FEAT: 1d conduction, fixed BCs

Author: aaronjridley

day_6/2023/conduction_v0.py

@@ -0,0 +1,56 @@
+#!/usr/bin/env python
+
+import numpy as np
+import matplotlib.pyplot as plt
+from tridiagonal import solve_tridiagonal
+
+# ----------------------------------------------------------------------
+# Main code
+# ----------------------------------------------------------------------
+
+if __name__ == "__main__":
+
+    dx = 0.25
+
+    # set x with 1 ghost cell on both sides:
+    x = np.arange(-dx, 10 + 2 * dx, dx)
+
+    t_lower = 200.0
+    t_upper = 1000.0
+
+    nPts = len(x)
+
+    # set default coefficients for the solver:
+    a = np.zeros(nPts) + 1
+    b = np.zeros(nPts) - 2
+    c = np.zeros(nPts) + 1
+    d = np.zeros(nPts)
+
+    # boundary conditions (bottom - fixed):
+    a[0] = 0
+    b[0] = 1
+    c[0] = 0
+    d[0] = t_lower
+
+    # top - fixed:
+    a[-1] = 0
+    b[-1] = 1
+    c[-1] = 0
+    d[-1] = t_upper
+
+    # solve for Temperature:
+    t = solve_tridiagonal(a, b, c, d)
+
+    # plot:
+    fig = plt.figure(figsize = (10,10))
+    ax = fig.add_subplot(111)
+
+    ax.plot(x, t)
+
+    plotfile = 'conduction_v0.png'
+    print('writing : ',plotfile)    
+    fig.savefig(plotfile)
+    plt.close()
+    
+    
+