{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bf7176b6",
   "metadata": {},
   "source": [
    "# 1D transient diffusion\n",
    "\n",
    "Transient diffusion problem is one of the most common phenomenon of real flow problems. Compared to the steady-state diffusion problem, non steady-state diffusion problem need to consider **the impact of time derivatives** on constant variables."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc05b0ae",
   "metadata": {},
   "source": [
    "## Problem setup\n",
    "\n",
    "Consider a one-dimensional non steady-state advection problem where a field variable $\\phi$ is transported through the non steady-state diffusion process from $x = 0$ to $x = L$ in a one-dimensional domain. All the initial temprature is $ T = 200^\\circ C$. At one moment, the the east of the field instantly transforms into $0^\\circ C$, while the west maintains insulation. The fluid volumetric heat capacity($\\rho c $) is $1. 0 \\times1 0^{7} \\mathrm{~ J / ( m^{3} \\cdot~ K ) ~} $, $L = 0.02$ m, and the thermal conductivity $k=10$ W/(m $\\cdot$ K). The domain is shown in the figure below.\n",
    "\n",
    "![Adiabatic rod](images/transient_diffusion1d.jpg)\n",
    "\n",
    "The mathematical model for one-dimensional non steady-state diffusion problem is\n",
    "$$\n",
    "\\rho c \\frac{\\partial T}{\\partial t} = \\frac{\\partial}{\\partial x} \\left( k \\frac{\\partial T}{\\partial x} \\right)\n",
    "$$\n",
    "\n",
    "The initial conditions are $T = 200^\\circ C (t=0 \\text{ s})$.\n",
    "The boundary conditions are\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\frac{\\partial T}{\\partial x} &= 0 \\quad && (x=0, t>0 \\text{ s}) \\\\\n",
    "T &= 0 ^\\circ \\text{C} \\quad && (x=L, t>0 \\text{ s})\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "The analytical solution for the problem is\n",
    "\n",
    "$$\n",
    "\\frac{T(x,t)}{200} = \\frac{4}{\\pi} \\sum_{n=1}^{\\infty} \\frac{(-1)^{n+1}}{2n-1} \\exp(-\\alpha \\lambda_n^2 t) \\cos(\\lambda_n x)\n",
    "$$\n",
    "where\n",
    "$$\n",
    "\\lambda_n = \\frac{(2n-1)\\pi}{2L}, \\quad \\alpha = \\frac{k}{\\rho c}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d937ae1",
   "metadata": {},
   "source": [
    "## Solve problem\n",
    "\n",
    "### Define grid\n",
    "\n",
    "Divide the rod evenly into 5 control volumes, as a result, the length of each control volume becomes $\\Delta x=0.004$ m.\n",
    "\n",
    "![Grid](images/transient_diffusion1d_grid.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fb9685b",
   "metadata": {},
   "source": [
    "### Discrete the non steady-state advection equation\n",
    "\n",
    "The control equation of the 1d non steady-state advection equation is \n",
    " $$\\rho c \\; \\frac{\\partial T} {\\partial t}=\\frac{\\partial} {\\partial x} \\Big( k \\; \\frac{\\partial T} {\\partial x} \\Big)+S$$ \n",
    "where the$c$is the specific heat capacity of material and the$k$is the material thermal conductivity.\n",
    "Then we integrate the control equation during the $\\Delta t$ in control volumn.\n",
    "\n",
    "$$\\int_{t}^{t+\\Delta t} \\int_{\\Delta V} \\rho c \\frac{\\partial T} {\\partial t} \\mathrm{d} V \\mathrm{d} t=\\int_{t}^{t+\\Delta t} \\int_{\\Delta V} \\frac{\\partial} {\\partial x} \\Big( k \\frac{\\partial T} {\\partial x} \\Big) \\mathrm{d} V \\mathrm{d} t+\\int_{t}^{t+\\Delta t} \\int_{\\Delta V} S \\mathrm{d} V \\mathrm{d} t $$\n",
    "By Gaussian formula, the volume integral can be converted into area fraction.\n",
    "\n",
    "$$\\int_{\\Delta V} \\biggl[ \\int_{t}^{t+ \\Delta t} \\rho c \\ \\frac{\\partial\\, T} {\\partial t} \\mathrm{d} t \\biggr] \\mathrm{d} V=\\int_{t}^{t+\\Delta t} \\biggl[ \\Bigl( k A \\ \\frac{\\partial\\, T} {\\partial x} \\Bigr)_{e}-\\Bigl( k A \\ \\frac{\\partial\\, T} {\\partial x} \\Bigr)_{w} \\biggr] \\mathrm{d} t+\\int_{t}^{t+\\Delta t} \\overline{{S}} \\ \\Delta V \\mathrm{d} t $$\n",
    "\n",
    "We deal the time derivatives as $$\\frac{T_{P}-T_{P}^{0}} {\\Delta t}$$ where $T_{P}^{0}$ is the temperature of $P$ point at $t$ and $T_{P}$ is the temperature of $P$ point at $t+\\Delta t$.\n",
    "The left side can be wrote as\n",
    "$$\\int_{\\Delta V} \\biggl[ \\int_{t}^{t+\\Delta t} \\rho c \\ \\frac{\\partial\\, T} {\\partial t} \\mathrm{d} t \\biggl] \\mathrm{d} V \\approx\\int_{\\Delta V} \\biggl[ \\int_{t}^{t+\\Delta t} \\rho c \\ \\frac{T_{P}-T_{P}^{\\vee}} {\\Delta t} \\mathrm{d} t \\biggl] \\mathrm{d} V=\\rho c \\left( \\, T_{P}-T_{P}^{\\vee} \\, \\right) \\Delta V $$\n",
    "Eventually, the discreted equation is \n",
    "$$\\rho c({T_P} - T_P^0)\\Delta V = \\int_t^{t + \\Delta } [ ({k_e}A\\;\\frac{{{T_E} - {T_P}}}{{\\Delta {x_{PE}}}}) - ({k_w}A\\;\\frac{{{T_P} - {T_W}}}{{\\Delta {x_{WP}}}})]dt + \\int_t^{t + \\Delta t} {\\overline S } \\Delta Vdt$$\n",
    "\n",
