Adjust CFL formula

lessons/python/advection.ipynb

@@ -167,7 +167,7 @@
     "- Wind speed `v = 10` m/s\n",
     "- Grid spacing `dx = 500` m (see previous code block)\n",
     "- Total model run duration = 3 hours\n",
-    "- Calculate time step `dt` using the CFL criterion: `dt = 0.9 * v / dx`\n",
+    "- Calculate time step `dt` using the CFL criterion: `dt = 0.9 * dx / abs(v)`\n",
     "- Periodic boundary conditions: the solution at the left boundary depends on the solution at the right boundary if velocity is positive and vice versa for negative velocities. \n",
     "- Plot the wave every 10^5 iterations \n",
     "\n",
@@ -190,7 +190,7 @@
     "    if v > 0:\n",
     "        # here comes the solution of the advection equation  \n",
     "    \n",
-    "    if iter % 1e5 == 0: \n",
+    "    if iter % 10 == 0: \n",
     "        plt.plot(x/1.e3, T, 'b') \n",
     "        plt.xlim((0, max(x/1e3)))\n",
     "        plt.xlabel('x (km)')\n",
@@ -211,7 +211,7 @@
     "# Set parameter values\n",
     "v = 10\n",
     "run_duration = 3 * 60 * 60.0\n",
-    "dt = 0.9 * v / dx\n",
+    "dt = 0.9 * dx / abs(v)\n",
     "print(f\"Time step = {dt} s\")"
    ]
   },
@@ -245,7 +245,7 @@
     "        T[1:] -= v * dt / dx * np.diff(T)\n",
     "        T[0] = T[-1]\n",
     "\n",
-    "    if iter % 1e5 == 0:\n",
+    "    if iter % 10 == 0:\n",
     "        plt.plot(x / 1.0e3, T, \"b\")\n",
     "        plt.xlim((0, max(x / 1e3)))\n",
     "        plt.xlabel(\"x (km)\")\n",
@@ -312,7 +312,7 @@
     "        T[:-1] -= v * dt / dx * np.diff(T)\n",
     "        T[-1] = T[0]\n",
     "\n",
-    "    if iter % 1e5 == 0:\n",
+    "    if iter % 10 == 0:\n",
     "        plt.plot(x / 1.0e3, T, \"r\")\n",
     "        plt.xlim((0, max(x / 1e3)))\n",
     "        plt.xlabel(\"x (km)\")\n",
@@ -390,7 +390,7 @@
     "- Assume an advection velocity of 10 km/h (that is, the wind speed at which ash aerosols are advected towards the continent)\n",
     "- Calculate the time step by combining the CFL criterium for advection (see above) and diffusion:\n",
     "~~~\n",
-    "dt_a = 0.9*v/dx\n",
+    "dt_a = 0.9*dx/v\n",
     "dt_d = dx*dx/D/2.5\n",
     "dt = min(dt_a,dt_d)\n",
     "print('dt is: ' + str(dt) + 'hours')\n",
@@ -445,7 +445,7 @@
     "plt.scatter(x[ind_Bru], C[ind_Bru], c=\"r\")\n",
     "\n",
     "# Calculate a stable time step\n",
-    "dt_a = 0.9 * v / dx\n",
+    "dt_a = 0.9 * dx / v\n",
     "dt_d = dx * dx / D / 2.5\n",
     "dt = min(dt_a, dt_d)\n",
     "print(\"dt is: \" + str(dt) + \"hours\")"
@@ -539,9 +539,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Ivy",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
-   "name": "ivy"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {