From: David Wells Date: Sun, 12 Aug 2018 15:06:16 +0000 (-0400) Subject: Add a GridGenerator function for flow past a cylinder. X-Git-Tag: v9.1.0-rc1~801^2~1 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=4f1d922c60cc2e2da73a06981a6da630e9a04de4;p=dealii.git Add a GridGenerator function for flow past a cylinder. --- diff --git a/doc/doxygen/images/channel_with_cylinder_2d.png b/doc/doxygen/images/channel_with_cylinder_2d.png new file mode 100644 index 0000000000..e22e83b1ea Binary files /dev/null and b/doc/doxygen/images/channel_with_cylinder_2d.png differ diff --git a/doc/doxygen/images/channel_with_cylinder_2d_manifolds.png b/doc/doxygen/images/channel_with_cylinder_2d_manifolds.png new file mode 100644 index 0000000000..b862e0897b Binary files /dev/null and b/doc/doxygen/images/channel_with_cylinder_2d_manifolds.png differ diff --git a/doc/doxygen/images/channel_with_cylinder_3d.png b/doc/doxygen/images/channel_with_cylinder_3d.png new file mode 100644 index 0000000000..80deecf43e Binary files /dev/null and b/doc/doxygen/images/channel_with_cylinder_3d.png differ diff --git a/doc/news/changes/major/20180704DavidWells b/doc/news/changes/major/20180704DavidWells new file mode 100644 index 0000000000..0a093f6918 --- /dev/null +++ b/doc/news/changes/major/20180704DavidWells @@ -0,0 +1,6 @@ +New: A new function GridGenerator::channel_with_cylinder has been added. This +function generates a grid corresponding to the classic flow past a cylinder test +problem, and uses manifolds to blend between the description of the cylinder and +the Cartesian bulk geometry. +
+(2018/07/04, David Wells) diff --git a/include/deal.II/grid/grid_generator.h b/include/deal.II/grid/grid_generator.h index bd277e3592..4582bc531d 100644 --- a/include/deal.II/grid/grid_generator.h +++ b/include/deal.II/grid/grid_generator.h @@ -367,6 +367,99 @@ namespace GridGenerator const unsigned int n_slices = 2, const bool colorize = false); + /** + * Generate a grid consisting of a channel with a cylinder. This is a common + * benchmark for Navier-Stokes solvers. The geometry consists of a channel + * of size $[0, 2.2] \times [0, 0.41] \times [0, 0.41] $ (where the $z$ + * dimension is omitted in 2D) with a cylinder, parallel to the $z$ axis + * with diameter $0.1$, centered at $(0.2, 0.2, 0)$. The channel has three + * distinct regions: + *
    + *
  1. If @p n_shells is greater than zero, then there are that many shells + * centered around the cylinder,
    2. + *
  2. a blending region between the shells and the rest of the + * triangulation, and
    3. + *
  3. a bulk region consisting of Cartesian cells.
