 0.0564063, 0.0594842, 0.0626655, 0.0659531,
0.0693498, 0.0728588, 0.0764831, 0.0802261, 0.0840914,
0.0880824, 0.0922027, 0.0964564, 0.100847, 0.10538,
0.110058, 0.114885, 0.119868, 0.125009, 0.130314,
0.135789, 0.14139, 0.147074, 0.152839, 0.158682,
0.164603, 0.170599, 0.17667, 0.182814, 0.189028,
0.195312, 0.201665, 0.208083, 0.214567, 0.221115,
0.227724, 0.234394, 0.241123, 0.24791, 0.254753,
0.26165, 0.2686, 0.275601, 0.282653, 0.289753,
0.2969, 0.304093, 0.311329, 0.318609, 0.325929,
0.333289, 0.340686, 0.348121, 0.35559, 0.363093,
0.370629, 0.378194, 0.385789, 0.393412, 0.40106,
0.408734, 0.41643, 0.424148, 0.431886, 0.439643,
0.447417, 0.455207, 0.46301, 0.470827, 0.478654,
0.486491, 0.494337, 0.502189, 0.510046, 0.517907,
0.525769, 0.533632, 0.541494, 0.549354, 0.557209,
0.565059, 0.572902, 0.580736, 0.588559, 0.596371,
0.60417, 0.611953, 0.61972, 0.627469, 0.635198,
0.642906, 0.65059, 0.658251, 0.665886, 0.673493,
0.68107, 0.688617, 0.69613, 0.70361, 0.711054,
0.71846, 0.725827, 0.733154, 0.740438, 0.747679,
0.754875, 0.762025, 0.769127, 0.776181, 0.783185,
0.790139, 0.79704, 0.80389, 0.810685, 0.817426,
0.82411, 0.830738, 0.837307, 0.843817, 0.850265,
0.856652, 0.862974, 0.869233, 0.87538, 0.881373,
0.887216, 0.892913, 0.898467, 0.903883, 0.909163,
0.914311, 0.91933, 0.924224, 0.928996, 0.933648,
0.938183, 0.942606, 0.946917, 0.95112, 0.955217,
0.959212, 0.963107, 0.966904, 0.970605, 0.974213,
0.977731, 0.98116, 0.984503, 0.987762, 0.990939,
0.994036, 0.997056, 1.};
std::vector<double> y_upper{
0., 0.000899353, 0.0018231, 0.00276894, 0.00373508,
0.00472011, 0.0057226, 0.00674103, 0.0077738, 0.00881906,
0.00987467, 0.0109383, 0.0120074, 0.0130793, 0.0141511,
0.01522, 0.0162832, 0.0173387, 0.0183841, 0.0194179,
0.0204389, 0.021446, 0.0224386, 0.0234164, 0.0243794,
0.0253276, 0.0262612, 0.0271805, 0.028086, 0.0289783,
0.0298578, 0.0307252, 0.0315811, 0.0324262, 0.0332611,
0.0340861, 0.0349022, 0.0357098, 0.0365095, 0.0373016,
0.0380867, 0.0388652, 0.0396375, 0.0404039, 0.041165,
0.0419211, 0.0426722, 0.0434189, 0.0441614, 0.0448995,
0.0456336, 0.0463636, 0.0470894, 0.047811, 0.0485286,
0.0492423, 0.0499518, 0.0506574, 0.0513591, 0.0520569,
0.0527506, 0.0534343, 0.0541023, 0.054755, 0.0553921,
0.0560138, 0.05662, 0.0572108, 0.0577861, 0.0583462,
0.0588909, 0.0594202, 0.0599341, 0.0604325, 0.0609153,
0.0613826, 0.0618341, 0.06227, 0.06269, 0.0630941,
0.0634823, 0.0638544, 0.0642103, 0.06455, 0.0648734,
0.0651806, 0.0654713, 0.0657454, 0.0660031, 0.0662442,
0.0664685, 0.066676, 0.0668664, 0.0670398, 0.067196,
0.0673349, 0.0674562, 0.0675598, 0.0676456, 0.0677134,
0.0677629, 0.067794, 0.0678065, 0.0678, 0.0677743,
0.0677293, 0.0676646, 0.0675798, 0.0674748, 0.0673492,
0.0672027, 0.0670349, 0.0668456, 0.0666344, 0.066401,
0.066145, 0.0658661, 0.065564, 0.0652385, 0.064889,
