def main():
# Setup the grid and compute the initial flow solution
nu, nv, nw = 120, 60, 1
ncells = (nu - 1) * (nv - 1)
# Set some reference values
reference_values = {}
reference_values[0] = 1.2 # density
reference_values[1] = 100 # ro * vel-x
reference_values[2] = 10 # ro * vel-y
reference_values[3] = 100 # ro * energy
# Starting values
starting_variables = {}
primary_variables, secondary_variables, fluxes, boundary_conditions, grid_parameters = initial_setup(
nu, nv, nw)
areas = grid_parameters[7] # Will need this for later!
# Set the time-step
step = set_timestep(primary_variables, secondary_variables,
boundary_conditions, grid_parameters)
# Output iteration frequency
niter = 5
# Initialize delta properties
del_ro = np.zeros((nv, nu))
del_ro_vel_x = np.zeros((nv, nu))
del_ro_vel_y = np.zeros((nv, nu))
del_ro_energy = np.zeros((nv, nu))
# 'Corrected flow properties'
corrected_ro = np.zeros((nv, nu, nw))
corrected_ro_vel_x = np.zeros((nv, nu, nw))
corrected_ro_vel_y = np.zeros((nv, nu, nw))
corrected_ro_energy = np.zeros((nv, nu, nw))
# Display the following message everytime the program is initialized
display_item = str("""
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
TUNGSTEN
ver. 1.0.0
Copyright (c) 2016 by Pranay Seshadri
University of Cambridge, Cambridge, U.K.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"""
)
print(display_item)
nsteps = 100
# Two for-loops
for step_number in range(1, nsteps):
# Define some starting values
starting_variables_temp = set_starting_values(primary_variables)
starting_variables[0] = starting_variables_temp[0]
starting_variables[1] = starting_variables_temp[1]
starting_variables[2] = starting_variables_temp[2]
starting_variables[3] = starting_variables_temp[3]
for nrkut in range(1, 5):
# Define some starting values!
# setting frkut
frkut = 1.0 / (1.0 + 4 - nrkut)
# Set "secondary" variables!
secondary_variables = set_other_variables(primary_variables,
secondary_variables,
boundary_conditions,
grid_parameters)
# Enforce boundary conditions
primary_variables, secondary_variables = apply_boundary_conditions(
step_number, primary_variables, secondary_variables,
boundary_conditions, grid_parameters)
# Set the fluxes!
fluxes = flux.set_fluxes(primary_variables, secondary_variables,
fluxes, boundary_conditions,
grid_parameters)
# Unpack the fluxes
flux_i_mass = fluxes[0]
flux_j_mass = fluxes[1]
flux_i_xmom = fluxes[2]
flux_j_xmom = fluxes[3]
flux_i_ymom = fluxes[4]
flux_j_ymom = fluxes[5]
flux_i_enthalpy = fluxes[6]
flux_j_enthalpy = fluxes[7]
# Unpack the primary variables
ro = primary_variables[0]
ro_vel_x = primary_variables[1]
ro_vel_y = primary_variables[2]
ro_energy = primary_variables[3]
# Unpack the starting variables
start_ro = starting_variables[0]
start_ro_vel_x = starting_variables[1]
start_ro_vel_y = starting_variables[2]
start_ro_energy = starting_variables[3]
# Sum the fluxes
ro, del_ro = flux.sum_fluxes(flux_i_mass, flux_j_mass, ro,
start_ro, del_ro, frkut, step, areas)
ro_vel_x, del_ro_vel_x = flux.sum_fluxes(flux_i_xmom, flux_j_xmom,
ro_vel_x, start_ro_vel_x,
del_ro_vel_x, frkut, step,
areas)
ro_vel_y, del_ro_vel_y = flux.sum_fluxes(flux_i_ymom, flux_j_ymom,
ro_vel_y, start_ro_vel_y,
del_ro_vel_y, frkut, step,
areas)
ro_energy, del_ro_energy = flux.sum_fluxes(
flux_i_enthalpy, flux_j_enthalpy, ro_energy, start_ro_energy,
del_ro_energy, frkut, step, areas)
# Primary variables!
primary_variables[0] = ro
primary_variables[1] = ro_vel_x
primary_variables[2] = ro_vel_y
primary_variables[3] = ro_energy
# Recompute the secondary variables
secondary_variables = set_other_variables(primary_variables,
secondary_variables,
boundary_conditions,
grid_parameters)