    "To calculate the time integral of the diffusion term on the right side of equation above, we need to provide the relationship between the node temperatures $T_{P}$, $T_{E}$, and $T_{W}$ over time, which is unknown. The usual approach is to use the temperature at time $t$ (such as $T_{P}^{0}$) and the temperature at time $t+\\Delta t$ (such as $T_{P}$) to weight and combine them to form the average temperature within this time interval, and then integrate and calculate. Mathematically, it manifests as \n",
    "$$\\overline{{{{T_{P}}}}}=\\theta T_{P}+( 1-\\theta) \\ T_{P}^{0} $$\n",
    "The time integration is \n",
    "$$I_{T}=\\int_{t}^{t+\\Delta t} T_{P} \\, \\mathrm{d} t=\\left[ \\theta T_{P}+\\left( 1-\\theta\\right) T_{P}^{0} \\right] \\Delta t $$\n",
    "Take it into the discreted equation and to be divided by $A \\Delta t$, we can get \n",
    "\n",
    "$$\\begin{array} {l} {{{{\\rho c \\Big( \\frac{T_{P}-T_{P}^{0}} {\\Delta t} \\Big) \\Delta x=\\theta\\bigg[ \\frac{k_{e} ( T_{E}-T_{P} )} {\\Delta x_{P E}}-\\frac{k_{w} ( T_{P}-T_{W} )} {\\Delta x_{W P}} \\bigg]}}}}  {{{{+( 1-\\theta) \\bigg[ \\frac{k_{e} ( T_{E}^{0}-T_{P}^{0} )} {\\Delta x_{P E}}-\\frac{k_{w} ( T_{P}^{0}-T_{W}^{0} )} {\\Delta x_{W P}} \\bigg]+\\bar{S} \\Delta x}}}} \\\\ \\end{array} $$\n",
    "\n",
    "Organize it into something familiar to us \n",
    "$$\\begin{aligned} {{a_{P} T_{P}=}} & {{} {{} a_{W} \\big[ \\theta T_{W}+( 1 \\!-\\! \\theta) \\, T_{W}^{0} \\big]+a_{E} \\big[ \\theta T_{E}+( 1 \\!-\\! \\theta) \\, T_{E}^{0} \\big]+\\big[ a_{P}^{0} \\!-\\! ( 1 \\!-\\! \\theta) a_{W}-( 1 \\!-\\! \\theta) a_{E} \\big] T_{P}^{0}+b}} \\\\ \\end{aligned} $$\n",
    "where\n",
    "$$\n",
    "a_{W}=\\frac{k_{w}} {\\Delta x_{W P}} \\,, \\, \\, a_{E}=\\frac{k_{e}} {\\Delta x_{P E}} \\,, \\, \\, a_{P}=a_{P}^{0} \\,, \\, \\, a_{P}^{0}=\\rho c \\, \\, \\frac{\\Delta x} {\\Delta t} \\,, b=\\bar{S}\\Delta x\n",
    "$$\n",
    "The choose of $\\theta$ can determine the specific form of the equation, as the table \n",
    "\n",
    "\n",
    "| $\\theta$      | Description |\n",
    "| :---        |    :----:   |\n",
    "| 0      | Explicit scheme       |\n",
    "| 0.5   | Crank-Niclsion scheme(Implicit)        |\n",
    "| 1   | Completely implicit scheme(Implicit)        |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81ba5306",
   "metadata": {},
   "source": [
    "### Solve the equation by explicit method\n",
    "\n",
    "We can linearization the sourse term as \n",
    "$$b = S_u + S_p T_p^0$$\n",
    "and take \n",
    "$$\\theta = 0$$\n",
    "into the equation above.\n",
    "The discreted non steady-state advection equation by explicit method is \n",
    "$$ a_{P} \\, T_{P} \\!=\\! a_{W} T_{W}^{0} \\!+\\! a_{E} T_{E}^{0} \\!+\\! \\big[ \\, a_{P}^{0} \\!-\\! ( a_{W} \\!+\\! a_{E} \\!-\\! S_{P} ) \\, \\big] T_{P}^{0} \\!+\\! S_{u} $$\n",
    ", where \n",
    "$$a_{W}=\\frac{k_{w}} {\\Delta x_{W P}} \\,, \\, \\, a_{E}=\\frac{k_{e}} {\\Delta x_{P E}} \\,, \\, \\, a_{P}=a_{P}^{0} \\,, \\, \\, a_{P}^{0}=\\rho c \\, \\, \\frac{\\Delta x} {\\Delta t} $$\n",
    "\n",
    "\n",
    "According to the requirement of boundedness in discrete equations, all coefficients in the equation should be positive values, and the source term should be zero. Therefore we have  \n",
    "$$a_{P}^{0}-a_{W}-a_{E} > 0. $$\n",
    "and we can solve it as\n",
    "$$ \\Delta t \\leq\\rho c \\; {\\frac{( \\Delta x )^{2}} {2 k}} $$\n",
    ", which also means the discrate equation imposes a fairly strict constraint on the maximum value of the calculation time step $\\Delta t $ for explicit formats. This will result in significant costs for improving computational accuracy in actual calculations, as the maximum possible time step decreases as the grid spatial scale decreases (grid refinement). Therefore, the explicit format is not suitable for calculating non-stationary problems in general situations. However, when the time interval is carefully selected to meet the requirements of limit above, the explicit format is still effective for calculating simple diffusion problems.\n",
    "\n",
    "Here we go! \n",
    "\n",
    "**Internal Nodes 2, 3, 4**\n",
    "\n",
    "The discrete equation satisfied by the internal nodes is\n",
    "\n",
    "$$ a_{P} \\, T_{P} \\!=\\! a_{W} T_{W}^{0} \\!+\\! a_{E} T_{E}^{0} \\!+\\! \\big[ \\, a_{P}^{0} \\!-\\! ( a_{W} \\!+\\! a_{E} \\!-\\! S_{P} ) \\, \\big] T_{P}^{0} \\!+\\! S_{u} $$\n",
    "\n",
    "where\n",
    "\n",
    "$$a_{W}=\\frac{k_{w}} {\\Delta x_{W P}} \\,, \\, \\, a_{E}=\\frac{k_{e}} {\\Delta x_{P E}} \\,, \\, \\, a_{P}=a_{P}^{0} \\,, \\, \\, a_{P}^{0}=\\rho c \\, \\, \\frac{\\Delta x} {\\Delta t} $$\n",
    "\n",
    "**Boundary Nodes 1**\n",
    "\n",
    "$$\\int_{\\Delta V} \\biggl[ \\int_{t}^{t+\\Delta t} \\rho c \\ \\frac{\\partial\\, T} {\\partial t} \\mathrm{d} t \\biggl] \\mathrm{d} V \\approx\\int_{\\Delta V} \\biggl[ \\int_{t}^{t+\\Delta t} \\rho c \\ \\frac{T_{P}-T_{P}^{\\vee}} {\\Delta t} \\mathrm{d} t \\biggl] \\mathrm{d} V=\\rho c \\left( \\, T_{P}-T_{P}^{\\vee} \\, \\right) \\Delta V $$\n",
    "\n",
    "Under adiabatic conditions, take $\\theta=0$, $\\bar{S} = 0$, $k_{w}= 0$ into above equation. The control equation for the boundary node 1 is\n",
    "\n",
    "$$\\rho c \\Big( \\frac{T_{P}-T_{P}^{0}} {\\Delta t} \\Big) \\Delta x=\\Big[ \\frac{k \\, ( \\, T_{E}^{0}-T_{P}^{0} \\, )} {\\Delta x} \\Big] $$\n",
    "\n",
    "**Boundary Nodes 5**\n",
    "\n",
    "The temperature of east interface node is a constant $T_{B}$. The control equation for the boundary node 5 is\n",
    "$$ \\rho c \\Big( \\frac{T_{P}-T_{P}^{0}} {\\Delta t} \\Big) \\Delta x=\\left[ \\frac{k ( T_{B}-T_{P}^{0} )} {\\frac{\\Delta x} {2}} \\right]-\\left[ \\frac{k ( T_{P}^{0}-T_{W}^{0} )} {\\Delta x} \\right] $$\n",
    "\n",
    "**Organize coefficient matrix**\n",
    "By organizing the coefficient of above nodes, we can get \n",
    "\n",
    "\n",
    "| node     | $a_{W}$ | $a_{E}$ | $a_{P}^{0}$ | $a_{P}$ | $S_{P}$ | $S_{u}$ |\n",
    "| :---     |    :----:   | :----:   | :----:   | :----:   | :----:   |:----:   |\n",
    "|  1   | 0    |   ${\\frac{k} {\\Delta x}}$   | $\\rho c {\\frac {\\Delta x}{\\Delta t}}$ | $a_{P}^{0}$|0|0|\n",
    "| 2,3,4   |    ${\\frac{k} {\\Delta x}}$   |${\\frac{k} {\\Delta x}}$| $\\rho c {\\frac {\\Delta x}{\\Delta t}}$ | $a_{P}^{0}$ |0|0|\n",
    "|  5  | ${\\frac{k} {\\Delta x}}$   |  0 | $\\rho c {\\frac {\\Delta x}{\\Delta t}}$ | $a_{P}^{0}$ |$-{\\frac{2k} {\\Delta x}}$|  ${\\frac{2k} {\\Delta x}} T_{B}$|\n",
    "\n",
    "**Limitation of $\\Delta t$ by explicit method**\n",
    "\n",
    "$$\n",
    "\\Delta t \\! < \\! \\rho c \\; \\frac{( \\Delta x )^{2}} {2 k} \\!=\\! 8 \\; \\mathrm{s} \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eaf2531d",
   "metadata": {},
   "source": [
    "### Solve algebraic equations (explicit method)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ef9f89d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                      # for array operation\n",
    "from matplotlib import pyplot as plt    # for plotting figures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3ff6aadb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# -----------------------------------------------------------------------\n",
    "dt = 2.0                                # time step size(dt<8)\n",
    "# -----------------------------------------------------------------------\n",
    "total_time = 120                        # total simulation time\n",
    "nx = 5                                  # number of spatial grid points\n",
    "L = 0.02                                # length of the domain\n",
    "dx = L / nx                             # spatial grid size\n",
    "x = np.linspace(0.5*dx, L-0.5*dx, nx)   # spatial grid points\n",
    "T0 = 200                                # initial temperature\n",
    "rho_c = 1.0e7                           # fluid density plus specific heat\n",
    "k = 10                                  # thermal conductivity\n",
    "aW = k/dx\n",
    "aE = k/dx\n",
    "ap0 = rho_c * dx / dt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7621b99f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate numerical solution\n",
    "def analytical_solution(x, t, k=k, rho_c=rho_c, L=L):\n",
    "    result = np.zeros_like(x)           # initialize result array\n",
    "    alpha = k / rho_c\n",
    "    for i in range(1, 1000):\n",
    "        lamda_i = (2 * i - 1) * np.pi / (2 * L)\n",
    "        result += 800 / np.pi * (-1) ** (i + 1)/(2 * i - 1) * np.exp(-alpha * lamda_i**2 * t) * np.cos(lamda_i * x)\n",
    "    \n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4c176d39",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Renew coefficients\n",
    "def renew_explicit(a, b, nx):\n",
    "    for i in range(1, nx + 1):\n",
    "        a[i][i] = ap0\n",
    "    \n",
    "    b[1] = aE * T_old[2] + (ap0 - (aE + 0 - 0)) * T_old[1]\n",
    "    \n",
    "    for i in range(2, nx):\n",
    "        b[i] = aW * T_old[i - 1] + aE * T_old[i + 1] + (ap0 - (aW + aE - 0)) * T_old[i]\n",
    "    \n",
    "    b[nx] = aW * T_old[nx - 1] + (ap0 - (aW + 0 + 2 * aW)) * T_old[nx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ec9879f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# TDMA iteration\n",
    "def TDMA(a, b, T, nx):\n",
    "    C = np.zeros(nx + 1)\n",
    "    phi = np.zeros(nx + 1)\n",
    "    alph = np.zeros(nx + 1)\n",
    "    belt = np.zeros(nx + 1)\n",
    "    D = np.zeros(nx + 1)\n",
    "    A = np.zeros(nx + 1)\n",
    "    Cpi = np.zeros(nx + 1)\n",
    "    \n",
    "    for j in range(1, nx + 1):\n",
    "        belt[j] = -a[j][j - 1]\n",
    "        D[j] = a[j][j]\n",
    "        alph[j] = -a[j][j + 1] if j < nx else 0\n",
    "        C[j] = b[j]\n",
    "    \n",
    "    for j in range(1, nx + 1):\n",
    "        denom = D[j] - belt[j] * A[j - 1]\n",
    "        A[j] = alph[j] / denom if denom != 0 else 0\n",
    "        Cpi[j] = (belt[j] * Cpi[j - 1] + C[j]) / denom if denom != 0 else 0\n",
    "    \n",
    "    phi[nx] = Cpi[nx]\n",
    "    for j in range(nx - 1, 0,  - 1):\n",
    "        phi[j] = A[j] * phi[j + 1] + Cpi[j]\n",