0.0645151, 0.0641169, 0.0636938, 0.0632454, 0.0627715,
0.0622718, 0.061746, 0.0611937, 0.0606145, 0.0600083,
0.0593747, 0.0587136, 0.0580244, 0.0573069, 0.0565607,
0.0557853, 0.0549807, 0.0541461, 0.0532814, 0.0523863,
0.0514606, 0.0505046, 0.0495188, 0.0485042, 0.047462,
0.0463943, 0.0453031, 0.0441914, 0.0430618, 0.0419174,
0.0407612, 0.0395961, 0.038425, 0.0372503, 0.0360742,
0.034899, 0.0337262, 0.0325572, 0.0313935, 0.030236,
0.029086, 0.0279442, 0.0268114, 0.0256966, 0.0246079,
0.023545, 0.0225073, 0.0214947, 0.0205065, 0.0195422,
0.0186011, 0.0176826, 0.0167863, 0.0159112, 0.0150567,
0.0142221, 0.0134066, 0.0126095, 0.0118301, 0.0110678,
0.0103219, 0.00959177, 0.00887695, 0.00817697, 0.00749135,
0.00681977, 0.0061621, 0.00551806, 0.00488739, 0.00427007,
0.00366612, 0.00307588, 0.0024997};
std::vector<double> x_lower{
0., 3.22311e-05, 0.000136327, 0.000324365, 0.000606007,
0.000986654, 0.00146626, 0.00204126, 0.00270571, 0.00345312,
0.00427708, 0.00517234, 0.00613428, 0.00715943, 0.00824517,
0.00938973, 0.0105917, 0.0118504, 0.0131652, 0.0145362,
0.0159635, 0.0174476, 0.0189891, 0.0205889, 0.0222479,
0.0239675, 0.0257488, 0.0275934, 0.0295028, 0.031479,
0.0335237, 0.035639, 0.0378271, 0.04009, 0.0424303,
0.0448502, 0.0473523, 0.049939, 0.0526132, 0.0553774,
0.0582343, 0.0611868, 0.0642377, 0.0673899, 0.0706465,
0.0740105, 0.077485, 0.0810733, 0.0847788, 0.088605,
0.0925553, 0.0966336, 0.100844, 0.10519, 0.109675,
0.114305, 0.119084, 0.124016, 0.129106, 0.134358,
0.139779, 0.145328, 0.150961, 0.156676, 0.162473,
0.168349, 0.174303, 0.180333, 0.186437, 0.192615,
0.198863, 0.205181, 0.211568, 0.21802, 0.224537,
0.231117, 0.237759, 0.24446, 0.251219, 0.258035,
0.264905, 0.271829, 0.278804, 0.285828, 0.292901,
0.30002, 0.307184, 0.314391, 0.321639, 0.328927,
0.336253, 0.343615, 0.351011, 0.358441, 0.365902,
0.373392, 0.38091, 0.388455, 0.396024, 0.403616,
0.41123, 0.418864, 0.426517, 0.434187, 0.441871,
0.44957, 0.457282, 0.465005, 0.472737, 0.480477,
0.488225, 0.495977, 0.503733, 0.511493, 0.519252,
0.527012, 0.53477, 0.542525, 0.550276, 0.55802,
0.565759, 0.573488, 0.581208, 0.588918, 0.596615,
0.604298, 0.611967, 0.61962, 0.627257, 0.634874,
0.642473, 0.65005, 0.657605, 0.665137, 0.672645,
0.680128, 0.687584, 0.695012, 0.702411, 0.70978,
0.717118, 0.724424, 0.731697, 0.738935, 0.746137,
0.753303, 0.76043, 0.767518, 0.774565, 0.78157,
0.788531, 0.795447, 0.802316, 0.809136, 0.815905,
0.822623, 0.829286, 0.835893, 0.842441, 0.84893,
0.855357, 0.86172, 0.868018, 0.874204, 0.880239,
0.886123, 0.891863, 0.89746, 0.902919, 0.908242,
0.913433, 0.918495, 0.923431, 0.928244, 0.932938,
0.937515, 0.941978, 0.94633, 0.950574, 0.954712,
0.958747, 0.962681, 0.966518, 0.970259, 0.973907,
0.977464, 0.980932, 0.984314, 0.987612, 0.990827,
