30 lines
1.1 KiB
Python
30 lines
1.1 KiB
Python
# common.py
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import numpy as np
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from Bar import Bar
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def fdm_heat_extraction(t_0, t_1, dx, bar:'Bar', order=2):
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'''Get the heat conduction at the point t_1 using Taylor series'''
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if order == 1:
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return -1 * bar.k * bar.area * (t_1 - t_0) / dx
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elif order == 2:
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return -1 * bar.k * bar.area * (((t_1 - t_0) / dx) + (bar.alpha**2 * dx * t_1 / 2))
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def fem_heat_extraction(t_0, t_1, dx, bar:'Bar'):
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'''Get the heat conduction at the point t_1 using FEM equation'''
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term_1 = (-1/dx + bar.alpha**2*dx/6) * t_0
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term_2 = (1/dx + 2*bar.alpha**2*dx/6) * t_1
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return -1 * bar.k * bar.area * (term_1 + term_2)
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def calc_error(exact, q_1):
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return np.abs((exact - q_1) / exact)
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def calc_beta(exact, q_1, q_2, dx_1, dx_2):
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return np.log(np.abs((exact - q_1)/(exact - q_2))) / np.log(dx_1 / dx_2)
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def calc_extrapolated(q1, q2, q3):
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'''Calcs the Richardson Extrapolation value based on 3 different meshes.
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Assumes that q3 is 2x finer than q2 is 2x finer than q1'''
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numerator = q1*q3 - q2**2
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denominator = q1 + q3 - 2*q2
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return numerator / denominator |