lectures/hyperbolicEquations.ipynb

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    "\n",
    "#  Hyperbolic equations\n",
    "\n",
    "\n",
    "## Introduction\n",
    "\n",
    "Hyperbolic equations is as subclass of second-order partial differential equations. All second-order partial differential equations can be written on the form\n",
    "\n",
    "$$A \\frac{\\partial^2 f}{\\partial x^2} + B \\frac{\\partial^2 f}{\\partial x \\partial y} + C \\frac{\\partial^2 f}{\\partial y^2} + D \\frac{\\partial f}{\\partial x} +  E \\frac{\\partial f}{\\partial y} + F f + G = 0$$\n",
    "\n",
    "An <i> hyperbolic</i> second-order partial differential equation is an equation on the form above where $B^2-AC > 0$.\n",
    "\n",
    "In science and engineering hyperbolic equations are used to model a variety of physical phenomena. One example is the wave equation, $\\nabla^2 u -\\frac{1}{c^2}\\partial^2_t u = 0$ which, among others,  can describe radio waves, light, sound and seismic waves. Other examples are the kinematic wave equation and the shallow water equation in fluid mechanics. \n",
    "We see that for the wave  equation we have $A= 1,C=-1$, while all the other pre-factors are zero, thus $B^2 - AC = 0 +1 = 1 > 0$, as required to be an hyperbolic equation. \n",
    "\n",
    "In the following we will investigate the numerical solution of the wave equation."
   ]
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    "# The wave equation\n",
    "The wave equation can describe waves in fluids or solid material like rocks or metal.\n",
    "To simplify we will consider the simplified situation with a one-dimensional wave, describing f.ex \n",
    "compression and stretching of a string.\n",
    "\n",
    "The wave equation derives from Newton's law and Hook's law\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "\\rho u_{tt}(x,t) & = & \\sigma_x(x,t) + f(x,t), \\label{eq:1} \\\\\n",
    "\\sigma(x,t)           & = & \\kappa u_x (x,t)\n",
    "            \\label{eq:2}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "Here $u(x,t)$ is the displacement (from equilibrium) of the string\n",
    "and $\\sigma$ is the stress (force per length unit) in the string.\n",
    "The displacement describes motion along the string, i.e. stretching and compression.\n",
    "$\\kappa(x)$ is the stiffness and $\\rho$ is the density of the string.\n",
    "$f(x,t)$ is a driving force (source).\n",
    "\n",
    "Differentiating the second equation above  with respect to $x$ and inserting into\n",
    "the first equation we get\n",
    "\\begin{eqnarray}\n",
    "  \\frac{\\rho}{\\kappa} u_{tt} = u_{xx} + \\frac{f}{\\kappa}.\n",
    "\\end{eqnarray}\n",
    "Where we assume that $\\rho$ is constant. The\n",
    "wave velocity is given by $c^{-2} = \\rho/\\kappa$, so we have\n",
    "\\begin{eqnarray}\n",
    "  c^{-2}(x) u_{tt}(x,t) = u_{xx}(x,t) + s(x,t).\n",
    "\\end{eqnarray}\n",
    "where $s(x,t) = \\frac{f(x,t)}{\\kappa}$.\n",
    "\n",
    "## Numerical Grid\n",
    "We create a grid out of the $x$ and $t$ coordinates as follows\n",
    "\\begin{eqnarray}\n",
    "  x_i & = & i\\Delta x = i h, \\, i=1,\\cdots,n\\\\\n",
    "  t_j & = & j\\Delta t = j k, \\, j=1,\\cdots,m.\n",
    "\\end{eqnarray}\n",
    "We want to compute an approximate solution, $u_{i,j}$ to the true solution\n",
    "$u(x_i,t_j)$ for all gridpoints in the grid.\n",
    "\n",
    "![grid.png](grid.png)\n",
    "\n",
    "## Finite Difference Solution\n",
    "The second order derivatives are approximated with a central difference\n",
    "\\begin{eqnarray}\n",
    "\\frac{u_{i,j+1} -2 u_{i,j} + u_{i,j-1}}{k^2} =\n",
    "c^2_i\\frac{u_{i+1,j} - 2u_{i,j} + u_{i-1,j}}{h^2} + s_{i,j}\n",
    "\\end{eqnarray}\n",
    "This is equal to\n",
    "\\begin{eqnarray}\n",
    "u_{i,j+1} -2 u_{i,j} + u_{i,j-1} =\n",
    "\\frac{k^2c^2_i}{h^2}(u_{i+1,j} - 2u_{i,j} + u_{i-1,j}) + s_{i,j}k^2\n",
    "\\end{eqnarray}\n",
    "Introduce $r^2_i = \\left(\\frac{kc_i}{h}\\right)^2$ to get\n",
    "\\begin{eqnarray}\n",
    "u_{i,j+1} -2 u_{i,j} + u_{i,j-1} =\n",
    "r^2_i(u_{i+1},j - 2u_{i,j} + u_{i-1,j}) + s_{i,j} k^2\n",
    "                                        \\label{eq:diff}\n",
    "\\end{eqnarray}\n",
    "\n",
    "which is solved by\n",
    "\\begin{eqnarray}\n",
    "u_{i,j+1} = 2 u_{i,j} - u_{i,j-1}\n",
    "+r^2_i(u_{i+1},j - 2u_{i,j} + u_{i-1,j}) + s_{i,j} k^2\n",
    "                                        \\label{eq:sol}\n",
    "\\end{eqnarray}\n",
    "\n",
    "## Stability\n",