0.993963, 0.997019, 1.};
std::vector<double> y_lower{
0., -0.000899234, -0.00182108, -0.00275889, -0.00370397,
-0.00464681, -0.00557909, -0.00649452, -0.0073895, -0.00826265,
-0.00911444, -0.00994611, -0.0107598, -0.0115578, -0.0123422,
-0.0131152, -0.0138788, -0.0146348, -0.0153851, -0.0161313,
-0.0168749, -0.0176173, -0.0183597, -0.0191032, -0.0198489,
-0.0205974, -0.0213498, -0.0221064, -0.0228678, -0.0236341,
-0.0244053, -0.0251817, -0.0259627, -0.0267482, -0.0275378,
-0.0283309, -0.029127, -0.0299255, -0.0307258, -0.0315273,
-0.0323295, -0.0331322, -0.0339346, -0.0347366, -0.035538,
-0.0363383, -0.0371378, -0.037936, -0.0387331, -0.0395288,
-0.0403228, -0.0411152, -0.0419054, -0.0426933, -0.0434778,
-0.0442587, -0.0450347, -0.045805, -0.0465681, -0.0473225,
-0.0480666, -0.0487929, -0.0494941, -0.0501695, -0.0508179,
-0.0514387, -0.052031, -0.0525942, -0.0531277, -0.0536309,
-0.0541035, -0.054545, -0.0549547, -0.0553323, -0.0556773,
-0.0559891, -0.056267, -0.0565107, -0.0567191, -0.0568918,
-0.0570281, -0.0571272, -0.0571886, -0.0572116, -0.0571958,
-0.0571405, -0.0570453, -0.0569098, -0.0567339, -0.0565171,
-0.0562594, -0.0559608, -0.055621, -0.0552405, -0.0548193,
-0.0543577, -0.0538564, -0.0533157, -0.0527365, -0.0521197,
-0.0514661, -0.0507767, -0.0500525, -0.0492947, -0.0485041,
-0.0476819, -0.0468294, -0.0459474, -0.0450371, -0.0440995,
-0.0431356, -0.0421465, -0.0411333, -0.0400971, -0.039039,
-0.0379601, -0.0368617, -0.0357451, -0.0346114, -0.0334621,
-0.0322983, -0.0311217, -0.0299336, -0.0287354, -0.0275285,
-0.0263145, -0.025095, -0.0238717, -0.0226459, -0.0214194,
-0.020194, -0.0189714, -0.0177534, -0.016542, -0.015339,
-0.0141466, -0.0129671, -0.0118026, -0.0106558, -0.00952898,
-0.00842491, -0.00734634, -0.00629613, -0.00527714, -0.0042922,
-0.00334424, -0.00243619, -0.00157086, -0.000750868, 2.13187e-05,
0.000743489, 0.00141373, 0.00203031, 0.00259174, 0.00309711,
0.00354599, 0.00393819, 0.00427381, 0.00455352, 0.00477839,
0.00494994, 0.00506989, 0.00514012, 0.0051629, 0.00514197,
0.0050815, 0.0049854, 0.00485738, 0.0047009, 0.00451919,
0.0043152, 0.00409157, 0.00385071, 0.00359475, 0.00332561,
0.00304503, 0.00275452, 0.00245546, 0.00214904, 0.00183633,
0.00151827, 0.00119574, 0.00086945, 0.00054002, 0.000208013,
-0.000126036, -0.000461602, -0.000798383, -0.0011363, -0.00147529,
-0.00181444, -0.00215832, -0.0024967};
return {{x_upper, y_upper, x_lower, y_lower}};
} else {
AssertThrow(false, dealii::ExcMessage("Invalid ONERA serial number"));
}
}
/**
* @todo Documentation
*/
std::array<std::function<double(const double)>, 3>
create_psi(const std::vector<double> &x_upper,
const std::vector<double> &y_upper,
const std::vector<double> &x_lower,
const std::vector<double> &y_lower,
const double x_center,
const double y_center,
const double scaling = 1.)