#print ro, start_ro
# Write out convergence parameters at every niter iterations
# Smoothing!
#plot_to_grid(grid_parameters, primary_variables, secondary_variables, 500)
#print 'Smoothing routine'
#ro, corrected_ro = smooth(ro, corrected_ro, boundary_conditions, grid_parameters)
#ro_vel_x, corrected_ro_vel_x = smooth(ro_vel_x, corrected_ro_vel_x, boundary_conditions, grid_parameters)
#ro_vel_y, corrected_ro_vel_y = smooth(ro_vel_y, corrected_ro_vel_y, boundary_conditions, grid_parameters)
#ro_energy, corrected_ro_energy = smooth(ro_energy, corrected_ro_energy, boundary_conditions, grid_parameters)
#print 'Smoothing routine done.'
#plot_to_grid(grid_parameters, primary_variables, secondary_variables, 600)
if (np.mod(step_number, niter) == 0):
check_convergence(grid_parameters, primary_variables,
starting_variables, reference_values,
step_number, ncells)
plot_to_grid(grid_parameters, primary_variables,
secondary_variables, step_number)
step = set_timestep(primary_variables, secondary_variables,
boundary_conditions, grid_parameters)
def main():
# Setup the grid and compute the initial flow solution
nu, nv, nw = 120, 60, 1
ncells = (nu - 1) * (nv - 1)
# Set some reference values
reference_values = {}
reference_values[0] = 1.2 # density
reference_values[1] = 100 # ro * vel-x
reference_values[2] = 10 # ro * vel-y
reference_values[3] = 100 # ro * energy
# Starting values
starting_variables = {}
primary_variables, secondary_variables, fluxes, boundary_conditions, grid_parameters = initial_setup(nu, nv, nw)
areas = grid_parameters[7] # Will need this for later!
# Set the time-step
step = set_timestep(primary_variables, secondary_variables, boundary_conditions, grid_parameters)
# Output iteration frequency
niter = 5
# Initialize delta properties
del_ro = np.zeros((nv, nu))
del_ro_vel_x = np.zeros((nv, nu))
del_ro_vel_y = np.zeros((nv, nu))
del_ro_energy = np.zeros((nv, nu))
# 'Corrected flow properties'
corrected_ro = np.zeros((nv, nu, nw))
corrected_ro_vel_x = np.zeros((nv, nu, nw))
corrected_ro_vel_y = np.zeros((nv, nu, nw))
corrected_ro_energy = np.zeros((nv, nu, nw))
# Display the following message everytime the program is initialized
display_item = str("""
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
TUNGSTEN
ver. 1.0.0
Copyright (c) 2016 by Pranay Seshadri
University of Cambridge, Cambridge, U.K.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~""")
print(display_item)
nsteps = 100
# Two for-loops
for step_number in range(1, nsteps):
# Define some starting values
starting_variables_temp = set_starting_values(primary_variables)
starting_variables[0] = starting_variables_temp[0]
starting_variables[1] = starting_variables_temp[1]
starting_variables[2] = starting_variables_temp[2]
starting_variables[3] = starting_variables_temp[3]
for nrkut in range(1, 5):
# Define some starting values!
# setting frkut
frkut = 1.0/(1.0 + 4 - nrkut)
# Set "secondary" variables!
secondary_variables = set_other_variables(primary_variables, secondary_variables, boundary_conditions, grid_parameters)
# Enforce boundary conditions
primary_variables, secondary_variables = apply_boundary_conditions(step_number, primary_variables, secondary_variables, boundary_conditions, grid_parameters)
# Set the fluxes!
fluxes = flux.set_fluxes(primary_variables, secondary_variables, fluxes, boundary_conditions, grid_parameters)
# Unpack the fluxes
flux_i_mass = fluxes[0]
flux_j_mass = fluxes[1]
flux_i_xmom = fluxes[2]
flux_j_xmom = fluxes[3]
flux_i_ymom = fluxes[4]
flux_j_ymom = fluxes[5]
flux_i_enthalpy = fluxes[6]
flux_j_enthalpy = fluxes[7]
# Unpack the primary variables
ro = primary_variables[0]
ro_vel_x = primary_variables[1]
ro_vel_y = primary_variables[2]
ro_energy = primary_variables[3]
# Unpack the starting variables
start_ro = starting_variables[0]
start_ro_vel_x = starting_variables[1]
start_ro_vel_y = starting_variables[2]
start_ro_energy = starting_variables[3]
# Sum the fluxes
ro, del_ro = flux.sum_fluxes(flux_i_mass, flux_j_mass, ro, start_ro, del_ro, frkut, step, areas)
ro_vel_x, del_ro_vel_x = flux.sum_fluxes(flux_i_xmom, flux_j_xmom, ro_vel_x, start_ro_vel_x, del_ro_vel_x, frkut, step, areas)
ro_vel_y, del_ro_vel_y = flux.sum_fluxes(flux_i_ymom, flux_j_ymom, ro_vel_y, start_ro_vel_y, del_ro_vel_y, frkut, step, areas)
ro_energy, del_ro_energy = flux.sum_fluxes(flux_i_enthalpy, flux_j_enthalpy, ro_energy, start_ro_energy, del_ro_energy, frkut, step, areas)
