added "vectorized" version of method of characteristics
This commit is contained in:
Brantegger Georg
@@ -240,7 +240,7 @@ class Druckrohrleitung_class:
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self.v[i] = 0.5*(self.v_old[i+1]+self.v_old[i-1])-0.5/(rho*c)*(self.p_old[i+1]-self.p_old[i-1]) \
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+dt*g*np.sin(alpha)-f_D*dt/(4*D)*(abs(self.v_old[i+1])*self.v_old[i+1]+abs(self.v_old[i-1])*self.v_old[i-1])
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self.p[i] = 0.5*(self.p_old[i+1]+self.p_old[i-1]) - 0.5*rho*c*(self.v_old[i+1]-self.v_old[i-1]) \
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self.p[i] = 0.5*(self.p_old[i+1]+self.p_old[i-1])-0.5*rho*c*(self.v_old[i+1]-self.v_old[i-1]) \
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+f_D*rho*c*dt/(4*D)*(abs(self.v_old[i+1])*self.v_old[i+1]-abs(self.v_old[i-1])*self.v_old[i-1])
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# update overall min and max values for pressure and velocity per node
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@@ -254,3 +254,35 @@ class Druckrohrleitung_class:
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# else one can overwrite data by accidient and change two variables at once without noticing
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self.p_old = self.p.copy()
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self.v_old = self.v.copy()
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def timestep_characteristic_method_vectorized(self):
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# use the method of characteristics to calculate the pressure and velocities at all nodes except the boundary ones
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# they are set with the .set_boundary_conditions_next_timestep() method beforehand
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# constants for cleaner formula
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rho = self.density # density of liquid
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c = self.c # pressure propagation velocity
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f_D = self.f_D # Darcy friction coefficient
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dt = self.dt # timestep
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D = self.dia # pipeline diameter
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g = self.g # graviational acceleration
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alpha = self.angle # pipeline angle
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# Vectorized loop
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self.v[1:-1] = 0.5*(self.v_old[2:]+self.v_old[:-2])-0.5/(rho*c)*(self.p_old[2:]-self.p_old[:-2]) \
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+dt*g*np.sin(alpha)-f_D*dt/(4*D)*(np.abs(self.v_old[2:])*self.v_old[2:]+np.abs(self.v_old[:-2])*self.v_old[:-2])
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self.p[1:-1] = 0.5*(self.p_old[2:]+self.p_old[:-2])-0.5*rho*c*(self.v_old[2:]-self.v_old[:-2]) \
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+f_D*rho*c*dt/(4*D)*(np.abs(self.v_old[2:])*self.v_old[2:]-np.abs(self.v_old[:-2])*self.v_old[:-2])
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# update overall min and max values for pressure and velocity per node
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self.p_min = np.minimum(self.p_min,self.p)
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self.p_max = np.maximum(self.p_max,self.p)
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self.v_min = np.minimum(self.v_min,self.v)
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self.v_max = np.maximum(self.v_max,self.v)
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# prepare for next call
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# use .copy() to write data to another memory location and avoid the usual python reference pointer
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# else one can overwrite data by accidient and change two variables at once without noticing
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self.p_old = self.p.copy()
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self.v_old = self.v.copy()
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@@ -2,7 +2,7 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -22,7 +22,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -80,48 +80,9 @@
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The pipeline has the following attributes: \n",
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"----------------------------- \n",
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"Length = 1013.0 m \n",
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"Diameter = 0.9 m \n",
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"Hydraulic head = 105.0 m \n",
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"Number of segments = 50 \n",
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"Number of nodes = 51 \n",
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"Length per segments = 20.26 m \n",
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"Pipeline angle = 0.104 rad \n",
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"Pipeline angle = 5.95° \n",
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"Darcy friction factor = 0.014 \n",
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"Density of liquid = 1000.0 kg/m³ \n",
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"Pressure wave vel. = 500.0 m/s \n",
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"Simulation timestep = 0.04052 s \n",
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"----------------------------- \n",
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"Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object\n",
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"The pipeline has the following attributes: \n",
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"----------------------------- \n",
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"Length = 1013.0 m \n",
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"Diameter = 0.9 m \n",
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"Hydraulic head = 105.0 m \n",
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"Number of segments = 50 \n",
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"Number of nodes = 51 \n",
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"Length per segments = 20.26 m \n",
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"Pipeline angle = 0.104 rad \n",
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"Pipeline angle = 5.95° \n",
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"Darcy friction factor = 0.014 \n",
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"Density of liquid = 1000.0 kg/m³ \n",
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"Pressure wave vel. = 500.0 m/s \n",
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"Simulation timestep = 0.04052 s \n",
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"----------------------------- \n",
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"Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object\n"
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]
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}
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],
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"outputs": [],
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"source": [
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"# create objects\n",
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"\n",
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@@ -137,7 +98,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -168,7 +129,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@@ -193,48 +154,9 @@
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"execution_count": null,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The cuboid reservoir has the following attributes: \n",
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"----------------------------- \n",
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"Base area = 74.0 m² \n",
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"Outflux area = 0.636 m² \n",
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"Current level = 8.0 m\n",
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"Critical level low = 0.0 m \n",
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"Critical level high = inf m \n",
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"Volume in reservoir = 592.0 m³ \n",
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"Current influx = 0.773 m³/s \n",
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"Current outflux = 0.773 m³/s \n",
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"Current outflux vel = 1.215 m/s \n",
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"Current pipe pressure = 7.854 mWS \n",
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"Simulation timestep = 0.001013 s \n",
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"Density of liquid = 1000.0 kg/m³ \n",
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"----------------------------- \n",
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"\n",
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"The pipeline has the following attributes: \n",
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"----------------------------- \n",
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"Length = 1013.0 m \n",
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"Diameter = 0.9 m \n",
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"Hydraulic head = 105.0 m \n",
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"Number of segments = 50 \n",
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"Number of nodes = 51 \n",
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"Length per segments = 20.26 m \n",
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"Pipeline angle = 0.104 rad \n",
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"Pipeline angle = 5.95° \n",
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"Darcy friction factor = 0.014 \n",
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"Density of liquid = 1000.0 kg/m³ \n",
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"Pressure wave vel. = 500.0 m/s \n",
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"Simulation timestep = 0.04052 s \n",
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"----------------------------- \n",
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"Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object\n"
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]
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}
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],
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"outputs": [],
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"source": [
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"for it_pipe in range(1,nt+1):\n",
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"# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n",
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@@ -257,7 +179,7 @@
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" v_boundary_res[it_pipe] = pipe.get_current_velocity_distribution()[0]\n",
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"\n",
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" # perform the next timestep via the characteristic method\n",
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" pipe.timestep_characteristic_method()\n",
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" pipe.timestep_characteristic_method_vectorized()\n",
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"\n",
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" # prepare for next loop\n",
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" p_old = pipe.get_current_pressure_distribution()\n",
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@@ -283,7 +205,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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