{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from IPython.display import Image\n",
    "\n",
    "\n",
    "from tyssue import config, Sheet, SheetGeometry, History, EventManager\n",
    "from tyssue.draw import sheet_view\n",
    "from tyssue.generation import three_faces_sheet\n",
    "from tyssue.draw.plt_draw import plot_forces\n",
    "\n",
    "from tyssue.dynamics import PlanarModel\n",
    "\n",
    "from tyssue.solvers.viscous import EulerSolver\n",
    "from tyssue.draw.plt_draw import create_gif\n",
    "\n",
    "\n",
    "geom  = SheetGeometry\n",
    "model = PlanarModel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebooks demonstrates usage of the time dependant solver `EulerSolver` in the simplest case where we solve\n",
    "$$\\eta_i \\frac{d\\mathbf{r}_i}{dt}  = \\mathbf{F}_i = - \\mathbf{\\nabla}_i E$$\n",
    "\n",
    "The model is defined in the same way it is defined for the quasistatic solver."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Simple forward Euler solver\n",
    "\n",
    "$$\\mathbf{r}_i(t+dt) = \\mathbf{r}_i(t) + \\frac{\\mathbf{F}_i(t)}{\\eta} dt$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sheet = Sheet('3', *three_faces_sheet())\n",
    "geom.update_all(sheet)\n",
    "sheet.settings['threshold_length'] = 1e-3\n",
    "\n",
    "sheet.update_specs(config.dynamics.quasistatic_plane_spec())\n",
    "sheet.face_df[\"prefered_area\"] = sheet.face_df[\"area\"].mean()\n",
    "history = History(sheet, extra_cols={\"edge\":[\"dx\", \"dy\"]})\n",
    "\n",
    "sheet.vert_df['viscosity'] = 1.0\n",
    "sheet.edge_df.loc[[0, 17],  'line_tension'] *= 4\n",
    "\n",
    "fig, ax = plot_forces(sheet, geom, model, ['x', 'y'], 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solver instanciation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "solver = EulerSolver(\n",
    "    sheet,\n",
    "    geom,\n",
    "    model,\n",
    "    history=history,\n",
    "    auto_reconnect=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The solver's `solve` method accepts a `on_topo_change` function as argument. This function is executed each time a topology change occurs. Here, we reste the line tension to its original value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def on_topo_change(sheet):\n",
    "    print(\"reseting tension\")\n",
    "    sheet.edge_df[\"line_tension\"] = sheet.specs[\"edge\"][\"line_tension\"]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving from $t = 0$ to $t = 8$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "res = solver.solve(tf=8, dt=0.05, on_topo_change=on_topo_change,\n",
    "                   topo_change_args=(solver.eptm,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Showing the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "create_gif(solver.history, \"sheet3.gif\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Image(\"sheet3.gif\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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