    "    \n",
    "    for j in range(1, nx + 1):\n",
    "        T[j] = phi[j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1eb0f1e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Jacobi iteration\n",
    "def Jacobi(A,b,T,k):\n",
    "    AA = A[1 : nx + 1, 1 : nx + 1]\n",
    "    bb = b[1 : nx + 1]\n",
    "    n = AA.shape[1]\n",
    "    D = np.eye(n)\n",
    "    D[np.arange(n),np.arange(n)] = AA[np.arange(n),np.arange(n)]\n",
    "    LU = D - AA\n",
    "    X = np.zeros(n)\n",
    "    for i in range(k):\n",
    "        D_inv = np.linalg.inv(D)\n",
    "        X =  np.dot(np.dot(D_inv,LU),X) + np.dot(D_inv,bb)\n",
    "    for i in range(1 ,nx + 1):\n",
    "        T[i] = X[i - 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d575eb01",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Output results\n",
    "def output():\n",
    "    print(\"-----------\")\n",
    "    print(\"time = {}\".format(time))\n",
    "    for i in range(1, nx + 1):\n",
    "        print(T[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f94de955",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----------\n",
      "time = 2.0\n",
      "200.0\n",
      "200.0\n",
      "200.0\n",
      "200.0\n",
      "150.0\n",
      "-----------\n",
      "time = 4.0\n",
      "200.0\n",
      "200.0\n",
      "200.0\n",
      "193.75\n",
      "118.75\n",
      "-----------\n",
      "time = 6.0\n",
      "200.0\n",
      "200.0\n",
      "199.21875\n",
      "185.15625\n",
      "98.4375\n",
      "-----------\n",
      "time = 8.0\n",
      "200.0\n",
      "199.90234375\n",
      "197.55859375\n",
      "176.07421875\n",
      "84.66796875\n",
      "-----------\n",
      "time = 10.0\n",
      "199.98779296875\n",
      "199.62158203125\n",
      "195.166015625\n",
      "167.333984375\n",
      "74.9267578125\n",
      "-----------\n",
      "time = 12.0\n",
      "199.9420166015625\n",
      "199.11041259765625\n",
      "192.24395751953125\n",
      "159.2620849609375\n",
      "67.7459716796875\n",
      "-----------\n",
      "time = 14.0\n",
      "199.83806610107422\n",
      "198.3560562133789\n",
      "188.97953033447266\n",
      "151.94530487060547\n",
      "62.248992919921875\n",
      "-----------\n",
      "time = 16.0\n",
      "199.6528148651123\n",
      "197.36924171447754\n",
      "185.52231788635254\n",
      "145.36254405975342\n",
      "57.898783683776855\n",
      "-----------\n",
      "time = 18.0\n",
      "199.36736822128296\n",
      "196.17382287979126\n",
      "181.98321163654327\n",
      "139.44954574108124\n",
      "54.35705780982971\n",
      "-----------\n",
      "time = 20.0\n",
      "198.9681750535965\n",
      "194.79918964207172\n",
      "178.44032980501652\n",
      "134.12969298660755\n",
      "51.404354348778725\n",
      "-----------\n",
      "time = 22.0\n",
      "198.4470518771559\n",
      "193.27545533888042\n",
      "174.9463576823473\n",
      "129.32785525918007\n",
      "48.89393309131265\n",
      "-----------\n",
      "time = 24.0\n",
      "197.80060230987146\n",
      "191.63076769909821\n",
      "171.53518208651803\n",
      "124.97592779109254\n",
      "46.72469008946791\n",
      "-----------\n",
      "time = 26.0\n",
      "197.0293729835248\n",
      "189.89004882387235\n",
      "168.22722350116237\n",
      "121.01442986531765\n",
      "44.824922279804014\n",
      "-----------\n",
      "time = 28.0\n",
      "196.13695746356828\n",
      "188.07461117849016\n",
      "165.03347746202053\n",
      "117.39234062160904\n",
      "43.142380158042215\n",
      "-----------\n",
      "time = 30.0\n",
      "195.12916417793352\n",
      "186.20226274956622\n",
      "161.9584770715278\n",
      "114.06623766871463\n",
      "41.63803017647752\n",
      "-----------\n",
      "time = 32.0\n",
      "194.0133014993876\n",
      "184.28765221835735\n",
      "159.00242035593095\n",
      "110.99924165753664\n",
      "40.28204856888778\n",
      "-----------\n",
      "time = 34.0\n",
      "192.79759533925883\n",
      "182.34270439568283\n",
      "156.16267700143496\n",
      "108.15998985875483\n",
      "39.051185562746944\n",
      "-----------\n",
      "time = 36.0\n",
      "191.49073397131187\n",
      "180.37706233934887\n",
      "153.43484453288093\n",
      "105.52172521458888\n",
      "37.926989709061196\n",
      "-----------\n",
      "time = 38.0\n",
      "190.1015250173165\n",
      "178.39849406753578\n",
      "150.81348184390293\n",
      "103.06152319118443\n",
      "36.89458421998686\n",
      "-----------\n",
      "time = 40.0\n",
      "188.63864614859392\n",
      "176.41324640830425\n",
      "148.29261354026724\n",
      "100.75965065137456\n",
      "35.94180553638984\n",
      "-----------\n",
      "time = 42.0\n",
      "187.1104711810577\n",
      "174.42634226733585\n",
      "145.86607228766027\n",
      "98.59904037311306\n",
      "35.058584791665474\n",
      "-----------\n",
      "time = 44.0\n",
