Assignment 01

Assignments2025/Assignment01.ipynb

@@ -2000,7 +2000,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22359a38-73f5-44f0-b41f-c4435d9a2a30",
+   "id": "8f21e65e-f1fa-41d2-9670-83a8a91047c5",
    "metadata": {
     "editable": true,
     "slideshow": {
@@ -2014,6 +2014,31 @@
     "*Text/markdown answer here.*  (use more cells if desired)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "22359a38-73f5-44f0-b41f-c4435d9a2a30",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "### Q4.2: Solve for the characterstics numerically\n",
+    "\n",
+    "We can iterartively solve for characterstics by \n",
+    "- defining a grid in x and t (note I made these more finely resolved than the non-linear solution otherwise it is not very accurate)\n",
+    "- From the first time step, propagating the positive and negative characterstics forward in time to the second time step.\n",
+    "- We now know R+, R- at values of x at the next time step, interpolate these onto the x-grid\n",
+    "- now we know R+ and R- on the x-grid so solve for the new $u$ and $d$.\n",
+    "- repeat for the next time step.\n",
+    "\n",
+    "Plot the water level as a Hovmoller diagram and compare to your non-linear simulation.  Note the location of any shocks or rarefactions.\n",
+    "\n",
+    "Using the solution, calcculate a series of characteristics emanating from the time origin, and discuss how they correspond to the shock or rarefaction.  "
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -15895,6 +15920,7 @@
       "state": {
        "_data_url": 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",
        "_figure_label": "Figure 166",
+       "_message": "x=530. y=8.75",
        "_model_module_version": "^0.11",
        "_size": [
         640,