{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0ba4268d-6b8a-4773-a640-e1c0db2c18f6",
   "metadata": {},
   "source": [
    "#   $\\hspace 4.cm $                     1D Advection Equation - Particle Method                  #\n",
    "-------------------------------------------------------------------------------------\n",
    "\n",
    "\n",
    "Let $V(t,z) \\in \\mathbb R^d$ be a time-dependent vector field and\n",
    "consider the following linear transport equation\n",
    "$$\n",
    "    \\begin{array}{l}\n",
    "\\displaystyle      \\partial_t \\mu + {\\rm div}_z\\left( V(t,z)\\, \\mu\\right)  \\,=\\, 0,\n",
    "  \\\\[0.9em]\n",
    "  \\mu(0,z) = \\mu^{in}(z)\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "When $\\mu^{in}$ is only a positive measure or $L^1(\\mathbb R^d)$ function, we may define  a\n",
    "notion of weak solution.\n",
    "\n",
    "A weak solution of the Cauchy problem for the conservative transport\n",
    "equation  an element of $\\mu \\in \\mathcal C ([0, T ]; w-\\mathcal M(\\mathbb R^d ))$ that satisfies the initial condition\n",
    "and the equality\n",
    "$$\n",
    "\\int_0^T\\int_{\\mathbb R^d} \\left( \\partial_t + V(t,z)\\cdot\n",
    "  \\nabla_z\\right)\\varphi(t,z) \\,\\mu(t,dz)\\,dt = 0,\n",
    "$$\n",
    "for each $\\varphi \\in \\mathcal C_c^1((0,T)\\times\\mathbb R^d)$.\n",
    "\n",
    "\n",
    "\n",
    "In this Exercise Session, we want to illustrate different numerical phenomena\n",
    "\n",
    "-1- initialization of the data $\\mu^{in}$ using  deterministic and random methods\n",
    "\n",
    "-2- time discretization solver of the characteristic curves : second order scheme\n",
    "\n",
    "-3- numerical reconstruction using spline methods (polynomials of degree 1 and 3)\n",
    "\n",
    "-4- transport phenomena in one dimension\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1e1f78d2-a4ea-43a1-8e58-31eca079ee38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max value exact:     1.0001\n",
      "Max value deposited: 0.9927\n",
      "Total mass exact:    3.5449\n",
      "Total mass deposited:3.5449\n"
     ]
    }
   ],
   "source": [
    "#    1D Advection Equation - Particle Method using Lagrangian particles that carry the quantity $f$.\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#========================= PARAMETERS =========================\n",
    "\n",
    "L  = 15.0             # Domain length\n",
    "T  = 0.10             # Final time\n",
    "Np = 100             # Number of particles\n",
    "Nz = 100             # Number of mesh points \n",
    "dz = L / Nz          # Space step  \n",
    "dt = 0.05            # Time step\n",
    "\n",
    "#  Velocity V(z)\n",
    "def V(z):\n",
    "    return (z-7.50)*(z-7.50)\n",
    "\n",
    "# Initial condition: Gaussian pulse\n",
    "def initial_condition(z):\n",
    "    return np.exp(-((z - 6.0)**2)) + np.exp(-((z-9.0)**2))\n",
    "#    return np.tanh(5*(z - 5.0)) + np.tanh(-5*(z-8.0))\n",
    "\n",
    "\n",
    "#============== INITIALIZE PARTICLES ===============\n",
    "\n",
    "# Deterministic uniform initialization \n",
    "Zp = np.linspace(dz/2, L - dz/2, Np)          \n",
    "Wp = initial_condition(Zp) * (L / Np)      \n",
    "\n",
    "# Random initialization (alternative)\n",
    "#Zp = np.random.uniform(0, L, Np)\n",
    "#Wp = initial_condition(Zp) * (L / Np)\n",
    "\n",
    "\n",
    "# ============= DEPOSIT FUNCTION (P0) =============\n",
    "\n",
    "Z = np.linspace(0, L, Nz, endpoint=False)\n",
    "\n",
    "def deposit_particle0(Zp, Wp, Nz, dz):\n",
    "    rho = np.zeros(Nz)\n",
    "    z_norm = (Zp / dz) % Nz\n",
    "    i = np.floor(z_norm).astype(int)\n",
    "\n",
    "    # Distribute mass to one cell\n",
    "    np.add.at(rho, i,(Wp / dz))\n",
    "    return rho\n",
    "\n",
    "# ============= DEPOSIT FUNCTION (P1) =============\n",
    "\n",
    "\n",
    "def deposit_particle1(Zp, Wp, Nz, dz):\n",