    "Stability condition\n",
    "\\begin{eqnarray}\n",
    " r = ck/h \\le 1\n",
    "\\end{eqnarray}\n",
    "\n",
    "If $r=1$ the numerical solution is exact!\n",
    "An exact solution to the wave equation is a \n",
    "plane monochromatic wave with frequency $\\omega$ and\n",
    "wavenumber $k_x$ which are constants.\n",
    "\\begin{eqnarray}\n",
    "u(x,t) = \\exp i(k_x x - \\omega t)\n",
    "\\end{eqnarray}\n",
    "Prove that this is a solution!\n",
    "\n",
    "We will now find the stability condition by using\n",
    "the plane wave as a trial solution in the\n",
    "finite-difference solution.\n",
    "\n",
    "First, to avoid confusion, we replace $i$ and $j$ in the\n",
    "finite-difference solution above with indices $m$ (x) and \n",
    "$n$ (time). We then have the displacement $u$ as:\n",
    "    \n",
    "\\begin{eqnarray}\n",
    "u_{m,n} = \\exp i(k_x m h - \\omega n k)\n",
    "\\end{eqnarray}\n",
    "\n",
    "If we insert the above expression for $u$ into the \n",
    "finite-difference solution above (changing $i$ to $m$ \n",
    "and $j$ to $n$ one gets:\n",
    "                                  \n",
    "\\begin{eqnarray}\n",
    "  \\exp(-i\\omega k )  = 2 -\\exp(i\\omega k)   \n",
    "                    + r^2[\\exp(ik_x h)- 2 + \\exp(-ik_x h)]\n",
    "\\end{eqnarray}\n",
    "                                  \n",
    "This can be rearranged to:\n",
    "\\begin{eqnarray}\n",
    "\\exp(-i\\omega k) + \\exp(i\\omega k) = (2-2r^2) +\n",
    "                                     r^2[\\exp(ik_x m h)] + \\exp(-ik_x m h)]\n",
    "\\end{eqnarray}\n",
    "                                  \n",
    "Since $2\\cos(x) = \\exp(ix)+\\exp(-ix)$\n",
    "\n",
    "the relation above can be rewritten to\n",
    "                                  \n",
    "\\begin{eqnarray}\n",
    "\\cos(\\omega k) = (1-r^2) + r^2\\cos(k_x m h) \n",
    "\\end{eqnarray}\n",
    "                \n",
    "                           \n",
    "1. For $r=1$ this gives $\\omega h = k_x m $ which\n",
    "   is the so-called dispersion relation for a plane \n",
    "   wave, which means that $r=1$ corresponds to the exact solution.\n",
    "                            \n",
    "2. For $r < 1$ the finite-difference solution is stable, but not exact.\n",
    "\n",
    "3. For $r>1$ the finite-difference solution is unstable.\n",
    "                                  \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\"Solve 1D elastic equations using displacement\"\"\"\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as pl\n",
    "from math import *\n",
    "\n",
    "#-----------------------------\n",
    "# functions\n",
    "#-----------------------------\n",
    "def ricker(fp,tp,M,dt) :\n",
    "   s=np.zeros((M))\n",
    "   for k in range(0,M):\n",
    "       t=k*dt\n",
    "       wp=2.0*3.14159*fp\n",
    "       s[k] =(1-0.5*pow(wp,2)*pow((t-tp),2))*exp(-0.25*pow(wp,2)*pow(t-tp,2))\n",
    "   return(s)\n",
    "\n",
    "#------------------------------\n",
    "# Main script\n",
    "#-------------------------------\n",
    "M=5000 #No of timesteps\n",
    "N=1000 #No of x grdipoints\n",
    "h=5.0  #Size of each gridcell in the x-direction\n",
    "k=0.0005 #Size of timesteps\n",
    "k=0.001 #This value leads to unstability\n",
    "v0=1500.0 #Wave velocity in m/s\n",
    "v1=2500.0\n",
    "c=np.zeros(N)\n",
    "c[0:int(N/4)]=v0\n",
    "c[int(N/4):N]=v1\n",
    "\n",
    "x=np.linspace(0,N*h,num=N)\n",
    "t=np.linspace(0,M*k,num=M)\n",
    "pl.plot(x,c)\n",
    "pl.xlabel(\"Distance (m)\")\n",
    "pl.ylabel(\"Velocity (m/s)\")\n",
    "pl.show()\n",
    "\n",
    "r=((k*c)/h) \n",
    "spos=N/2\n",
    "s=ricker(15.0,0.1,M,k)\n",
    "\n",
    "pl.plot(t,s)\n",
    "pl.xlabel(\"Time (sec)\")\n",
    "pl.ylabel(\"Amplitude \")\n",
    "pl.show()\n",
    "\n",
    "u=np.zeros((N,M))\n",
    "\n",
    "for j in range(1,M-1):\n",
    "  for i in range(1,N-1):\n",
    "    u[i,j+1] = 2*u[i,j] - u[i,j-1] + r[i]*r[i]*(u[i+1,j]- 2*u[i,j]+u[i-1,j])\n",
    "    if i == spos:\n",
    "      u[i,j+1] = u[i,j+1]+s[j]*k*k\n",
    "\n",
    "    \n",
    "#Set aspect ratio\n",
    "pl.imshow(u,cmap='gray',extent=[0,M*k,N*h,0])\n",
    "ar=1.0\n",
    "ax=pl.gca()\n",
    "asr = 1.0/(ax.get_data_ratio()*ar)\n",
    "pl.Axes.set_aspect(ax,asr)\n",
    "pl.ylabel(\"Distance (m)\")\n",
    "pl.xlabel(\"Time (sec)\")\n",
    "\n",
    "pl.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15081acf",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}