# Primary variables!
primary_variables[0] = ro
primary_variables[1] = ro_vel_x
primary_variables[2] = ro_vel_y
primary_variables[3] = ro_energy
# Recompute the secondary variables
secondary_variables = set_other_variables(primary_variables, secondary_variables, boundary_conditions, grid_parameters)
#print ro, start_ro
# Write out convergence parameters at every niter iterations
# Smoothing!
#plot_to_grid(grid_parameters, primary_variables, secondary_variables, 500)
#print 'Smoothing routine'
#ro, corrected_ro = smooth(ro, corrected_ro, boundary_conditions, grid_parameters)
#ro_vel_x, corrected_ro_vel_x = smooth(ro_vel_x, corrected_ro_vel_x, boundary_conditions, grid_parameters)
#ro_vel_y, corrected_ro_vel_y = smooth(ro_vel_y, corrected_ro_vel_y, boundary_conditions, grid_parameters)
#ro_energy, corrected_ro_energy = smooth(ro_energy, corrected_ro_energy, boundary_conditions, grid_parameters)
#print 'Smoothing routine done.'
#plot_to_grid(grid_parameters, primary_variables, secondary_variables, 600)
if(np.mod(step_number, niter) == 0):
check_convergence(grid_parameters, primary_variables, starting_variables, reference_values, step_number, ncells)
plot_to_grid(grid_parameters, primary_variables, secondary_variables, step_number)
step = set_timestep(primary_variables, secondary_variables, boundary_conditions, grid_parameters)
def initial_setup(nu, nv, nw):
#--------------------------------------------------------------
#
# Read in the boundary conditions file and save variables
#
#--------------------------------------------------------------
# Read in boundary condition file!
bcfile = open('boundary_conditions.txt', 'r')
input_data = bcfile.readlines()
bcfile.close()
# Skip the header and proceed with the initialization!
line_2 = input_data[1].split()
rgas = np.float(line_2[2])
line_3 = input_data[2].split()
gamma = np.float(line_3[2])
line_4 = input_data[3].split()
pressure_stag_inlet = np.float(line_4[2])
line_5 = input_data[4].split()
temp_stag_inlet = np.float(line_5[2])
line_6 = input_data[5].split()
alpha_1 = np.float(line_6[2])
line_7 = input_data[6].split()
pressure_static_exit = np.float(line_7[2])
line_8 = input_data[7].split()
cfl = np.float(line_8[2])
line_9 = input_data[8].split()
smooth_fac_input = np.float(line_9[2])
line_10 = input_data[9].split()
nsteps = np.float(line_10[2])
line_11 = input_data[10].split()
conlim_in = np.float(line_11[2])
boundary_conditions = [
rgas, gamma, pressure_stag_inlet, temp_stag_inlet, alpha_1,
pressure_static_exit, cfl, smooth_fac_input, nsteps, conlim_in
]
#----------------------------------------------
#
# Setup other variables!
#
#----------------------------------------------
cp = rgas * gamma / (gamma - 1.0)
cv = cp / (gamma * 1.0)
gamma_factor = (gamma - 1.0) / (gamma * 1.0)