    "    rho = np.zeros(Nz)\n",
    "    z_norm = (Zp / dz) % Nz\n",
    "    i = np.floor(z_norm).astype(int)\n",
    "    frac = z_norm - i\n",
    "    \n",
    "    # Distribute mass to two neighboring cells\n",
    "    np.add.at(rho, i, (1.0 - frac) * (Wp / dz))\n",
    "    np.add.at(rho, (i + 1) % Nz, frac * (Wp / dz))\n",
    "    \n",
    "    return rho\n",
    "\n",
    "# ============= DEPOSIT FUNCTION (P3) =============\n",
    "\n",
    "# ================= CUBIC SPLINE  =================\n",
    "\n",
    "def cubic_spline_kernel(q):\n",
    "    q = np.abs(q)\n",
    "    w = np.zeros_like(q)\n",
    "    \n",
    "    mask1 = q <= 1.0\n",
    "    mask2 = (q > 1.0) & (q <= 2.0)\n",
    "    \n",
    "    w[mask1] = (2/3) - q[mask1]**2 + 0.5 * q[mask1]**3\n",
    "    w[mask2] = (1/6) * (2 - q[mask2])**3\n",
    "    \n",
    "    return w\n",
    "\n",
    "# ================= DEPOSIT   =================\n",
    "\n",
    "def deposit_particle3(Zp, Wp, Nz, dz):\n",
    "    rho = np.zeros(Nz)\n",
    "  \n",
    "    for i, x_i in enumerate(Zp):\n",
    "        dist = Z - x_i\n",
    "        dist = np.minimum(np.abs(dist), L - np.abs(dist))   # shortest periodic distance\n",
    "        q    = dist / dz\n",
    "        # Kernel values\n",
    "        W = cubic_spline_kernel(q) / dz                     # normalized kernel\n",
    "        # Add contribution\n",
    "        rho += Wp[i] * W\n",
    "    \n",
    "    return rho\n",
    "\n",
    "# ============= PLOT INITIAL SOLUTION =============\n",
    "\n",
    "mu = deposit_particle3(Zp, Wp, Nz, dz)\n",
    "\n",
    "plt.figure(figsize=(12, 4))\n",
    "plt.plot(Z, mu, 'r-', label='Deposited from particles', linewidth=2)\n",
    "plt.plot(Z, initial_condition(Z), 'b--', label='Exact initial condition', linewidth=2)\n",
    "plt.xlabel('z')\n",
    "plt.ylabel(r'$\\mu(z)$')\n",
    "plt.title('Initial Density - Particle Method')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Diagnostic\n",
    "print(f\"Max value exact:     {initial_condition(Z).max():.4f}\")\n",
    "print(f\"Max value deposited: {mu.max():.4f}\")\n",
    "print(f\"Total mass exact:    {np.sum(initial_condition(Z)) * dz:.4f}\")\n",
    "print(f\"Total mass deposited:{np.sum(mu) * dz:.4f}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c04cfcb8-e78d-461e-adbb-23589c18c05e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ========================= TIME STEPPING =========================\n",
    "\n",
    "n_steps = int(T / dt)\n",
    "tn  = 0.  \n",
    "Zp1 = Zp \n",
    "Wp1 = Wp \n",
    "\n",
    "for step in range(n_steps):\n",
    "    # first stage Runge-Kutta scheme\n",
    "    Zp1 = Zp + 0.5*V(Zp) * dt                     # Advect particles\n",
    "    Zp1 = Zp1 % L                                 # Periodic boundary\n",
    "    # second stage Runge-Kutta scheme\n",
    "    Zp  = Zp + V(Zp1) * dt                        # Advect particles\n",
    "    Zp = Zp % L                                   # Periodic boundary\n",
    "\n",
    "\n",
    "# ============= PLOT FINAL SOLUTION =============\n",
    "\n",
    "mu0 = deposit_particle0(Zp, Wp, Nz, dz)\n",
    "mu1 = deposit_particle1(Zp, Wp, Nz, dz)\n",
    "mu3 = deposit_particle3(Zp, Wp, Nz, dz)\n",
    "\n",
    "plt.figure(figsize=(12, 4))\n",
    "plt.plot(Z,mu0, 'b.', label='P0 reconstruction distribution', linewidth=1)\n",
    "plt.plot(Z,mu1, 'r-', label='P1 reconstruction distribution', linewidth=3)\n",
    "plt.plot(Z,mu3, 'g--',label='P3 reconstruction distribution', linewidth=2)\n",
    "plt.xlabel('z')\n",
    "plt.ylabel(r'$\\mu(z)$')\n",
    "plt.title('Final density Np=100')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c212444b-da73-4ca3-a930-e40489944f9f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5007b531-b5d0-4ec8-93a4-949063371d71",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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