diff --git a/docs/_toc.yml b/docs/_toc.yml
index a6e812e..87e5c95 100644
--- a/docs/_toc.yml
+++ b/docs/_toc.yml
@@ -13,4 +13,5 @@ parts:
     - file: euler-riemann.ipynb
     - file: euler.ipynb
     - file: convergence.ipynb
+    - file: hse-reconstruction.ipynb
     - file: hse.ipynb
diff --git a/docs/hse-reconstruction.ipynb b/docs/hse-reconstruction.ipynb
new file mode 100644
index 0000000..762f5b2
--- /dev/null
+++ b/docs/hse-reconstruction.ipynb
@@ -0,0 +1,233 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "c37ac15a-66a3-452b-8d2f-1e02daafe7cc",
+   "metadata": {},
+   "source": [
+    "# Hydrostatic equilibrum reconstruction"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1ffb1bcd-749b-4e26-98e3-51b4b79cf1a0",
+   "metadata": {},
+   "source": [
+    "Here we explore the reconstruction of the pressure when in hydrostatic equilibrium"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "id": "e9274186-dea7-4254-a5e1-1c10e4ede36c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from ppmpy.euler import Euler\n",
+    "from ppmpy.gravity import constant_gravity\n",
+    "from ppmpy.initial_conditions import hse\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e856cdf1-b7a7-4b27-85dc-51b6e9f1f6bd",
+   "metadata": {},
+   "source": [
+    "HSE atmosphere defaults"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "id": "51d959b0-aa90-4b20-bbdc-39426b00bf6e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "params = {\"base_density\": 1.0, \"base_pressure\": 1.0, \"g_const\": -1.0}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3832cea4-6c6c-4321-a10a-f1080ed0247f",
+   "metadata": {},
+   "source": [
+    "## Normal PPM reconstruction\n",
+    "\n",
+    "Here we use reflecting boundaries and the standard PPM reconstruction, with limiting."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "id": "a92c60c9-d3d6-4a79-85c0-85c14b822849",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "nx = 16\n",
+    "e = Euler(nx, 0.5, init_cond=hse,\n",
+    "          grav_func=constant_gravity,\n",
+    "          bc_left_type=\"reflect\", bc_right_type=\"reflect\", params=params)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bbfc6dfc-2d78-4e69-b5f8-79a6f98d4881",
+   "metadata": {},
+   "source": [
+    "We can look at the reflecting boundary conditions to see what they do to the atmosphere"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "id": "14122168-688f-4897-93b7-dd7cb2b93595",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5, 0, 'x')"
+      ]
+     },
+     "execution_count": 53,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 960x720 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots()\n",
+    "q = e.cons_to_prim()\n",
+    "ax.plot(e.grid.x, q[:, e.v.qp], marker=\"x\")\n",
+    "ax.set_ylabel(\"p\")\n",
+    "ax.set_xlabel(\"x\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "64ecf400-7bdd-4a05-b08d-32f795e741ea",
+   "metadata": {},
+   "source": [
+    "Now we can visualize how PPM reconstructs pressure near the lower boundary"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "id": "39799ee0-3491-4dfa-ade3-5b0b2c9fbfaf",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 2880x720 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "gp = e.grid.draw(lo_index=3, hi_index=8, stretch=6)\n",
+    "e.draw_prim(gp, e.v.qp)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "94add942-9fcd-4edf-ad3b-301b11976e50",
+   "metadata": {},
+   "source": [
+    "Notice that the first interior zone has a flat profile, so there is no pressure gradient and that zone will not be in HSE\n",
+    "when we use the pressure coming from the Riemann problem to balance the gravitational source term."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "19c07300-f8a8-4aa2-9c5f-63db3ac4647b",
+   "metadata": {},
+   "source": [
+    "## Hydrostatic pressure reconstruction"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "id": "43b9e555-d716-4b32-bc71-f94d26e22865",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "nx = 16\n",
+    "e = Euler(nx, 0.5, init_cond=hse,\n",
+    "          grav_func=constant_gravity,\n",
+    "          use_hse_reconstruction=True,\n",
+    "          bc_left_type=\"reflect\", bc_right_type=\"reflect\", params=params)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "id": "f49a2e09-8fb6-44c4-bbc3-1ad90e1f4a58",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 2880x720 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "gp2 = e.grid.draw(lo_index=3, hi_index=8, stretch=6)\n",
+    "e.draw_prim(gp2, e.v.qp)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eee42e2e-509d-46d0-9abe-64089c958c83",
+   "metadata": {},
+   "source": [
+    "In this case, we see that the pressure in the first interior zone has a gradient that matches the needed HSE pressure gradient.\n",
+    "\n",
+    "For the simulations, we will need to reflect the interface states across the boundary so the Riemann solver does not generate a flux through the boundary."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.12.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}