      "185.5249550668425\n",
      "172.44182463409166\n",
      "143.52772704580133\n",
      "96.56486241475051\n",
      "34.23649554143006\n",
      "-----------\n",
      "time = 46.0\n",
      "183.88956376274868\n",
      "170.46295373964924\n",
      "141.27163116545626\n",
      "94.64417463446681\n",
      "33.468417515237604\n",
      "-----------\n",
      "time = 48.0\n",
      "182.21123750986123\n",
      "168.49236467076256\n",
      "139.0921144208567\n",
      "92.82563706093684\n",
      "32.748282776331855\n",
      "-----------\n",
      "time = 50.0\n",
      "180.4963784049739\n",
      "166.53219249441165\n",
      "136.98383603210496\n",
      "91.09927744535119\n",
      "32.07088136782452\n",
      "-----------\n",
      "time = 52.0\n",
      "178.75085516615363\n",
      "164.5841711754436\n",
      "134.94181076654908\n",
      "89.45629775900458\n",
      "31.431710535559223\n",
      "-----------\n",
      "time = 54.0\n",
      "176.98001966731488\n",
      "162.64971162317056\n",
      "132.96141669171783\n",
      "87.88891348201697\n",
      "30.826856304600092\n",
      "-----------\n",
      "time = 56.0\n",
      "175.18873116179685\n",
      "160.72996326225703\n",
      "131.03839065693683\n",
      "86.39021923605249\n",
      "30.25289937562718\n",
      "-----------\n",
      "time = 58.0\n",
      "173.3813851743544\n",
      "158.82586267403448\n",
      "129.1688158049913\n",
      "84.95407568110987\n",
      "29.70683951427355\n",
      "-----------\n",
      "time = 60.0\n",
      "171.56194486181442\n",
      "156.93817212794409\n",
      "127.34910414813653\n",
      "83.57501367574051\n",
      "29.1860341565597\n",
      "-----------\n",
      "time = 62.0\n",
      "169.73397327008064\n",
      "155.06751022220195\n",
      "125.57597633656296\n",
      "82.2481525448924\n",
      "28.68814805731738\n",
      "-----------\n",
      "time = 64.0\n",
      "167.90066538909582\n",
      "153.21437636748192\n",
      "123.84644009830902\n",
      "80.96912995790436\n",
      "28.211111603934913\n",
      "-----------\n",
      "time = 66.0\n",
      "166.0648792613941\n",
      "151.37917046153706\n",
      "122.15776836440506\n",
      "79.73404143120877\n",
      "27.753085997197363\n",
      "-----------\n",
      "time = 68.0\n",
      "164.229165661412\n",
      "149.5622087993777\n",
      "120.50747775989701\n",
      "78.53938786860688\n",
      "27.31243392714945\n",
      "-----------\n",
      "time = 70.0\n",
      "162.3957960536577\n",
      "147.76373702719687\n",
      "118.89330790342083\n",
      "77.38202986233597\n",
      "26.88769468804427\n",
      "-----------\n",
      "time = 72.0\n",
      "160.5667886753501\n",
      "145.98394076503246\n",
      "117.31320178875724\n",
      "76.25914772068512\n",
      "26.477562912819664\n",
      "-----------\n",
      "time = 74.0\n",
      "158.74393268656038\n",
      "144.22295438178776\n",
      "115.76528740228264\n",
      "75.16820637821095\n",
      "26.080870285597936\n",
      "-----------\n",
      "time = 76.0\n",
      "156.9288103984638\n",
      "142.4808682974462\n",
      "114.24786064671183\n",
      "74.1069244946433\n",
      "25.69656972577508\n",
      "-----------\n",
      "time = 78.0\n",
      "155.1228176358366\n",
      "140.75773510373162\n",
      "112.75936958404505\n",
      "73.07324716754334\n",
      "25.32372164043984\n",
      "-----------\n",
      "time = 80.0\n",
      "153.3271823193235\n",
      "139.05357473028394\n",
      "111.29839997194317\n",
      "72.06532177871811\n",
      "24.961481921217818\n",
      "-----------\n",
      "time = 82.0\n",
      "151.54298137069358\n",
      "137.3683788341213\n",
      "109.86366204258265\n",
      "71.08147657068372\n",
      "24.609091423100903\n",
      "-----------\n",
      "time = 84.0\n",
      "149.77115605362206\n",
      "135.70211455225052\n",
      "108.45397845753763\n",
      "70.12020161122324\n",
      "24.26586671077353\n",
      "-----------\n",
      "time = 86.0\n",
      "148.01252586595064\n",
      "134.05472772808284\n",
      "107.06827336358745\n",
      "69.18013185445633\n",
      "23.93119189563636\n",
      "-----------\n",
      "time = 88.0\n",
      "146.26780109871717\n",
      "132.42614569975441\n",
      "105.705562470508\n",
      "68.26003204824524\n",
      "23.60451141657977\n",
      "-----------\n",
      "time = 90.0\n",
      "144.53759417384683\n",
      "130.81627972096896\n",
      "104.36494407138096\n",
      "67.3587832720699\n",
      "23.285323641393013\n",
      "-----------\n",
      "time = 92.0\n",
      "142.8224298672371\n",
      "129.2250270713802\n",
      "103.04559092766559\n",
      "66.47537091814918\n",
      "22.97317518487937\n",
      "-----------\n",
      "time = 94.0\n",
      "141.122754517755\n",
      "127.65227290289799\n",
      "101.74674294444037\n",
      "65.60887395268001\n",
      "22.66765585531825\n",
      "-----------\n",
      "time = 96.0\n",
      "139.43894431589786\n",
