First try for optimisation of initial conditions

graph_opti.py

+# -*- coding: utf-8 -*-
+
+from scipy.integrate import solve_ivp
+import matplotlib.pyplot as mpl
+        
+
+def couche_lim(eta, f):
+    return (f[1],f[2],-3*f[0]*f[2] + 2*(f[1]**2) - f[3], f[4],-3*Pr*f[0]*f[4])
+
+def optim(Pr, f_2_0,th_1_0):
+    n = 7
+    sol = solve_ivp(couche_lim, (0,40), [0,0,f_2_0,1,th_1_0])
+    while abs(sol.y[1][-1]) > 0.001:
+        if n > 50 :
+            print("n > 50")
+            break
+        
+        if sol.y[1][-1] > 0.001:
+            f_2_0 *= 1 - 1/(2**(n+1))
+            th_1_0 *= 1 - 1/(2**n)
+        elif sol.y[1][-1] < -0.001:
+            f_2_0 *= 1 + 1/(2**(n+1))
+            th_1_0 *= 1 + 1/(2**n)
+            
+        sol = solve_ivp(couche_lim, (0,40), [0,0,f_2_0,1,th_1_0])
+        n += 1
+    return sol
+    
+
+
+if __name__ == "__main__":
+    print("Couche limite de vitesses")
+    Pr = 0.01
+    f_2_0 = 1.01
+    th_1_0 = -0.06
+    sol = optim(Pr, f_2_0,th_1_0)
+    mpl.plot(sol.t,sol.y[1], label = "f'(η)")
+    mpl.plot(sol.t,sol.y[3], label = "θ(η)")
+    mpl.legend()
+    mpl.show()
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