{
Assert(x_upper.size() >= 2, dealii::ExcInternalError());
Assert(x_upper.front() == 0. && x_upper.back() == 1.,
dealii::ExcInternalError());
Assert(std::is_sorted(x_upper.begin(), x_upper.end()),
dealii::ExcInternalError());
Assert(x_lower.size() >= 2, dealii::ExcInternalError());
Assert(x_lower.front() == 0. && x_lower.back() == 1.,
dealii::ExcInternalError());
Assert(std::is_sorted(x_lower.begin(), x_lower.end()),
dealii::ExcInternalError());
Assert(y_upper.size() == x_upper.size(), dealii::ExcInternalError());
Assert(y_upper.front() == 0., dealii::ExcInternalError());
Assert(y_lower.size() == x_lower.size(), dealii::ExcInternalError());
Assert(y_lower.front() == 0., dealii::ExcInternalError());
Assert(y_lower.back() < y_upper.back(), dealii::ExcInternalError());
Assert(0. < x_center && x_center < 1., dealii::ExcInternalError());
#ifdef DEAL_II_WITH_GSL
CubicSpline upper_airfoil(x_upper, y_upper);
auto psi_upper =
[upper_airfoil, x_center, y_center, scaling](const double x_hat) {
/* Past the trailing edge return the the final upper y position: */
const double x = x_hat / scaling;
if (x > 1. - x_center)
return scaling * (upper_airfoil.eval(1.0) - y_center);
return scaling * (upper_airfoil.eval(x + x_center) - y_center);
};
CubicSpline lower_airfoil(x_lower, y_lower);
auto psi_lower =
[lower_airfoil, x_center, y_center, scaling](const double x_hat) {
/* Past the trailing edge return the the final lower y position: */
const double x = x_hat / scaling;
if (x > 1. - x_center)
return scaling * (lower_airfoil.eval(1.0) - y_center);
return scaling * (lower_airfoil.eval(x + x_center) - y_center);
};
/*
* Create a combined point set for psi_front:
*/
std::vector<double> x_combined;
std::vector<double> y_combined;
for (std::size_t i = 0; i < x_upper.size(); ++i) {
if (x_upper[i] >= x_center)
break;
x_combined.push_back(x_upper[i]);
y_combined.push_back(y_upper[i]);
}
/*
* We are about to create a spline interpolation in polar coordinates
* for the front part. In order to blend this interpolation with the
* two splines for the upper and lower part that we have just created
* we have to add some additional sample points around the
* coordinates were we glue together
*/
for (double x : {x_center, x_center + 0.01, x_center + 0.02}) {
x_combined.push_back(x);
y_combined.push_back(upper_airfoil.eval(x));
}
std::reverse(x_combined.begin(), x_combined.end());
std::reverse(y_combined.begin(), y_combined.end());
x_combined.pop_back();
y_combined.pop_back();
for (std::size_t i = 0; i < x_lower.size(); ++i) {
if (x_lower[i] >= x_center)
break;
x_combined.push_back(x_lower[i]);
y_combined.push_back(y_lower[i]);
}
for (double x : {x_center, x_center + 0.01, x_center + 0.02}) {
x_combined.push_back(x);
y_combined.push_back(lower_airfoil.eval(x));
}
/* Translate into polar coordinates: */
for (unsigned int i = 0; i < y_combined.size(); ++i) {
const auto x = x_combined[i] - x_center;
const auto y = y_combined[i] - y_center;
const auto rho = std::sqrt(x * x + y * y);
auto phi = std::atan2(y, x);
if (phi < 0)
phi += 2 * dealii::numbers::PI;
x_combined[i] = phi;
y_combined[i] = rho;
}
/* Ensure that x_combined is monotonically increasing: */
if (x_combined.back() == 0.)