      "126.09789185994792\n",
      "100.46770056527754\n",
      "64.75845531447985\n",
      "22.36839415365891\n",
      "-----------\n",
      "time = 98.0\n",
      "137.77131275890412\n",
      "124.56174950510788\n",
      "99.20781882076163\n",
      "63.92335332572694\n",
      "22.0750532603468\n",
      "-----------\n",
      "time = 100.0\n",
      "136.1201173521796\n",
      "123.04370357628912\n",
      "97.96650196942556\n",
      "63.10287400443377\n",
      "21.787327453432617\n",
      "-----------\n",
      "time = 102.0\n",
      "134.4855656301933\n",
      "121.5436050974175\n",
      "96.74319867465954\n",
      "62.2963841811826\n",
      "21.504938908949608\n",
      "-----------\n",
      "time = 104.0\n",
      "132.86782056359633\n",
      "120.06129936116974\n",
      "95.53739766581967\n",
      "61.5033053338381\n",
      "21.22763484074133\n",
      "-----------\n",
      "time = 106.0\n",
      "131.26700541329302\n",
      "118.59662679955431\n",
      "94.34862383624073\n",
      "60.7231080636987\n",
      "20.955184942193096\n",
      "-----------\n",
      "time = 108.0\n",
      "129.6832080865757\n",
      "117.14942375585744\n",
      "93.17643473508718\n",
      "59.95530714507825\n",
      "20.687379096833023\n",
      "-----------\n",
      "time = 110.0\n",
      "128.11648504523595\n",
      "115.71952316960095\n",
      "92.02041741393235\n",
      "59.19945708779872\n",
      "20.42402532865542\n",
      "-----------\n",
      "time = 112.0\n",
      "126.56686481078158\n",
      "114.30675518459675\n",
      "90.88018559262423\n",
      "58.455148158672515\n",
      "20.16494796638448\n",
      "-----------\n",
      "time = 114.0\n",
      "125.03435110750848\n",
      "112.9109476888733\n",
      "89.75537711237683\n",
      "57.72200281388047\n",
      "19.909985998824368\n",
      "-----------\n",
      "time = 116.0\n",
      "123.51892568017908\n",
      "111.53192679414065\n",
      "88.64565164712684\n",
      "56.999672499310506\n",
      "19.65899160100029\n",
      "-----------\n",
      "time = 118.0\n",
      "122.02055081942427\n",
      "110.16951726151873\n",
      "87.55068864702653\n",
      "56.28783478049877\n",
      "19.411828813038994\n",
      "-----------\n",
      "time = 120.0\n",
      "120.53917162468609\n",
      "108.82354287944541\n",
      "86.4701854905221\n",
      "55.58619076788228\n",
      "19.168372355711718\n",
      "-----------\n",
      "time = 122.0\n",
      "119.07471803153102\n",
      "107.49382679898508\n",
      "85.40385582380753\n",
      "54.89446280669093\n",
      "18.928506568305107\n"
     ]
    }
   ],
   "source": [
    "# Major routine\n",
    "a = np.zeros((nx + 1, nx + 1))      # left side of matrix\n",
    "b = np.zeros(nx + 1)                # right side of matrix\n",
    "T = np.zeros(nx + 1)                # temperature at current time step\n",
    "T_old = np.zeros(nx + 1)            # temperature at previous time step\n",
    "time = 0.0                          # current time\n",
    "\n",
    "for i in range(1, nx + 1):\n",
    "    T[i] = T0\n",
    "    T_old[i] = T0\n",
    "\n",
    "output_explicit_dt_2 = np.zeros((3, nx))    # to store output for dt=2\n",
    "maker = 0\n",
    "\n",
    "# Time loop\n",
    "while time <= total_time:\n",
    "    time += dt\n",
    "    renew_explicit(a, b, nx)                # calculate explicit coefficients\n",
    "    # TDMA(a, b, T, nx)                     # solve the system of equations using TDMA\n",
    "    Jacobi(a, b, T, nx)                     # solve the system of equations using Jacobi\n",
    "    for i in range(1, nx + 1):\n",
    "        T_old[i] = T[i]                     # update previous temperature values\n",
    "    output()\n",
    "    if time % 40 == 0:\n",
    "        output_explicit_dt_2[maker, :] = T[1:nx + 1]\n",
    "        maker += 1   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ffcb3d84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualization\n",
    "T_true_40 = analytical_solution(x, 40)  # calculate the analytical solution\n",
    "T_true_80 = analytical_solution(x, 80)  \n",
    "T_true_120 = analytical_solution(x, 120)\n",
    "plt.figure()                           \n",
    "plt.plot(x, output_explicit_dt_2[0], '-g', label='Numerical solution of 40s')\n",
    "plt.plot(x, output_explicit_dt_2[1], '-r', label='Numerical solution of 80s')\n",
    "plt.plot(x, output_explicit_dt_2[2], '-b', label='Numerical solution of 120s')\n",
    "plt.scatter(x, T_true_40, s=50, c='g', marker='+', label='Analytical solution of 40s')\n",
    "plt.scatter(x, T_true_80, s=50, c='r', marker='*', label='Analytical solution of 80s')\n",
    "plt.scatter(x, T_true_120, s=50, c='b', marker='o', label='Analytical solution of 120s')\n",
    "plt.xlabel('$x$ (m)')\n",
    "plt.ylabel('$T$($^\\circ C$)')\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(0, 0.02)\n",
    "ax.set_ylim(0, 200)\n",
    "plt.legend(loc='lower left')\n",