#----------------------------------------------
#
# Here we initialize the flow variables!
#
#-----------------------------------------------
ro = np.zeros((nv, nu, nw)) # Density
ro_vel_x = np.zeros((nv, nu, nw)) # Density * Velocity in "x" direction
ro_vel_y = np.zeros((nv, nu, nw)) # Density * Velocity in "y" direction
pressure = np.zeros((nv, nu, nw)) # static pressure
ro_energy = np.zeros((nv, nu, nw)) # Density * energy
vel_x = np.zeros((nv, nu, nw)) # velocity-x
vel_y = np.zeros((nv, nu, nw)) # velocity-y
enthalpy_stag = np.zeros((nv, nu, nw)) # Stagnation enthalpy
#----------------------------------------------
#
# Here we initialize the fluxes!
#
#-----------------------------------------------
flux_i_mass = np.zeros((nv, nu)) # Mass
flux_j_mass = np.zeros((nv, nu))
flux_i_xmom = np.zeros((nv, nu)) # X-MOMENTUM
flux_j_xmom = np.zeros((nv, nu))
flux_i_ymom = np.zeros((nv, nu)) # Y-MOMENTUM
flux_j_ymom = np.zeros((nv, nu))
flux_i_enthalpy = np.zeros((nv, nu)) # Enthalpy
flux_j_enthalpy = np.zeros((nv, nu))
flow = np.zeros((nu, 1)) # total mass flow rate across each "i"
#----------------------------------------------
#
# new guess subroutine
#
#-----------------------------------------------
jmid = nv / 2.0
temp_static_exit = temp_stag_inlet * (pressure_static_exit /
pressure_stag_inlet)**gamma_factor
vel_exit = np.sqrt(2 * cp * (temp_stag_inlet - temp_static_exit))
ro_exit = pressure_static_exit / rgas / temp_static_exit
pressure_static_inlet = 55000
temp_static_inlet = temp_stag_inlet * (pressure_static_inlet /
pressure_stag_inlet)**gamma_factor
vel_inlet = np.sqrt(2 * cp * (temp_stag_inlet - temp_static_inlet))
ro_inlet = pressure_static_inlet / rgas / temp_static_inlet
# Get the grid!
grid_parameters = create_grid(nu, nv, nw)
point_x = grid_parameters[0]
point_y = grid_parameters[1]
point_z = grid_parameters[2]
# Initial guess!
for j in range(0, nv):
for i in range(0, nu):
ro[j, i, 0] = 1.2
ro_vel_x[j, i, 0] = 100 * (i * 1.0) / (nu * 1.0)
ro_vel_y[j, i, 0] = 0.0
pressure[j, i, 0] = 100000 * (0.9 + 0.1 * (i * 1.0) / (nu * 1.0))
enthalpy_stag[j, i, 0] = 300000
ro_energy[j, i, 0] = pressure[j, i, 0] / (gamma - 1.0)
for j in range(0, nv):
for i in range(0, nu - 1):
dx = point_x[jmid, i + 1, 0] - point_x[jmid, i, 0]
dy = point_y[jmid, i + 1, 0] - point_y[jmid, i, 0]
ds = np.sqrt(dx * dx + dy * dy)
vel_local = vel_inlet + (vel_exit - vel_inlet) * (1.0 * (i - 1.0) /
(nu - 1.0))
ro_local = ro_inlet + (ro_exit - ro_inlet) * (1.0 * (i - 1.0) /
(nu - 1.0))
temp_local = temp_static_inlet + (temp_static_exit -
temp_static_inlet) * (1.0 *
(i - 1.0) /
(nu - 1.0))
velx = vel_local * dx / ds
vely = vel_local * dy / ds
ro_vel_x[j, i, 0] = ro_local * velx
ro_vel_y[j, i, 0] = ro_local * vely
ro[j, i, 0] = ro_local
ro_energy[j, i, 0] = ro_local * (cv * temp_local +
0.5 * vel_local * vel_local)
ro_vel_x[j, nu - 1, 0] = ro_vel_x[j, nu - 2, 0]
ro_vel_y[j, nu - 1, 0] = ro_vel_y[j, nu - 2, 0]
ro[j, nu - 1, 0] = ro[j, nu - 2, 0]
ro_energy[j, nu - 1, 0] = ro_energy[j, nu - 2, 0]
#-------------------------------------------------------------------------
#
# Output initial flow solution with grid
#
#-------------------------------------------------------------------------
gridToVTK("./initial_flow",
point_x,
point_y,
point_z,
pointData={
"pressure": pressure,
"density": ro,
"density-velx": ro_vel_x
})
#-------------------------------------------------------------------------
#
# Setting primary & secondary flow variables
#
#-------------------------------------------------------------------------
primary_variables = {}
secondary_variables = {}
primary_variables[0] = ro
primary_variables[1] = ro_vel_x
primary_variables[2] = ro_vel_y
primary_variables[3] = ro_energy
secondary_variables[0] = vel_x
secondary_variables[1] = vel_y
secondary_variables[2] = pressure
secondary_variables[3] = enthalpy_stag
#-------------------------------------------------------------------------
#
# Setting the fluxes
#
#-------------------------------------------------------------------------
fluxes = {}
fluxes[0] = flux_i_mass
fluxes[1] = flux_j_mass
fluxes[2] = flux_i_xmom
fluxes[3] = flux_j_xmom
fluxes[4] = flux_i_ymom
fluxes[5] = flux_j_ymom
fluxes[6] = flux_i_enthalpy
fluxes[7] = flux_j_enthalpy
fluxes[8] = flow
secondary_variables = set_other_variables(primary_variables,
secondary_variables,
boundary_conditions,
grid_parameters)
return primary_variables, secondary_variables, fluxes, boundary_conditions, grid_parameters
def initial_setup(nu, nv, nw):