x_combined.back() = 2. * dealii::numbers::PI;
Assert(std::is_sorted(x_combined.begin(), x_combined.end()),
dealii::ExcInternalError());
CubicSpline front_airfoil(x_combined, y_combined);
auto psi_front = [front_airfoil, x_center, scaling](const double phi) {
/* By convention we return the "back length" for phi == 0.: */
if (phi == 0.)
return scaling * (1. - x_center);
return scaling * front_airfoil.eval(phi);
};
return {{psi_front, psi_upper, psi_lower}};
#else
AssertThrow(false, dealii::
ExcNotImplemented("Airfoil grid needs deal.II with GSL"));
return {};
#endif
}
} // namespace
/**
* A namespace for a number of benchmark geometries and dealii::GridIn
* wrappers.
*
* @ingroup Mesh
*/
namespace Geometries
{
/**
* A generic 2D Airfoil
*
* This class implements a generic 2D airfoil. Various runtime
* parameters select the airfoil type (such as NACA 4 digit, some ONERA
* airfoils, etc) and meshing behavior. The mesh construction is
* divided into various steps:
*
* 1/ Parametrization:
*
* Depending on various runtime parameters a parameterization \f$ y =
* \psi_{\text{up./lo.}}(x)\f$ on the upper and lower trailing edge as
* well as a parameterization in polar coordinates
* \f$ r = \psi_{\text{fr.}}(\phi) \f$ for the nose part is constructed.
* This is done by taking a sample of points on the upper and lower
* part of the airfoil and computing intermediate points with a cubic
* spline interpolation. Relevant runtime parameters are `airfoil type`
* to specify the type and serial number, `psi samples` to control the
* number of samples taken (if admissible), and `psi center` to control
* the center point for constructing the parametrizations
* \f$\psi_{\text{x}}\f$. The samples are assumed to be normalized so
* that the front is located at \f$(0,0)\f$ and the trailing (or blunt
* edge) at \f$(1,0)\f$, or \f$(1,\ast)\f$, respectively. The
* coordinate system is then shifted by the `psi center` point so that
* the parameterizations \f$y = \hat\psi_{\text{up./lo.}}(x)\f$ expect
* input in the range \f$\hat x\in[0,1-x_{\text{psi center}}]\f$. In the
* same spirit \f$\hat\psi_{\text{fr.}}(\phi)\f$ expects input in the
* range \f$\pi/2\le\phi\le3\pi/2\f$ and will return
* \f$\psi_{\text{fr.}}(\pi) = -x_{\text{psi center}}\f$. Also a final
* step the normalized parametrizations \f$\hat\psi\f$ are rescaled
* with the runtime parameter `airfoil length` so that the resulting
* airfoil has overall length `airfoil length` instead of 1.