    "plt.show()                              # show the figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "32b7cd49",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----------\n",
      "time = 8.0\n",
      "200.0\n",
      "200.0\n",
      "200.0\n",
      "200.0\n",
      "0.0\n",
      "-----------\n",
      "time = 16.0\n",
      "200.0\n",
      "200.0\n",
      "200.0\n",
      "100.0\n",
      "100.0\n",
      "-----------\n",
      "time = 24.0\n",
      "200.0\n",
      "200.0\n",
      "150.0\n",
      "150.0\n",
      "0.0\n",
      "-----------\n",
      "time = 32.0\n",
      "200.0\n",
      "175.0\n",
      "175.0\n",
      "75.0\n",
      "75.0\n",
      "-----------\n",
      "time = 40.0\n",
      "187.5\n",
      "187.5\n",
      "125.0\n",
      "125.0\n",
      "0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Investigate the effects of time step\n",
    "dt = 8.0                                # time step size(dt<=08)\n",
    "nx = 5                                  # number of spatial grid points\n",
    "L = 0.02                                # length of the domain\n",
    "dx = L / nx                             # spatial grid size\n",
    "x = np.linspace(0.5*dx, L-0.5*dx, nx)   # spatial grid points\n",
    "T0 = 200                                # initial temperature\n",
    "rho_c = 1.0e7                           # fluid density plus specific heat\n",
    "k = 10                                  # thermal conductivity\n",
    "aW = k/dx\n",
    "aE = k/dx\n",
    "ap0 = rho_c * dx / dt\n",
    "a = np.zeros((nx + 1, nx + 1))\n",
    "b = np.zeros(nx + 1)\n",
    "T = np.zeros(nx + 1)\n",
    "T_old = np.zeros(nx + 1)\n",
    "time = 0.0\n",
    "\n",
    "for i in range(0, nx+1):\n",
    "    T[i] = T0\n",
    "    T_old[i] = T0\n",
    "\n",
    "# Time loop\n",
    "while time < 40:\n",
    "    time += dt\n",
    "    renew_explicit(a, b, nx)\n",
    "    # TDMA(a, b, T, nx)\n",
    "    Jacobi(a, b, T, nx)\n",
    "    for i in range(1, nx+1):\n",
    "        T_old[i] = T[i]\n",
    "    output()\n",
    "\n",
    "output_explicit_dt_8 = T[1:nx+1]\n",
    "plt.figure()                            # create a new figure\n",
    "plt.plot(x, output_explicit_dt_2[0], '-k', label='Numerical solution of 40s (dt=2)')\n",
    "plt.plot(x, output_explicit_dt_8, '--k', label='Numerical solution of 40s (dt=8)')\n",
    "plt.scatter(x, T_true_40, s=50, c='k', marker='+', label='Analytical solution of 40s')\n",
    "plt.xlabel('$x$ (m)')\n",
    "plt.ylabel('$T$($^\\circ C$)')\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(0, 0.02)\n",
    "ax.set_ylim(0, 200)\n",
    "plt.legend(loc='lower left')\n",
    "plt.show()                              # show the figure"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec045aec",
   "metadata": {},
   "source": [
    "```{note}\n",
    "Reducing the time step can effectively improve the accuracy of numerical calculation results.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "876a6539",
   "metadata": {},
   "source": [
    "### Solve the equation by completely implicit method\n",
    "\n",
    "We can linearization the sourse term as \n",
    "$$b = S_u + S_p T_p$$\n",
    "and take \n",
    "$$\\theta = 0$$\n",
    "into the equation \n",
    "$$\\begin{aligned} {{a_{P} T_{P}=}} & {{} {{} a_{W} \\big[ \\theta T_{W}+( 1 \\!-\\! \\theta) \\, T_{W}^{0} \\big]+a_{E} \\big[ \\theta T_{E}+( 1 \\!-\\! \\theta) \\, T_{E}^{0} \\big]+\\big[ a_{P}^{0} \\!-\\! ( 1 \\!-\\! \\theta) a_{W}-( 1 \\!-\\! \\theta) a_{E} \\big] T_{P}+b}} \\\\ \\end{aligned} $$\n",
    "The discreted non steady-state advection equation by completely implicit method is \n",
    "$$ a_{P} \\, T_{P} \\!=\\! a_{W} T_{W} \\!+\\! a_{E} T_{E} \\!+\\! \\, a_{P}^{0}  \\,  T_{P}^{0} \\!+\\! S_{u} $$\n",
    ", where \n",
    "\n",
    "$$a_{W}=\\frac{k_{w}} {\\Delta x_{W P}} \\,, \\, \\, a_{E}=\\frac{k_{e}} {\\Delta x_{P E}} \\,, \\, \\, a_{P}^{0}=\\rho c \\, \\, \\frac{\\Delta x} {\\Delta t} \\,, \\, \\, a_{P}=a_{P}^{0}+a_{W}+a_{E}-S_{P} $$\n",
    "\n",
    "\n",
    "From the above equation, it can be seen that all coefficients maintain positive values So the fully implicit format is unconditionally stable for any time step At However, the calculation accuracy is only first-order intercept, and to ensure the calculation accuracy, a smaller time step should also be selected The fully implicit scheme is widely used in solving various non-stationary problems due to its unconditional stability and good convergence.\n",
    "\n",
    "Here we go! \n",
    "\n",
    "**Internal Nodes 2, 3, 4**\n",
    "\n",
    "$$ a_{P} \\, T_{P} \\!=\\! a_{W} T_{W} \\!+\\! a_{E} T_{E} \\!+\\! \\, a_{P}^{0}  \\,  T_{P}^{0} \\!+\\! S_{u} $$\n",
    ", where \n",
    "\n",
    "$$a_{W}=\\frac{k_{w}} {\\Delta x_{W P}} \\,, \\, \\, a_{E}=\\frac{k_{e}} {\\Delta x_{P E}} \\,, \\, \\, a_{P}^{0}=\\rho c \\, \\, \\frac{\\Delta x} {\\Delta t} \\,, \\, \\, a_{P}=a_{P}^{0}+a_{W}+a_{E}-S_{P} $$\n",
    "\n",
    "**Boundary Nodes 1**\n",
