{ "cells": [ { "cell_type": "markdown", "metadata": { "tags": [ "remove_cell" ] }, "source": [ "
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Ingenieurinformatik – Übung

\n", " Lehrstuhl Computational Civil Engineering
\n", " Kontakt: Email senden | Individuelle Kontakte siehe Webseite des Lehrstuhls
\n", " Links: \n", " Vorlesungsskript | \n", " Webseite des Lehrstuhls\n", "
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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Temperaturgleichung" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Die Lösung einer gewöhnlichen Differentialgleichung, hier der Temperaturentwicklung, wird in dieser Aufgabe nochmals vorgestellt. Dabei wird die Gleichung erweitert und ein komplexer Quellterm implementiert. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aufgabenteil A\n", "\n", "In der Vorlesung wurde folgende Differentialgleichung vorgestellt. \n", "\n", "$$ \\sf T'(t) = -(T-T_\\infty) + Q(t) $$\n", "\n", "Verwenden Sie die Funktion `scipy.integrate.solve_ivp` um die Gleichung für $\\sf T_0 = 20$ mit $\\sf T_\\infty=10$ und $\\sf Q=0$ zu lösen. Die Lösung soll bis $\\sf t=25$ berechnet werden. Erstellen und beschriften Sie den Lösungsplot." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lösungshinweis\n", "\n", "Die Ausgabe könnte wie folgt aussehen.\n", "\n", "![](teil1.png)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "loesung", "hide-cell" ] }, "source": [ "### Lösungsvorschlag" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.integrate" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "# Rechte-Hand-Seite der Gleichung, hier mit Q=0\n", "def f_T1(t, T):\n", " Tinfty = 10\n", " return -(T-Tinfty)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "# Anfangswert der Lösung\n", "T0 = 20\n", "\n", "# Aufruf des Lösers\n", "res1 = scipy.integrate.solve_ivp(f_T1, [0, 25], [T0])" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(res1.t, res1.y[0], marker='.')\n", "plt.xlabel(\"Zeit t\")\n", "plt.ylabel(\"Temperatur T\")\n", "plt.grid()\n", "\n", "# Ausgabe für den Lösungshinweis\n", "# plt.savefig('teil1.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aufgabenteil B\n", "\n", "Fügen Sie einen neuen Koeffizienten $\\sf \\beta$ als Vorfaktor vor den ersten Term auf der rechten Seite der Gleichung. Lösen Sie nun die Gleichung für $\\sf \\beta=0.2$. Stellen Sie graphisch die Lösungen mit und ohne das $\\sf \\beta$ in einer Graphik dar." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lösungshinweis\n", "\n", "Die Ausgabe könnte wie folgt aussehen.\n", "\n", "![](teil2.png)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "loesung", "hide-cell" ] }, "source": [ "### Lösungsvorschlag" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "def f_T2(t, T):\n", " Tinfty = 10\n", " beta = 0.2\n", " return -beta*(T-Tinfty)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "T0 = 20\n", "res2 = scipy.integrate.solve_ivp(f_T2, [0, 25], [T0])" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(res1.t, res1.y[0], marker='.', label='beta=1')\n", "plt.plot(res2.t, res2.y[0], marker='.', label='beta=0.2')\n", "\n", "plt.xlabel(\"Zeit t\")\n", "plt.ylabel(\"Temperatur T\")\n", "plt.grid()\n", "plt.legend()\n", "\n", "# Ausgabe für den Lösungshinweis\n", "# plt.savefig('teil2.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aufgabenteil C\n", "\n", "Nun wird der Quellterm $\\sf Q(t)$ erweitert. Dieser soll für die Zeit zwischen 5 und 25 zwei volle Sinus-Schwingungen mit einer Amplitude von 10 durchführen, sonst ist er Null. Lösen Sie die Gleichung mit $\\sf \\beta=0.2$ bis zur Zeit $\\sf t=50$. Stellen Sie neben der Lösung auch die Quelltermfunktion $\\sf Q(t)$ in einer gemeinsamen Graphik dar." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lösungshinweis\n", "\n", "Die Ausgabe könnte wie folgt aussehen.\n", "\n", "![](teil3.png)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "loesung", "hide-cell" ] }, "source": [ "### Lösungsvorschlag" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "def f_Q(t):\n", " Q = 0\n", " if t >= 5 and t <= 25: \n", " Q = 10 * np.sin((t-5)/20 * 4 * np.pi)\n", " return Q" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "def f_T3(t, T):\n", " Tinfty = 10\n", " return -0.2*(T-Tinfty) + f_Q(t)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "T0 = 20\n", "res3 = scipy.integrate.solve_ivp(f_T3, [0, 50], [T0])" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(res3.t, res3.y[0], marker='.', label='T(t)')\n", "\n", "Q = np.zeros_like(res3.t)\n", "for i in range(len(Q)):\n", " Q[i] = f_Q(res3.t[i])\n", " \n", "plt.plot(res3.t, Q, marker='.', label='Q(t)')\n", "\n", "plt.xlabel(\"Zeit t\")\n", "plt.ylabel(\"Funktionswert\")\n", "plt.grid()\n", "plt.legend()\n", "\n", "# Ausgabe für den Lösungshinweis\n", "# plt.savefig('teil3.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aufgabenteil D\n", "\n", "Die graphische Darstellung, siehe Lösungshinweis, deutet auf eine sehr sprunghafte Lösung. Verwenden Sie das optionale Argument `max_step` der Funktion `scipy.integrate.solve_ivp` um einen kleineren Zeitschritt, z.B. $\\sf \\Delta t=0.25$, zu wählen. Vergleichen Sie nun die beiden Lösungen. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lösungshinweis\n", "\n", "Die Ausgabe könnte wie folgt aussehen.\n", "\n", "![](teil4.png)" ] }, { "cell_type": "markdown", "metadata": { "tags": [ "loesung", "hide-cell" ] }, "source": [ "### Lösungsvorschlag" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [], "source": [ "T0 = 20\n", "res4 = scipy.integrate.solve_ivp(f_T3, [0, 50], [T0], max_step=0.5)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "tags": [ "loesung", "hide-cell" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(res3.t, res3.y[0], marker='.', label='T(t) – dt variabel')\n", "plt.plot(res4.t, res4.y[0], marker='.', label='T(t) – dt max 0.5')\n", "\n", "Q = np.zeros_like(res4.t)\n", "for i in range(len(Q)):\n", " Q[i] = f_Q(res4.t[i])\n", " \n", "plt.plot(res4.t, Q, marker='.', label='Q(t)')\n", "\n", "plt.xlabel(\"Zeit t\")\n", "plt.ylabel(\"Funktionswert\")\n", "plt.grid()\n", "plt.legend()\n", "\n", "# Ausgabe für den Lösungshinweis\n", "# plt.savefig('teil4.png')" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Tags", "kernelspec": { "display_name": "Python 3", "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }