update EX11

OlafKolditz · Jul 15, 2021 · 66cb284 · 66cb284
1 parent 33d923b
commit 66cb284
Showing 1 changed file with 45 additions and 19 deletions.
diff --git a/BHYWI-08-11/EX11-jupyter-notebook-c++2.ipynb b/BHYWI-08-11/EX11-jupyter-notebook-c++2.ipynb
@@ -25,22 +25,47 @@
     "***Exercise EX10 - Open channel flow*** <br/>"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This figure is summarizing and illustrating the concept of the lecture \"Hydroinformatics II\"\n",
+    "<img src=\"lecture_concept.png\" alt=\"drawing\" width=\"500\"/>\n",
+    "The final exercise \"EX11\" is dealing with open channel flow. A sketch for model set-up is shown in the below figure (Paine 1991)\n",
+    "<img src=\"paine1.png\" alt=\"drawing\" width=\"250\"/>\n",
+    "The theoretical basis is founded by the energy balance law (Bernoulli equation):\n",
+    "\\begin{eqnarray}\n",
+    "f(h)\n",
+    "=\n",
+    "\\left( h + \\frac{Q^2}{2gA^2} \\right)\\mid_D\n",
+    "-\n",
+    "\\left( h + \\frac{Q^2}{2gA^2} \\right)\\mid_U\n",
+    "+\n",
+    "\\Delta x \\frac{(S_{f,U} + S_{f,D})}{2}\n",
+    "\\nonumber\\\\\n",
+    "\\label{eqn:paine7}\n",
+    "\\end{eqnarray}\n",
+    "Based on the energy conversation, a Newton scheme is constructed for solving the non-linear open channel flow equation:\n",
+    "\\begin{eqnarray}\n",
+    "h_{k+1}\n",
+    "=\n",
+    "h_k\n",
+    "+\n",
+    "\\frac{f(h_k)}{f'(h_k)}\n",
+    "=\n",
+    "h_k\n",
+    "+\n",
+    "\\frac{\\mathbf R_k}{\\mathbf J_k}\n",
+    "\\label{eqn:newton}\n",
+    "\\end{eqnarray}\n",
+    "We use a Jupyter notebook, which is using two kernels Python3 und C++."
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Hello Jupyter!\n",
-      "This is Hydroinformatics II 2021: EX10 (open channel flow) on Jupter\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "#include <iostream>\n",
     "using namespace std;\n",
@@ -54,10 +79,11 @@
    "metadata": {},
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.1"
+     "ename": "SyntaxError",
+     "evalue": "invalid syntax (<ipython-input-2-af3b3f6effbc>, line 4)",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-2-af3b3f6effbc>\"\u001b[1;36m, line \u001b[1;32m4\u001b[0m\n\u001b[1;33m    using namespace std;\u001b[0m\n\u001b[1;37m                  ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
      ]
     }
    ],
@@ -324,7 +350,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.5"
+   "version": "3.7.4"
   }
  },
  "nbformat": 4,