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started work on e-RK-4 for outflux calculation

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Brantegger Georg
2022-06-13 15:03:01 +02:00
parent 12b362523e
commit aa2939bf8b
1 changed files with 45 additions and 13 deletions
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58
Ausgleichsbecken.py
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@@ -1,8 +1,8 @@
import numpy as np import numpy as np
def Volume_trend(influx,outflux,timestep=1,V_0=0): def Volume_trend(influx, outflux, timestep=1, V_0=0):
''' '''
Returns the trend and the volume and the final volume, defined Returns the trend and the volume and the final volume, defined
by influx and outflux patterns. The optional parameter timestep by influx and outflux patterns. The optional parameter timestep
defines the time increment over which the fluxes are changing. defines the time increment over which the fluxes are changing.
''' '''
@@ -10,26 +10,58 @@ def Volume_trend(influx,outflux,timestep=1,V_0=0):
delta_V = net_flux*timestep delta_V = net_flux*timestep
V_trend = V_0+np.cumsum(delta_V) V_trend = V_0+np.cumsum(delta_V)
V_end = V_trend[-1] V_end = V_trend[-1]
return V_end, V_trend return V_end, V_trend
def Height_trend(V_trend,area=1,h_crit_low=-np.inf,h_crit_high=np.inf): def Height_trend(V_trend, area=1, h_crit_low=-np.inf, h_crit_high=np.inf):
''' '''
Returns the trend and the height and the final height, defined Returns the trend and the height and the final height, defined
by influx and outflux patterns as well as the crosssection area. by influx and outflux patterns as well as the crosssection area.
The optional parameters h_crit_low/high indicate limits that the height The optional parameters h_crit_low/high indicate limits that the height
should never exceed. If this occures, TRUE is returned in the corresponding should never exceed. If this occures, TRUE is returned in the corresponding
h_crit_flag. h_crit_flag.
''' '''
h_trend = V_trend/area h_trend = V_trend/area
h_crit_flag_low = np.any(h_trend <= h_crit_low) h_crit_flag_low = np.any(h_trend <= h_crit_low)
h_crit_flag_high = np.any(h_trend >= h_crit_high) h_crit_flag_high = np.any(h_trend >= h_crit_high)
h_end = h_trend[-1] h_end = h_trend[-1]
return h_trend,h_end,h_crit_flag_low,h_crit_flag_high return h_trend, h_end, h_crit_flag_low, h_crit_flag_high
def get_h_halfstep(initial_height, influx, outflux, timestep, area):
h0 = initial_height
Q_in = influx
Q_out = outflux
dt = timestep
A = area
h_halfstep = h0+1/A*(Q_in-Q_out)*dt/2
def get_p_halfstep(p0, p1):
p_halfstep = (p0+p1)/2
def FODE_function(x, h, alpha, p, rho=1000, g=9.81):
f = x**2/h*alpha+g+p/(rho*h)
return f
def e_RK_4(yn, h, dt, Q0, Q1, A0, A1, p0, p1):
alpha = (A1/A0-1)
h_hs = get_h_halfstep(h, Q0, Q1, dt, A0)
p_hs = get_p_halfstep(p0, p1)
Y1 = yn
Y2 = yn + dt/2*FODE_function(Y1, h, alpha, p0)
Y3 = yn + dt/2*FODE_function(Y2, h_hs, alpha, p_hs)
Y4 = yn + dt*FODE_function(Y3, h_hs, alpha, p_hs)
ynp1 = yn + dt/6*(FODE_function(Y1, h, alpha, p)+2*FODE_function(Y2, h_hs, alpha, p_hs)+ \
2*FODE_function(Y3, h_hs, alpha, p_hs)+ FODE_function(Y4, h, alpha, p))
## testing ## testing
if __name__ == "__main__": # if __name__ == "__main__":
influx = np.full([1,100], 6) # influx = np.full([1, 100], 6)
outflux = np.full_like(influx, 4) # outflux = np.full_like(influx, 4)
V_end, V_trend = Volume_trend(influx, outflux,timestep=0.5,V_0 = 100) # V_end, V_trend = Volume_trend(influx, outflux, timestep=0.5, V_0 = 100)
print(V_end) # print(V_end)
print(V_trend) # print(V_trend)