{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Tutorial 9: Stokes equation"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "    This tutorial is under construction, but the code below is already functional.\n",
    "\n",
    "Driver that computes the lid-driven cavity benchmark at low Reynolds numbers\n",
    "when using a mixed FE Q(k)/Pdisc(k-1)."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Load Gridap library"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using Gridap"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Discrete model"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "n = 100\n",
    "domain = (0,1,0,1)\n",
    "partition = (n,n)\n",
    "model = CartesianDiscreteModel(domain, partition)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Define Dirichlet boundaries"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "labels = get_face_labeling(model)\n",
    "add_tag_from_tags!(labels,\"diri1\",[6,])\n",
    "add_tag_from_tags!(labels,\"diri0\",[1,2,3,4,5,7,8])"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Define test FESpaces (Q2/P1(disc) pair)"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "V = TestFESpace(\n",
    "  reffe=:QLagrangian, conformity=:H1, valuetype=VectorValue{2,Float64},\n",
    "  model=model, labels=labels, order=2, dirichlet_tags=[\"diri0\",\"diri1\"])\n",
    "Q = TestFESpace(\n",
    "  reffe=:PLagrangian, conformity=:L2, valuetype=Float64,\n",
    "  model=model, order=1, constraint=:zeromean)\n",
    "Y = MultiFieldFESpace([V,Q])"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Define trial FESpaces from Dirichlet values"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "u0 = VectorValue(0,0)\n",
    "u1 = VectorValue(1,0)\n",
    "U = TrialFESpace(V,[u0,u1])\n",
    "P = TrialFESpace(Q)\n",
    "X = MultiFieldFESpace([U,P])"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Define integration mesh and quadrature"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "trian = get_triangulation(model); degree = 2\n",
    "quad = CellQuadrature(trian,degree)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Define and solve the FE problem"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "function a(x,y)\n",
    "  v,q = y\n",
    "  u,p = x\n",
    "  ∇(v)⊙∇(u) - (∇⋅v)*p + q*(∇⋅u)\n",
    "end\n",
    "t_Ω = LinearFETerm(a,trian,quad)\n",
    "op = AffineFEOperator(X,Y,t_Ω)\n",
    "uh, ph = solve(op)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Export results to vtk"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "writevtk(trian,\"results\",order=2,cellfields=[\"uh\"=>uh,\"ph\"=>ph])"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "---\n",
    "\n",
    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
   ],
   "metadata": {}
  }
 ],
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