{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pystencils as ps\n",
    "from lbmpy.session import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial 02: Setting up geometry and boundary conditions\n",
    "\n",
    "In this tutorial you will learn how to set up boundaries for your LBM simulation. \n",
    "We begin with simple setup for parametric geometries, then we'll see how to set up spatially and temporally varying velocity boundary conditions.\n",
    "\n",
    "## Geometry Setup\n",
    "\n",
    "Lets start with a 3D simulation of a pipe. The flow should be along the x axis, with a circular cross section \n",
    "in the y-z plane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "domain_size = (64, 16, 16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "lbm_config = LBMConfig(stencil=Stencil.D3Q27, method=Method.SRT, relaxation_rate=1.9, force=(1e-6, 0, 0))\n",
    "config = CreateKernelConfig(target=ps.Target.CPU)\n",
    "\n",
    "sc1 = LatticeBoltzmannStep(domain_size=domain_size,\n",
    "                           periodicity=(True, False, False),\n",
    "                           lbm_config=lbm_config,\n",
    "                           config=config)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For now the flow should be driven by an external force which we already specified. Additionally we have enabled perdiodicity in x direction. Now the circular pipe needs to be created. Therefor we use a mask callback function that gets x,y,z coordiante arrays that have the same shape as the domain. The callback function has to return a boolean array, where the boundary is set in cells that are marked with True."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.uint32(2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def pipe_geometry_callback(x, y, z):\n",
    "    radius = domain_size[1] / 2\n",
    "    y_mid = domain_size[1] / 2\n",
    "    z_mid = domain_size[2] / 2\n",
    "    return (y - y_mid) ** 2 + (z - z_mid) ** 2 > radius ** 2\n",
    "\n",
    "\n",
    "wall = NoSlip()\n",
    "sc1.boundary_handling.set_boundary(wall, mask_callback=pipe_geometry_callback)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we plot a cross section through our domain to see if the boundary setup worked. A slice has to be passed in to specify which plane of the 3D domain we want to plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1280x960 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=200)\n",
    "plt.boundary_handling(sc1.boundary_handling, ps.make_slice[0.5, :, :])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the setup is complete. We can run it and look at the velocity profile in the pipe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1280x960 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sc1.run(500)\n",
    "plt.figure(dpi=200)\n",
    "plt.scalar_field(sc1.velocity[domain_size[0] // 2, :, :, 0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Boundary Setup\n",
    "\n",
    "Now instead of creating a periodic, force driven channel, we want to drive the flow with a velocity bounce back boundary condition (UBB) at the inlet and a outflow boundary at the outlet. We want the inflow velocity boundary set up to already prescribe the correct, parabolic flow profile. That means we need a different velocity value at each cell. The outflow boundary condition takes the following form:\n",
    "$$ f_{\\overline{1}jkxyzt} = f_{\\overline{1}jk(x - \\Delta x)yz(t - \\Delta t)} \\left(c \\theta^{\\frac{1}{2}} -u \\right) \\frac{\\Delta t}{\\Delta x} + \\left(1 - \\left(c \\theta^{\\frac{1}{2}} -u \\right) \\frac{\\Delta t}{\\Delta x} \\right) f_{\\overline{1}jk(x - \\Delta x)yzt}$$\n",
    "More information on the outflow condition can be found in appendix F in https://doi.org/10.1016/j.camwa.2015.05.001\n",
    "\n",
    "Again, we set up a scenario, but this time without external force and without periodicity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "lbm_config = LBMConfig(stencil=Stencil.D3Q27, method=Method.SRT, relaxation_rate=1.9)\n",
    "config = CreateKernelConfig(target=ps.Target.CPU)\n",
    "\n",
    "sc2 = LatticeBoltzmannStep(domain_size=domain_size,\n",
    "                           lbm_config=lbm_config,\n",
    "                           config=config)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now another callback function is required to specify the velocities. This callback gets a boundaryData object, that can be used to get an array of `linkPositions`, `fluidCellPositions` and `boundaryCellPositions` of all boundary links. The object also behaves like a dict where the boundary data can be queried and set by name.\n",
    "Which data one can set, and how its called depends on the concrete boundary condition. The UBB has `vel_0` until `vel_2` data for the x,y and z components of the velocity.\n",
    "\n",
    "This example also demonstrates how to change boundary parameters during simulation. Here we introduced an activate flag: when True a parabolic inflow is set, when False no inflow velocity is prescribed. \n",
    "We'll see later how this is used to turn the inflow on and off. With this technique also time dependent boundary information can be set. Reconfiguring the boundary is costly when running GPU simulations, since the data has to be transferred from CPU to GPU."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.uint32(4)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def velocity_info_callback(boundary_data, activate=True, **_):\n",
    "    boundary_data['vel_1'] = 0\n",
    "    boundary_data['vel_2'] = 0\n",
    "    \n",
    "    if activate:\n",
    "        u_max = 0.1\n",
    "        y, z = boundary_data.link_positions(1), boundary_data.link_positions(2)\n",
    "        radius = domain_size[1] // 2\n",
    "        centered_y = y - radius\n",
    "        centered_z = z - radius\n",
    "        dist_to_center = np.sqrt(centered_y**2 + centered_z**2)\n",
    "        boundary_data['vel_0'] = u_max * (1 - dist_to_center / radius)\n",
    "    else:\n",
    "        boundary_data['vel_0'] = 0\n",
    "    \n",
    "    \n",
    "inflow = UBB(velocity_info_callback, dim=sc2.method.dim)\n",
    "\n",
    "stencil = LBStencil(Stencil.D3Q27)\n",
    "outflow = ExtrapolationOutflow(stencil[4], sc2.method)\n",
    "\n",
    "sc2.boundary_handling.set_boundary(inflow, ps.make_slice[0, :, :])\n",
    "sc2.boundary_handling.set_boundary(outflow, ps.make_slice[-1, :, :])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lastly we can use the callback function from above to set the pipe geometry. This is intentionally done at the end of the setup to overwrite the in- and outflow boundaries in the outermost slices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.uint32(8)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc2.boundary_handling.set_boundary(wall, mask_callback=pipe_geometry_callback)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see the full setup, a few slices through the domain are plotted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2800x1600 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rc('figure', figsize=(14, 8), dpi=200)\n",
    "\n",
    "plt.subplot(231)\n",
    "plt.boundary_handling(sc2.boundary_handling, ps.make_slice[0, :, :], show_legend=False)\n",
    "plt.title('Inflow')\n",
    "\n",
    "plt.subplot(232)\n",
    "plt.boundary_handling(sc2.boundary_handling, ps.make_slice[0.5, :, :], show_legend=False)\n",
    "plt.title('Middle')\n",
    "\n",
    "plt.subplot(233)\n",
    "plt.boundary_handling(sc2.boundary_handling, ps.make_slice[-1, :, :], show_legend=False)\n",
    "plt.title('Outflow')\n",
    "\n",
    "plt.subplot(212)\n",
    "plt.boundary_handling(sc2.boundary_handling, ps.make_slice[:, 0.5, :], show_legend=True)\n",
    "plt.title('Cross section');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We run the channel for a few steps..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2800x1600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sc2.run(20)\n",
    "plt.figure(dpi=200)\n",
    "plt.scalar_field(sc2.velocity[:, 0.5, :, 0])\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then switch off the inflow..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "sc2.boundary_handling.trigger_reinitialization_of_boundary_data(activate=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2800x1600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sc2.run(50)\n",
    "plt.figure(dpi=200)\n",
    "plt.scalar_field(sc2.velocity[:, 0.5, :, 0])\n",
    "plt.colorbar();"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv (3.12.12)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}