*
* 2/ Meshing:
*
* TODO
*
* @ingroup Mesh
*/
template <int dim>
class Airfoil : public Geometry<dim>
{
public:
Airfoil(const std::string subsection)
: Geometry<dim>("airfoil", subsection)
{
/* Parameters affecting parameterization: */
airfoil_type_ = "NASA SC(2) 0714";
this->add_parameter(
"airfoil type", airfoil_type_, "airfoil type and serial number");
airfoil_length_ = 2.;
this->add_parameter("airfoil length",
airfoil_length_,
"length of airfoil (leading to trailing edge)");
psi_samples_ = 100;
this->add_parameter("psi samples",
psi_samples_,
"number of samples used for generating spline psi");
psi_center_[0] = 0.05;
this->add_parameter("psi center",
psi_center_,
"center position of airfoil for sampling psi");
psi_ratio_ = 0.30;
this->add_parameter(
"psi ratio",
psi_ratio_,
"Scaling parameter for averages in curved nose region, can be "
"adjusted by hand to equliabrate the size of faces at the nose "
"part of the airfoil");
airfoil_center_[0] = -.5;
this->add_parameter("airfoil center",
airfoil_center_,
"position of airfoil center in the mesh");
/* Parameters affecting mesh generation: */
grading_ = 5.5;
this->add_parameter(
"grading exponent", grading_, "graded mesh: exponent");
grading_epsilon_ = 0.02;
this->add_parameter("grading epsilon",
grading_epsilon_,
"graded mesh: regularization parameter");
grading_epsilon_trailing_ = 0.01;
this->add_parameter(
"grading epsilon trailing",
grading_epsilon_trailing_,
"graded mesh: regularization parameter for trailing cells");
height_ = 6.;
this->add_parameter(
"height", height_, "height of computational domain");
width_ = 1.;
this->add_parameter("width", width_, "width of computational domain");
n_anisotropic_refinements_airfoil_ = 1;
this->add_parameter(
"anisotropic pre refinement airfoil",
n_anisotropic_refinements_airfoil_,
"number of anisotropic pre refinement steps for the airfoil");
n_anisotropic_refinements_trailing_ = 3;
this->add_parameter("anisotropic pre refinement trailing",
n_anisotropic_refinements_trailing_,
"number of anisotropic pre refinement steps for "
"the blunt trailing edge cell");
subdivisions_z_ = 2;
this->add_parameter("subdivisions z",
subdivisions_z_,
"number of subdivisions in z direction");
}
virtual void create_triangulation(
typename Geometry<dim>::Triangulation &triangulation) final override
{
/*
* Step 1: Create parametrization:
*
* Runtime parameters: airfoil_type_, airfoil_length_, psi_center_,
* psi_samples_
*/
const auto [x_upper, y_upper, x_lower, y_lower] = [&]() {
if (airfoil_type_.rfind("NACA ", 0) == 0) {
return naca_4digit_points(airfoil_type_.substr(5), psi_samples_);
} else if (airfoil_type_.rfind("NASA SC(2) ", 0) == 0) {
return nasa_sc2(airfoil_type_.substr(11));
} else if (airfoil_type_.rfind("ONERA ", 0) == 0) {
return onera(airfoil_type_.substr(6));
}
AssertThrow(false, ExcMessage("Unknown airfoil type"));
}();
const auto [psi_front, psi_upper, psi_lower] =
create_psi(x_upper,
y_upper,
x_lower,
y_lower,
psi_center_[0],
psi_center_[1],
airfoil_length_);
/*
* Step 2: Create coarse mesh.