    "Take the bondary condition into the discreted equation like what we have done in explicit method, we will get \n",
    "$$\\rho c \\Big( \\frac{T_{P}-T_{P}^{0}} {\\Delta t} \\Big) \\Delta x=\\frac{k ( T_{E}^{0}-T_{P}^{0} )} {\\Delta x} $$\n",
    "\n",
    "**Boundary Nodes 5**\n",
    "$$\\rho c \\Big( \\frac{T_{P}-T_{P}^{0}} {\\Delta t} \\Big) \\Delta x=\\left[ \\frac{k \\left( T_{B}-T_{P}^{0} \\right)} {\\frac{\\Delta x} {2}}-\\frac{k \\left( T_{P}^{0}-T_{W}^{0} \\right)} {\\Delta x} \\right] $$\n",
    "\n",
    "**Organize coefficient matrix**\n",
    "By organizing the coefficient of above nodes, we can get \n",
    "\n",
    "\n",
    "| node     | $a_{W}$ | $a_{E}$ | $a_{P}^{0}$ | $a_{P}$ | $S_{P}$ | $S_{u}$ |\n",
    "| :---     |    :----:   | :----:   | :----:   | :----:   | :----:   |:----:   |\n",
    "|  1   | 0    |   ${\\frac{k} {\\Delta x}}$   | $\\rho c {\\frac {\\Delta x}{\\Delta t}}$ | 0|0|$a_{w} + a_{E}+a_{P}^{0} -S_{P}$|\n",
    "| 2,3,4   |    ${\\frac{k} {\\Delta x}}$   |${\\frac{k} {\\Delta x}}$| $\\rho c {\\frac {\\Delta x}{\\Delta t}}$ | 0 |0|$a_{w} + a_{E}+a_{P}^{0} -S_{P}$|\n",
    "|  5  | ${\\frac{k} {\\Delta x}}$   |  0 | $\\rho c {\\frac {\\Delta x}{\\Delta t}}$ | $-{\\frac{2k} {\\Delta x}}$ |$-{\\frac{2k} {\\Delta x}}T_{B}$| $a_{w} + a_{E}+a_{P}^{0} -S_{P}$|"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0072d7c",
   "metadata": {},
   "source": [
    "### Solve algebraic equations (completely implicit method)\n",
    "What we need to do is just ***change the renew function***. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a4bbb631",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Update coefficients for implicit method\n",
    "def renew_implicit(a, b, nx):\n",
    "    a[1, 1] = ap0 + aE - 0\n",
    "    a[1, 2] = -aE\n",
    "    for i in range(2, nx):\n",
    "        a[i][i - 1] = -aW\n",
    "        a[i][i] = ap0 + (aW + aE - 0)\n",
    "        a[i][i + 1] = -aE\n",
    "    a[nx, nx - 1] = -aW\n",
    "    a[nx, nx] = ap0 + aW + 2 * aW\n",
    "        \n",
    "    for i in range(1, nx + 1):\n",
    "        b[i] = ap0 * T_old[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ac2aac59",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----------\n",
      "time = 8.0\n",
      "199.44751381215474\n",
      "198.3425414364641\n",
      "193.92265193370167\n",
      "177.34806629834253\n",
      "115.4696132596685\n",
      "-----------\n",
      "time = 16.0\n",
      "197.85262965110962\n",
      "194.66286132901928\n",
      "184.11373279203934\n",
      "153.9467659717347\n",
      "76.97719849821435\n",
      "-----------\n",
      "time = 24.0\n",
      "195.0190109483703\n",
      "189.3517735428917\n",
      "173.06236056515792\n",
      "134.67020313366135\n",
      "57.72492002601801\n",
      "-----------\n",
      "time = 32.0\n",
      "191.00352102015404\n",
      "182.97254116372153\n",
      "162.18309654894873\n",
      "119.63512390175754\n",
      "47.01699279075872\n",
      "-----------\n",
      "time = 40.0\n",
      "186.004571656615\n",
      "176.00667292953688\n",
      "152.07703773408934\n",
      "107.93528490892314\n",
      "40.39385409808811\n"
     ]
    }
   ],
   "source": [
    "a = np.zeros((nx + 1, nx + 1))\n",
    "b = np.zeros(nx + 1)\n",
    "T = np.zeros(nx + 1)\n",
    "T_old = np.zeros(nx + 1)\n",
    "time = 0.0\n",
    "dt = 8.0\n",
    "\n",
    "for i in range(0, nx + 1):\n",
    "    T[i] = T0\n",
    "    T_old[i] = T0\n",
    "\n",
    "# Time loop\n",
    "while time < 40:\n",
    "    time += dt\n",
    "    renew_implicit(a, b, nx)\n",
    "    # TDMA(a, b, T, nx)\n",
    "    Jacobi(a, b, T, 100)\n",
    "    for i in range(1, nx + 1):\n",
    "        T_old[i] = T[i]\n",
    "    output()\n",
    "\n",
    "output_implicit_dt_8 = T[1:nx + 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a71ae4e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualization\n",
    "plt.figure()                            # create a new figure\n",
    "plt.plot(x, output_explicit_dt_8, '--*k', label='Explicit solution of 40s (dt=8)')\n",
    "plt.plot(x, output_implicit_dt_8, '-k', label='Implicit solution of 40s (dt=8)')\n",
    "plt.scatter(x, T_true_40, s=50, c='k', marker='+', label='Analytical solution of 40s')\n",
    "plt.xlabel('$x$ (m)')\n",
    "plt.ylabel(r'$T$')\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(0, 0.02)\n",
    "ax.set_ylim(0, 200)\n",
    "plt.legend(loc='lower left')\n",
    "plt.show()                              # show the figure"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adaa3355",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "1. Can you solve the problem by using the Crank-Nicolson scheme?\n",
    "\n",
    "2. Compare the results from the explicit, the Crank-Nicolson and the implict schemes regarding accuracy and stability."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "cfd-python",
   "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": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}