added more complex geometry for Clebsch coordinate calculations

Geometry used was taken from boutproject/BOUT-dev#2207
pollypparrot · Jul 12, 2023 · 0b5b598 · 0b5b598
1 parent 52e36d4
commit 0b5b598
Showing 1 changed file with 17 additions and 12 deletions.
diff --git a/MasterclassCode.ipynb b/MasterclassCode.ipynb
@@ -1785,7 +1785,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 20,
    "id": "0f97fbe7",
    "metadata": {
     "scrolled": true
@@ -1826,7 +1826,7 @@
     {
      "data": {
       "text/latex": [
-       "$\\displaystyle Jacobian = \\frac{h_{\\theta}}{B_{pol}} = h_{\\theta} x$"
+       "$\\displaystyle Jacobian = \\frac{h_{\\theta}}{B_{pol}} = 0.0081 \\left(0.111111111111111 x + 1\\right)^{2}$"
       ],
       "text/plain": [
        "<IPython.core.display.Math object>"
@@ -1838,7 +1838,7 @@
     {
      "data": {
       "text/latex": [
-       "$\\displaystyle Bpol = \\frac{1}{x}$"
+       "$\\displaystyle Bpol = \\frac{1}{0.01 x + 0.09}$"
       ],
       "text/plain": [
        "<IPython.core.display.Math object>"
@@ -1850,7 +1850,7 @@
     {
      "data": {
       "text/latex": [
-       "$\\displaystyle Btor = \\frac{1}{R}$"
+       "$\\displaystyle Btor = \\frac{1}{- \\left(0.01 x + 0.09\\right) \\cos{\\left(y \\right)} + 1}$"
       ],
       "text/plain": [
        "<IPython.core.display.Math object>"
@@ -1862,7 +1862,7 @@
     {
      "data": {
       "text/latex": [
-       "$\\displaystyle Bxy = \\sqrt{\\frac{1}{x^{2}} + \\frac{1}{R^{2}}}$"
+       "$\\displaystyle Bxy = 11.1111111111111 \\sqrt{\\frac{0.0081}{\\left(- \\left(0.01 x + 0.09\\right) \\cos{\\left(y \\right)} + 1\\right)^{2}} + \\frac{1}{\\left(0.111111111111111 x + 1\\right)^{2}}}$"
       ],
       "text/plain": [
        "<IPython.core.display.Math object>"
@@ -1874,7 +1874,7 @@
     {
      "data": {
       "text/latex": [
-       "$\\displaystyle gxx = \\frac{R^{2}}{x^{2}}$"
+       "$\\displaystyle gxx = \\frac{123.456790123457 \\left(- \\left(0.01 x + 0.09\\right) \\cos{\\left(y \\right)} + 1\\right)^{2}}{\\left(0.111111111111111 x + 1\\right)^{2}}$"
       ],
       "text/plain": [
        "<IPython.core.display.Math object>"
@@ -1886,7 +1886,7 @@
     {
      "data": {
       "text/latex": [
-       "$\\displaystyle gzz = \\frac{I^{2} R^{2}}{x^{2}} + \\frac{x^{2} \\left(\\frac{1}{x^{2}} + \\frac{1}{R^{2}}\\right)}{R^{2}}$"
+       "$\\displaystyle gzz = \\frac{123.456790123457 I^{2} \\left(- \\left(0.01 x + 0.09\\right) \\cos{\\left(y \\right)} + 1\\right)^{2}}{\\left(0.111111111111111 x + 1\\right)^{2}} + \\frac{0.0081 \\left(0.111111111111111 x + 1\\right)^{2} \\left(\\frac{1.0}{\\left(- \\left(0.01 x + 0.09\\right) \\cos{\\left(y \\right)} + 1\\right)^{2}} + \\frac{123.456790123457}{\\left(0.111111111111111 x + 1\\right)^{2}}\\right)}{\\left(- \\left(0.01 x + 0.09\\right) \\cos{\\left(y \\right)} + 1\\right)^{2}}$"
       ],
       "text/plain": [
        "<IPython.core.display.Math object>"
@@ -1924,7 +1924,7 @@
     {
      "data": {
       "text/latex": [
-       "$\\displaystyle b = z^{2} + 2 \\left(\\frac{I^{2} R^{2}}{x^{2}} + \\frac{x^{2} \\left(\\frac{1}{x^{2}} + \\frac{1}{R^{2}}\\right)}{R^{2}}\\right) \\left(x + y + \\sin{\\left(2 \\pi z \\right)}\\right)$"
+       "$\\displaystyle b = z^{2} + 2.0 \\left(\\frac{123.456790123457 I^{2} \\left(- \\left(0.01 x + 0.09\\right) \\cos{\\left(y \\right)} + 1\\right)^{2}}{\\left(0.111111111111111 x + 1\\right)^{2}} + \\frac{0.0081 \\left(0.111111111111111 x + 1\\right)^{2} \\left(\\frac{1.0}{\\left(- \\left(0.01 x + 0.09\\right) \\cos{\\left(y \\right)} + 1\\right)^{2}} + \\frac{123.456790123457}{\\left(0.111111111111111 x + 1\\right)^{2}}\\right)}{\\left(- \\left(0.01 x + 0.09\\right) \\cos{\\left(y \\right)} + 1\\right)^{2}}\\right) \\left(x + y + \\sin{\\left(2 \\pi z \\right)}\\right)$"
       ],
       "text/plain": [
        "<IPython.core.display.Math object>"
@@ -1938,7 +1938,7 @@
      "output_type": "stream",
      "text": [
       "result that is copiable to c++ NOTE: change  ** to pow(a,b) to avoid errors in c++\n",
-      "z**2 + 2*(I**2*R**2/x**2 + x**2*(x**(-2) + R**(-2))/R**2)*(x + y + sin(2*pi*z))\n",
+      "z**2 + 2.0*(123.456790123457*I**2*(-(0.01*x + 0.09)*cos(y) + 1)**2/(0.111111111111111*x + 1)**2 + 0.0081*(0.111111111111111*x + 1)**2*(1.0/(-(0.01*x + 0.09)*cos(y) + 1)**2 + 123.456790123457/(0.111111111111111*x + 1)**2)/(-(0.01*x + 0.09)*cos(y) + 1)**2)*(x + y + sin(2*pi*z))\n",
       "\n"
      ]
     }
@@ -1963,11 +1963,16 @@
     "#write Jacobian, metric tensors and functions for B and R\n",
     "#start with B functions as then, when the Jacobian and metric tensors are applied, the functions are subbed in.\n",
     "\n",
-    "Bpol = 1/x\n",
-    "Btor = 1/R\n",
+    "eps =.1\n",
+    "r = eps*(0.9 +0.1*x)\n",
+    "theta = y-pi\n",
+    "Rxy = 1 + r*cos(theta)\n",
+    "h=r\n",
+    "Bpol = 1/r\n",
+    "Btor = 1/Rxy\n",
     "Bxy = sqrt(Bpol**2 + Btor**2)\n",
     "JClebsch = h/Bpol\n",
-    "clebschMetricTensor = [(R*Bpol)**2, 1/(h)**2,I**2*(R*Bpol)**2+Bxy**2/(R*Bpol)**2]\n",
+    "clebschMetricTensor = [(Rxy*Bpol)**2, 1/(h)**2,I**2*(Rxy*Bpol)**2+Bxy**2/(Rxy*Bpol)**2]\n",
     "\n",
     "A = x+y+sin(2*pi*z)\n",
     "D = 1\n",