Add area-wide ablation

Author: danshapero

notebooks/frontal-ablation.ipynb

@@ -70,6 +70,19 @@
     "h = h_0.copy(deepcopy=True)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8587d44a-f4bd-4203-b233-c298f3171a8e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a = Constant(0.0)\n",
+    "m_0 = Constant(-1.0)\n",
+    "δm_δx = Constant(4.0)\n",
+    "m = max_value(0, δm_δx * x[0] + m_0)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -78,7 +91,7 @@
    "outputs": [],
    "source": [
     "ϕ = firedrake.TestFunction(Q)\n",
-    "F_cells = (Dt(h) * ϕ - inner(h * u, grad(ϕ))) * dx\n",
+    "F_cells = (Dt(h) * ϕ - inner(h * u, grad(ϕ)) - (a - m) * ϕ) * dx\n",
     "\n",
     "ν = firedrake.FacetNormal(mesh)\n",
     "f = max_value(0, h * inner(u, ν))\n",
@@ -101,13 +114,21 @@
     "t = Constant(0.0)\n",
     "dt = Constant(0.5 * δ / u_max)\n",
     "\n",
+    "lower = firedrake.Function(Q)\n",
+    "upper = firedrake.Function(Q)\n",
+    "upper.assign(np.inf)\n",
+    "bounds = (\"stage\", lower, upper)\n",
+    "\n",
     "params = {\n",
     "    \"solver_parameters\": {\n",
-    "        \"snes_type\": \"newtonls\",\n",
+    "        \"snes_type\": \"vinewtonrsls\",\n",
     "        \"ksp_type\": \"gmres\",\n",
     "        \"pc_type\": \"lu\",\n",
     "        \"pc_factor_mat_solver_type\": \"mumps\",\n",
     "    },\n",
+    "    \"stage_type\": \"value\",\n",
+    "    \"basis_type\": \"Bernstein\",\n",
+    "    \"bounds\": bounds,\n",
     "}\n",
     "\n",
     "solver = irksome.TimeStepper(F, method, t, dt, h, **params)"