{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "89cc443c",
   "metadata": {},
   "source": [
    "# 123.05: Constant pumping in a confined aquifer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0f52dce9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import timflow.transient as tft\n",
    "\n",
    "from bruggeman.flow1d import bruggeman_123_05_q"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bff96a01",
   "metadata": {},
   "source": [
    "View the function (this will be rendered in LaTeX if `sympy` is installed)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "70051a00",
   "metadata": {},
   "outputs": [],
   "source": [
    "bruggeman_123_05_q"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "088329c4",
   "metadata": {},
   "source": [
    "View the docstring to get a description of the input parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "380d233d",
   "metadata": {},
   "outputs": [],
   "source": [
    "help(bruggeman_123_05_q)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f1b0aca",
   "metadata": {},
   "source": [
    "Define some aquifer parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8080a6a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 5.0  # m/d, hydraulic conductivity\n",
    "D = 10.0  # m  # thickness aquifer\n",
    "Ss = 1e-3 / D  # m^-1, specific storage coeffecient\n",
    "Q = 2.0  # m^3/d, positive Q here means pumping in Timflow"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0338250e",
   "metadata": {},
   "source": [
    "Set up a `timflow` model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6a834ed2",
   "metadata": {},
   "outputs": [],
   "source": [
    "mlconf = tft.ModelMaq(kaq=k, z=[0, -D], Saq=Ss, tmin=1e-3, tmax=1e3, topboundary=\"conf\")\n",
    "ls = tft.DischargeLineSink1D(mlconf, tsandq=[(0, Q)], layers=[0])\n",
    "mlconf.solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bee5845",
   "metadata": {},
   "source": [
    "Compare `timflow` implementation to the analytical solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "629e4a3f",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0, 100, 101)\n",
    "y = np.zeros_like(x)\n",
    "t = np.logspace(-1, 0, 5)\n",
    "\n",
    "plt.figure(figsize=(10, 3))\n",
    "for i in range(len(t)):\n",
    "    h = mlconf.headalongline(x, y, t[i])\n",
    "    plt.plot(x, h.squeeze(), label=f\"t={t[i]:.2f} d\")\n",
    "    ha = bruggeman_123_05_q(x, t[i], -Q / 2, k, D, Ss * D)  # Q/2 because 2-sided flow\n",
    "    plt.plot(x, ha, \"k:\")\n",
    "plt.plot([], [], \"k:\", label=\"Bruggeman 123.05\")\n",
    "plt.legend(loc=(0, 1), frameon=False, ncol=6, fontsize=\"small\")\n",
    "plt.xlabel(\"x [m]\")\n",
    "plt.ylabel(\"drawdown [m]\")\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "da22f6f0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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