*
* Runtime parameters: airfoil_center_, height_,
*/
/* The radius of the radial front part of the mesh: */
const auto outer_radius = 0.5 * height_;
/* by convention, psi_front(0.) returns the "back length" */
const auto back_length = psi_front(0.);
/* sharp trailing edge? */
const bool sharp_trailing_edge =
std::abs(psi_upper(back_length) - psi_lower(back_length)) < 1.0e-10;
AssertThrow(
sharp_trailing_edge ||
std::abs(psi_upper(back_length) - psi_lower(back_length)) >
0.001 * back_length,
dealii::ExcMessage("Blunt trailing edge has a width of less than "
"0.1% of the trailing airfoil length."));
/* Front part: */
dealii::Triangulation<2> tria_front;
{
std::vector<dealii::Point<2>> vertices{
{-outer_radius, 0.0}, // 0
{airfoil_center_[0] - psi_front(M_PI), airfoil_center_[1]}, // 1
{-0.5 * outer_radius, -std::sqrt(3.) / 2. * outer_radius}, // 2
{0.5 * outer_radius, -std::sqrt(3.) / 2. * outer_radius}, // 3
{0., airfoil_center_[1] + psi_lower(-airfoil_center_[0])}, // 4
{airfoil_center_[0] + back_length, //
airfoil_center_[1] + psi_lower(back_length)}, // 5
{0., airfoil_center_[1] + psi_upper(-airfoil_center_[0])}, // 6
{-0.5 * outer_radius, std::sqrt(3.) / 2. * outer_radius}, // 7
{0.5 * outer_radius, std::sqrt(3.) / 2. * outer_radius}, // 8
};
std::vector<dealii::CellData<2>> cells(4);
assign(cells[0].vertices, {2, 3, 4, 5});
assign(cells[1].vertices, {0, 2, 1, 4});
assign(cells[2].vertices, {7, 0, 6, 1});
if (sharp_trailing_edge) {
assign(cells[3].vertices, {8, 7, 5, 6});
} else {
vertices.push_back({airfoil_center_[0] + back_length,
airfoil_center_[1] + psi_upper(back_length)});
assign(cells[3].vertices, {8, 7, 9, 6});
}
tria_front.create_triangulation(
vertices, cells, dealii::SubCellData());
}
/* Back part: */
dealii::Triangulation<2> tria_back;
if (sharp_trailing_edge) {
/* Back part for sharp trailing edge: */
const std::vector<dealii::Point<2>> vertices{
{0.5 * outer_radius, -std::sqrt(3.) / 2. * outer_radius}, // 0
{airfoil_center_[0] + back_length,
airfoil_center_[1] + psi_lower(back_length)}, // 1
{0.5 * outer_radius, std::sqrt(3.) / 2. * outer_radius}, // 2
{outer_radius, -0.5 * outer_radius}, // 3
{outer_radius, 0.0}, // 4
{outer_radius, 0.5 * outer_radius}, // 5
};
std::vector<dealii::CellData<2>> cells(2);
assign(cells[0].vertices, {0, 3, 1, 4});
assign(cells[1].vertices, {1, 4, 2, 5});
tria_back.create_triangulation(
vertices, cells, dealii::SubCellData());
} else {
/* Back part for blunt trailing edge: */
/* Good width for the anisotropically refined center trailing cell: */
double trailing_height =
0.5 / (0.5 + std::pow(2., n_anisotropic_refinements_airfoil_)) *
0.5 * outer_radius;
const std::vector<dealii::Point<2>> vertices{
{0.5 * outer_radius, -std::sqrt(3.) / 2. * outer_radius}, // 0
{airfoil_center_[0] + back_length,
airfoil_center_[1] + psi_lower(back_length)}, // 1
{airfoil_center_[0] + back_length,
airfoil_center_[1] + psi_upper(back_length)}, // 2
{0.5 * outer_radius, std::sqrt(3.) / 2. * outer_radius}, // 3
{outer_radius, -0.5 * outer_radius}, // 4
{outer_radius, -trailing_height}, // 5
{outer_radius, trailing_height}, // 6
{outer_radius, 0.5 * outer_radius}, // 7
};
std::vector<dealii::CellData<2>> cells(3);
assign(cells[0].vertices, {0, 4, 1, 5});
assign(cells[1].vertices, {1, 5, 2, 6});
assign(cells[2].vertices, {2, 6, 3, 7});
tria_back.create_triangulation(
vertices, cells, dealii::SubCellData());
}
dealii::Triangulation<2> coarse_triangulation;