From 7cb44220ef17b6af55257ec05d27474e15adb5c1 Mon Sep 17 00:00:00 2001
From: Philipp Holl <philipp.holl@tum.de>
Date: Sun, 15 Dec 2024 14:06:00 +0100
Subject: [PATCH] [demos] Update FVM_Cylinder_GMsh.ipynb

---
 examples/mesh/FVM_Cylinder_GMsh.ipynb | 29 ++++++++++++++++++++++++---
 1 file changed, 26 insertions(+), 3 deletions(-)

diff --git a/examples/mesh/FVM_Cylinder_GMsh.ipynb b/examples/mesh/FVM_Cylinder_GMsh.ipynb
index 943b477ff..b604aa12d 100644
--- a/examples/mesh/FVM_Cylinder_GMsh.ipynb
+++ b/examples/mesh/FVM_Cylinder_GMsh.ipynb
@@ -13,19 +13,26 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
-    "# %pip install --quiet phiflow\n",
+    "# %pip install --quiet phiflow meshio\n",
     "from phi.torch.flow import *\n",
     "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well.\n",
     "from tqdm.notebook import trange"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's download the example mesh file and visualize it!"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
@@ -59,10 +66,19 @@
     }
    ],
    "source": [
+    "!wget https://raw.githubusercontent.com/tum-pbs/PhiFlow/master/examples/mesh/cylinder.msh -O cylinder.msh\n",
+    "\n",
     "mesh = geom.load_gmsh('cylinder.msh', ('y-', 'x+', 'y+', 'x-', 'cyl+', 'cyl-'))\n",
     "plot(Box(x=6, y=6), mesh, overlay='args', size=(4, 3), title='cylinder.msh')"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Next we can define the fluid dynamics. The momentum equation uses diffusion and advection while incompressibility is maintained by solving a separate linear system via `make_incompressible`."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 3,
@@ -82,6 +98,13 @@
     "    return v"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now let's set the boundary and initial conditions and run the simulation!"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 11,