    4. + *
+ * Since the cylinder is slightly offset from the center of the channel, + * this geometry results in vortex shedding at moderate Reynolds + * numbers. Here is the grid (after one global refinement) in 2D: + * + * @image html channel_with_cylinder_2d.png + * + * and in 3D: + * + * @image html channel_with_cylinder_3d.png + * + * The resulting Triangulation uses three manifolds: a PolarManifold (in 2D) + * or CylindricalManifold (in 3D) with manifold id $0$, a + * TransfiniteInterpolationManifold with manifold id $1$, and a FlatManifold + * everywhere else. For more information on this topic see @ref + * GlossManifoldIndicator "the glossary entry on manifold indicators". The + * cell faces on the cylinder and surrounding shells have manifold ids of + * $0$, while the cell volumes adjacent to the shells (or, if they do not + * exist, the cylinder) have a manifold id of $1$. Put another way: this + * grid uses TransfiniteInterpolationManifold to smoothly transition from + * the shells (generated with GridGenerator::concentric_hyper_shells) to the + * bulk region. All other cell volumes and faces have manifold id + * numbers::flat_manifold_id and use FlatManifold. All cells with id + * numbers::flat_manifold_id are rectangular prisms aligned with the + * coordinate axes. + * + * The picture below shows part of the 2D grid (using all default arguments + * to this function) after two global refinements. The cells with manifold + * id $0$ are orange (the polar manifold id), cells with manifold id $1$ are + * yellow (the transfinite interpolation manifold id), and the ones with + * manifold id numbers::flat_manifold_id are cyan: + * + * @image html channel_with_cylinder_2d_manifolds.png + * + * @param tria Triangulation to create. Must be empty upon calling this + * function. + * + * @param shell_region_width Width of the layer of shells around the cylinder. + * This value should be between $0$ and $0.05$; the default value is $0.03$. + * + * @param n_shells Number of shells to use in the shell layer. + * + * @param skewness Parameter controlling how close the shells are + * to the cylinder: see the mathematical definition given in + * GridGenerator::concentric_hyper_shells. + * + * @param colorize Assign different boundary ids if set to true. For more + * information on boundary indicators see + * @ref GlossBoundaryIndicator "this glossary entry". + * The left boundary (at $x = 0$) is assigned an id of $0$, the right + * boundary (at $x = 2.2$) is assigned an id of $1$, the cylinder boundary + * is assigned an id of $2$, and the channel walls are assigned an id of + * $3$. + * + * See the original paper for more information: + * @code{.bib} + * @inbook{schafer1996, + * author = {Sch{\"a}fer, M. and Turek, S. and Durst, F. and Krause, E. + * and Rannacher, R.}, + * title = {Benchmark Computations of Laminar Flow Around a Cylinder}, + * bookTitle = {Flow Simulation with High-Performance Computers II: DFG + * Priority Research Programme Results 1993--1995}, + * year = {1996}, + * publisher = {Vieweg+Teubner Verlag}, + * address = {Wiesbaden}, + * pages = {547--566}, + * isbn = {978-3-322-89849-4}, + * doi = {10.1007/978-3-322-89849-4_39}, + * url = {https://doi.org/10.1007/978-3-322-89849-4_39} + * } + * @endcode + */ + template + void + channel_with_cylinder(Triangulation &tria, + const double shell_region_width = 0.03, + const unsigned int n_shells = 2, + const double skewness = 2.0, + const bool colorize = false); + /** * A general quadrilateral in 2d or a general hexahedron in 3d. It is the * responsibility of the user to provide the vertices in the right order (see @@ -954,7 +1047,7 @@ namespace GridGenerator torus(Triangulation &tria, const double R, const double r); /** - * This class produces a square in the xy-plane with a cylindrical + * This function produces a square in the xy-plane with a cylindrical * hole in the middle. The square and the circle are centered at the * origin. In 3d, this geometry is extruded in $z$ direction to the interval * $[0,L]$. @@ -1564,8 +1657,28 @@ namespace GridGenerator const double, const unsigned int, const bool); -#endif + template <> + void channel_with_cylinder(Triangulation<1> &, + const double, + const unsigned int, + const double, + const bool); + + template <> + void channel_with_cylinder(Triangulation<2> &, + const double, + const unsigned int, + const double, + const bool); + + template <> + void channel_with_cylinder(Triangulation<3> &, + const double, + const unsigned int, + const double, + const bool); +#endif } // namespace GridGenerator diff --git a/source/grid/grid_generator.cc b/source/grid/grid_generator.cc index c995c39781..ffe84275ee 100644 --- a/source/grid/grid_generator.cc +++ b/source/grid/grid_generator.cc @@ -26,7 +26,6 @@ #include #include -#include #include DEAL_II_NAMESPACE_OPEN @@ -1931,6 +1930,19 @@ namespace GridGenerator } + + template <> + void channel_with_cylinder(Triangulation<1> & /*tria*/, + const double /*shell_region_width*/, + const unsigned int /*n_shells*/, + const double /*skewness*/, + const bool /*colorize*/) + { + Assert(false, ExcNotImplemented()); + } + + + namespace internal { // helper function to check if point is in 2D box @@ -1957,9 +1969,10 @@ namespace GridGenerator length = std::min(length, cell->line(n)->diameter()); return length; } - } // namespace internal + + template <> void plate_with_a_hole(Triangulation<2> & tria, const double inner_radius, @@ -2187,6 +2200,253 @@ namespace GridGenerator + template <> + void channel_with_cylinder(Triangulation<2> & tria, + const double shell_region_width, + const unsigned int n_shells, + const double skewness, + const bool colorize) + { + Assert(0.0 <= shell_region_width && shell_region_width < 0.05, + ExcMessage("The width of the shell region must be less than 0.05 " + "(and preferably close to 0.03)")); + const types::manifold_id polar_manifold_id = 0; + const types::manifold_id tfi_manifold_id = 1; + + // We begin by setting up a grid that is 4 by 22 cells. While not + // squares, these have pretty good aspect ratios. + Triangulation<2> bulk_tria; + GridGenerator::subdivided_hyper_rectangle(bulk_tria, + {22u, 4u}, + Point<2>(0.0, 0.0), + Point<2>(2.2, 0.41)); + // bulk_tria now looks like this: + // + // +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ + // | | | | | | | | | | | | | | | | | | | | | | | + // +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ + // | |XX|XX| | | | | | | | | | | | | | | | | | | | + // +--+--O--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ + // | |XX|XX| | | | | | | | | | | | | | | | | | | | + // +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ + // | | | | | | | | | | | | | | | | | | | | | | | + // +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ + // + // Note that these cells are not quite squares: they are all 0.1 by + // 0.1025. + // + // The next step is to remove the cells marked with XXs: we will place + // the grid around the cylinder there later. The next loop does two + // things: + // 1. Determines which cells need to be removed from the Triangulation + // (i.e., find the cells marked with XX in the picture). + // 2. Finds the location of the vertex marked with 'O' and uses that to + // calculate the shift vector for aligning cylinder_tria with + // tria_without_cylinder. + std::set::active_cell_iterator> cells_to_remove; + Tensor<1, 2> cylinder_triangulation_offset; + for (const auto &cell : bulk_tria.active_cell_iterators()) + { + if ((cell->center() - Point<2>(0.2, 0.2)).norm() < 0.15) + cells_to_remove.insert(cell); + + if (cylinder_triangulation_offset == Tensor<1, 2>()) + { + for (unsigned int vertex_n = 0; + vertex_n < GeometryInfo<2>::vertices_per_cell; + ++vertex_n) + if (cell->vertex(vertex_n) == Point<2>()) + { + // cylinder_tria is centered at zero, so we need to + // shift it up and to the right by two cells: + cylinder_triangulation_offset = + 2.0 * (cell->vertex(3) - Point<2>()); + break; + } + } + } + Triangulation<2> tria_without_cylinder; + GridGenerator::create_triangulation_with_removed_cells( + bulk_tria, cells_to_remove, tria_without_cylinder); + + // set up the cylinder triangulation. Note that this function sets the + // manifold ids of the interior boundary cells to 0 + // (polar_manifold_id). + Triangulation<2> cylinder_tria; + GridGenerator::hyper_cube_with_cylindrical_hole(cylinder_tria, + 0.05 + shell_region_width, + 0.41 / 4.0); + // The bulk cells are not quite squares, so we need to move the left + // and right sides of cylinder_tria inwards so that it fits in + // bulk_tria: + for (auto &cell : cylinder_tria.active_cell_iterators()) + for (unsigned int vertex_n = 0; + vertex_n < GeometryInfo<2>::vertices_per_cell; + ++vertex_n) + { + if (std::abs(cell->vertex(vertex_n)[0] - -0.41 / 4.0) < 1e-10) + cell->vertex(vertex_n)[0] = -0.1; + else if (std::abs(cell->vertex(vertex_n)[0] - 0.41 / 4.0) < 1e-10) + cell->vertex(vertex_n)[0] = 0.1; + } + + // Assign interior manifold ids to be the TFI id. + for (auto &cell : cylinder_tria.active_cell_iterators()) + { + cell->set_manifold_id(tfi_manifold_id); + for (unsigned int face_n = 0; face_n < GeometryInfo<2>::faces_per_cell; + ++face_n) + if (!cell->face(face_n)->at_boundary()) + cell->face(face_n)->set_manifold_id(tfi_manifold_id); + } + if (0.0 < shell_region_width) + { + Assert(0 < n_shells, + ExcMessage("If the shell region has positive width then " + "there must be at least one shell.")); + Triangulation<2> shell_tria; + GridGenerator::concentric_hyper_shells(shell_tria, + Point<2>(), + 0.05, + 0.05 + shell_region_width, + n_shells, + skewness, + 8); + + // Make the tolerance as large as possible since these cells can + // be quite close together + const double vertex_tolerance = + std::min(internal::minimal_vertex_distance(shell_tria), + internal::minimal_vertex_distance(cylinder_tria)) * + 0.5; + + shell_tria.set_all_manifold_ids(polar_manifold_id); + Triangulation<2> temp; + GridGenerator::merge_triangulations( + shell_tria, cylinder_tria, temp, vertex_tolerance, true); + cylinder_tria = std::move(temp); + } + GridTools::shift(cylinder_triangulation_offset, cylinder_tria); + + // Compute the tolerance again, since the shells may be very close to + // each-other: + const double vertex_tolerance = + std::min(internal::minimal_vertex_distance(tria_without_cylinder), + internal::minimal_vertex_distance(cylinder_tria)) / + 10; + GridGenerator::merge_triangulations( + tria_without_cylinder, cylinder_tria, tria, vertex_tolerance, true); + + // Ensure that all manifold ids on a polar cell really are set to the + // polar manifold id: + for (auto &cell : tria.active_cell_iterators()) + if (cell->manifold_id() == polar_manifold_id) + cell->set_all_manifold_ids(polar_manifold_id); + + // Ensure that all other manifold ids (including the interior faces + // opposite the cylinder) are set to the flat manifold id: + for (const auto &cell : tria.active_cell_iterators()) + if (cell->manifold_id() != polar_manifold_id && + cell->manifold_id() != tfi_manifold_id) + cell->set_all_manifold_ids(numbers::flat_manifold_id); + + // We need to calculate the current center so that we can move it later: + // to start get a unique list of (points to) vertices on the cylinder + std::vector *> cylinder_pointers; + for (const auto &face : tria.active_face_iterators()) + if (face->manifold_id() == polar_manifold_id) + { + cylinder_pointers.push_back(&face->vertex(0)); + cylinder_pointers.push_back(&face->vertex(1)); + } + // de-duplicate + std::sort(cylinder_pointers.begin(), cylinder_pointers.end()); + cylinder_pointers.erase(std::unique(cylinder_pointers.begin(), + cylinder_pointers.end()), + cylinder_pointers.end()); + + // find the current center... + Point<2> center; + for (const Point<2> *const ptr : cylinder_pointers) + center += *ptr / double(cylinder_pointers.size()); + + // and recenter at (0.2, 0.2) + for (Point<2> *const ptr : cylinder_pointers) + *ptr += Point<2>(0.2, 0.2) - center; + + // attach manifolds + PolarManifold<2> polar_manifold(Point<2>(0.2, 0.2)); + tria.set_manifold(polar_manifold_id, polar_manifold); + TransfiniteInterpolationManifold<2> inner_manifold; + inner_manifold.initialize(tria); + tria.set_manifold(tfi_manifold_id, inner_manifold); + + if (colorize) + for (auto &face : tria.active_face_iterators()) + if (face->at_boundary()) + { + const Point<2> center = face->center(); + // left side + if (std::abs(center[0] - 0.0) < 1e-10) + face->set_boundary_id(0); + // right side + else if (std::abs(center[0] - 2.2) < 1e-10) + face->set_boundary_id(1); + // cylinder boundary + else if (face->manifold_id() == polar_manifold_id) + face->set_boundary_id(2); + // sides of channel + else + { + Assert(std::abs(center[1] - 0.00) < 1.0e-10 || + std::abs(center[1] - 0.41) < 1.0e-10, + ExcInternalError()); + face->set_boundary_id(3); + } + } + } + + + + template <> + void channel_with_cylinder(Triangulation<3> & tria, + const double shell_region_width, + const unsigned int n_shells, + const double skewness, + const bool colorize) + { + Triangulation<2> tria_2; + channel_with_cylinder( + tria_2, shell_region_width, n_shells, skewness, colorize); + extrude_triangulation(tria_2, 5, 0.41, tria, true); + + // set up the new 3D manifolds + const types::manifold_id cylindrical_manifold_id = 0; + const types::manifold_id tfi_manifold_id = 1; + const PolarManifold<2> *const m_ptr = + dynamic_cast *>( + &tria_2.get_manifold(cylindrical_manifold_id)); + Assert(m_ptr != nullptr, ExcInternalError()); + const Point<3> axial_point(m_ptr->center[0], m_ptr->center[1], 0.0); + const Tensor<1, 3> direction{{0.0, 0.0, 1.0}}; + + const CylindricalManifold<3> cylindrical_manifold(direction, axial_point); + TransfiniteInterpolationManifold<3> inner_manifold; + inner_manifold.initialize(tria); + tria.set_manifold(cylindrical_manifold_id, cylindrical_manifold); + tria.set_manifold(tfi_manifold_id, inner_manifold); + + // From extrude_triangulation: since the maximum boundary id of tria_2 was + // 3, the bottom boundary id is 4 and the top is 5: both are walls, so set + // them to 3 + if (colorize) + for (auto &face : tria.active_face_iterators()) + if (face->boundary_id() == 4 || face->boundary_id() == 5) + face->set_boundary_id(3); + } + + + template void hyper_cross(Triangulation & tria, diff --git a/tests/grid/channel_flow.cc b/tests/grid/channel_flow.cc new file mode 100644 index 0000000000..9e1ecb11a9 --- /dev/null +++ b/tests/grid/channel_flow.cc @@ -0,0 +1,95 @@ +// --------------------------------------------------------------------- +// +// Copyright (C) 2018 by the deal.II authors +// +// This file is part of the deal.II library. +// +// The deal.II library is free software; you can use it, redistribute +// it, and/or modify it under the terms of the GNU Lesser General +// Public License as published by the Free Software Foundation; either +// version 2.1 of the License, or (at your option) any later version. +// The full text of the license can be found in the file LICENSE.md at +// the top level directory of deal.II. +// +// --------------------------------------------------------------------- + +// Test GridGenerator::channel_with_cylinder(). The output generated here is +// similar to that generated in extrude_copy_manifold. + +#include +#include +#include + +#include "../tests.h" + +template +void +test() +{ + Triangulation triangulation; + GridGenerator::channel_with_cylinder(triangulation, 0.03, 4, 2.0, true); + + std::map>> + manifold_to_face_centers; + std::map>> + boundary_to_face_centers; + + for (const auto &face : triangulation.active_face_iterators()) + { + manifold_to_face_centers[face->manifold_id()].push_back(face->center()); + boundary_to_face_centers[face->boundary_id()].push_back(face->center()); + } + + deallog << "face centers:" << std::endl; + for (std::pair>> &key : + manifold_to_face_centers) + { + if (key.first == numbers::flat_manifold_id) + continue; + deallog << "manifold id: " << key.first << std::endl; + for (const Point &point : key.second) + { + deallog << point[0] << ", " << point[1]; + if (dim == 3) + deallog << ", " << point[2]; + deallog << std::endl; + } + } + for (std::pair>> &key : + boundary_to_face_centers) + { + if (key.first == numbers::internal_face_boundary_id) + continue; + deallog << "boundary id: " << key.first << std::endl; + for (const Point &point : key.second) + { + deallog << point[0] << ", " << point[1]; + if (dim == 3) + deallog << ", " << point[2]; + deallog << std::endl; + } + } + + // reenable if we want to look at pictures + if (false) + { + std::ofstream out("out-" + std::to_string(dim) + ".vtu"); + GridOut grid_out; + grid_out.write_vtu(triangulation, out); + } +} + + +int +main() +{ + initlog(); + + deallog.push("2d"); + test<2>(); + deallog.pop(); + + deallog.push("3d"); + test<3>(); + deallog.pop(); +} diff --git a/tests/grid/channel_flow.output b/tests/grid/channel_flow.output new file mode 100644 index 0000000000..1618d8bfbc --- /dev/null +++ b/tests/grid/channel_flow.output @@ -0,0 +1,1163 @@ + +DEAL:2d::face centers: +DEAL:2d::manifold id: 0 +DEAL:2d::0.268284, 0.171716 +DEAL:2d::0.268284, 0.228284 +DEAL:2d::0.228284, 0.268284 +DEAL:2d::0.171716, 0.268284 +DEAL:2d::0.131716, 0.228284 +DEAL:2d::0.131716, 0.171716 +DEAL:2d::0.171716, 0.131716 +DEAL:2d::0.228284, 0.131716 +DEAL:2d::0.272810, 0.200000 +DEAL:2d::0.256009, 0.176800 +DEAL:2d::0.251484, 0.251484 +DEAL:2d::0.256009, 0.223200 +DEAL:2d::0.223200, 0.256009 +DEAL:2d::0.200000, 0.272810 +DEAL:2d::0.176800, 0.256009 +DEAL:2d::0.148516, 0.251484 +DEAL:2d::0.143991, 0.223200 +DEAL:2d::0.127190, 0.200000 +DEAL:2d::0.143991, 0.176800 +DEAL:2d::0.148516, 0.148516 +DEAL:2d::0.200000, 0.127190 +DEAL:2d::0.176800, 0.143991 +DEAL:2d::0.251484, 0.148516 +DEAL:2d::0.223200, 0.143991 +DEAL:2d::0.260959, 0.200000 +DEAL:2d::0.248055, 0.180095 +DEAL:2d::0.243105, 0.243105 +DEAL:2d::0.248055, 0.219905 +DEAL:2d::0.219905, 0.248055 +DEAL:2d::0.200000, 0.260959 +DEAL:2d::0.180095, 0.248055 +DEAL:2d::0.156895, 0.243105 +DEAL:2d::0.151945, 0.219905 +DEAL:2d::0.139041, 0.200000 +DEAL:2d::0.151945, 0.180095 +DEAL:2d::0.156895, 0.156895 +DEAL:2d::0.200000, 0.139041 +DEAL:2d::0.180095, 0.151945 +DEAL:2d::0.243105, 0.156895 +DEAL:2d::0.219905, 0.151945 +DEAL:2d::0.254066, 0.200000 +DEAL:2d::0.244242, 0.181675 +DEAL:2d::0.238230, 0.238230 +DEAL:2d::0.244242, 0.218325 +DEAL:2d::0.218325, 0.244242 +DEAL:2d::0.200000, 0.254066 +DEAL:2d::0.181675, 0.244242 +DEAL:2d::0.161770, 0.238230 +DEAL:2d::0.155758, 0.218325 +DEAL:2d::0.145934, 0.200000 +DEAL:2d::0.155758, 0.181675 +DEAL:2d::0.161770, 0.161770 +DEAL:2d::0.200000, 0.145934 +DEAL:2d::0.181675, 0.155758 +DEAL:2d::0.238230, 0.161770 +DEAL:2d::0.218325, 0.155758 +DEAL:2d::0.250916, 0.200000 +DEAL:2d::0.242678, 0.182322 +DEAL:2d::0.236003, 0.236003 +DEAL:2d::0.242678, 0.217678 +DEAL:2d::0.217678, 0.242678 +DEAL:2d::0.200000, 0.250916 +DEAL:2d::0.182322, 0.242678 +DEAL:2d::0.163997, 0.236003 +DEAL:2d::0.157322, 0.217678 +DEAL:2d::0.149084, 0.200000 +DEAL:2d::0.157322, 0.182322 +DEAL:2d::0.163997, 0.163997 +DEAL:2d::0.200000, 0.149084 +DEAL:2d::0.182322, 0.157322 +DEAL:2d::0.236003, 0.163997 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