#--------------------------------------------------------------
#
# Read in the boundary conditions file and save variables
#
#--------------------------------------------------------------
# Read in boundary condition file!
bcfile = open('boundary_conditions.txt', 'r')
input_data = bcfile.readlines()
bcfile.close()
# Skip the header and proceed with the initialization!
line_2 = input_data[1].split()
rgas = np.float(line_2[2])
line_3 = input_data[2].split()
gamma = np.float(line_3[2])
line_4 = input_data[3].split()
pressure_stag_inlet = np.float(line_4[2])
line_5 = input_data[4].split()
temp_stag_inlet = np.float(line_5[2])
line_6 = input_data[5].split()
alpha_1 = np.float(line_6[2])
line_7 = input_data[6].split()
pressure_static_exit = np.float(line_7[2])
line_8 = input_data[7].split()
cfl = np.float(line_8[2])
line_9 = input_data[8].split()
smooth_fac_input = np.float(line_9[2])
line_10 = input_data[9].split()
nsteps = np.float(line_10[2])
line_11 = input_data[10].split()
conlim_in = np.float(line_11[2])
boundary_conditions = [rgas, gamma, pressure_stag_inlet, temp_stag_inlet, alpha_1, pressure_static_exit, cfl , smooth_fac_input, nsteps, conlim_in ]
#----------------------------------------------
#
# Setup other variables!
#
#----------------------------------------------
cp = rgas * gamma / (gamma - 1.0)
cv = cp / (gamma * 1.0)
gamma_factor = (gamma - 1.0) / (gamma * 1.0)
#----------------------------------------------
#
# Here we initialize the flow variables!
#
#-----------------------------------------------
ro = np.zeros((nv, nu, nw)) # Density
ro_vel_x = np.zeros((nv, nu, nw)) # Density * Velocity in "x" direction
ro_vel_y = np.zeros((nv, nu, nw)) # Density * Velocity in "y" direction
pressure = np.zeros((nv, nu, nw)) # static pressure
ro_energy = np.zeros((nv, nu, nw)) # Density * energy
vel_x = np.zeros((nv, nu, nw)) # velocity-x
vel_y = np.zeros((nv, nu, nw)) # velocity-y
enthalpy_stag = np.zeros((nv, nu, nw)) # Stagnation enthalpy
#----------------------------------------------
#
# Here we initialize the fluxes!
#
#-----------------------------------------------
flux_i_mass = np.zeros((nv, nu)) # Mass
flux_j_mass = np.zeros((nv, nu))
flux_i_xmom = np.zeros((nv, nu)) # X-MOMENTUM
flux_j_xmom = np.zeros((nv, nu))
flux_i_ymom = np.zeros((nv, nu)) # Y-MOMENTUM
flux_j_ymom = np.zeros((nv, nu))
flux_i_enthalpy = np.zeros((nv, nu)) # Enthalpy
flux_j_enthalpy = np.zeros((nv, nu))
flow = np.zeros((nu, 1)) # total mass flow rate across each "i"
#----------------------------------------------
#
# new guess subroutine
#
#-----------------------------------------------
jmid = nv / 2.0
temp_static_exit = temp_stag_inlet * (pressure_static_exit/pressure_stag_inlet)**gamma_factor
vel_exit = np.sqrt(2 * cp * (temp_stag_inlet - temp_static_exit))
ro_exit = pressure_static_exit / rgas / temp_static_exit
pressure_static_inlet = 55000
temp_static_inlet = temp_stag_inlet * (pressure_static_inlet / pressure_stag_inlet)**gamma_factor
vel_inlet = np.sqrt(2 * cp * (temp_stag_inlet - temp_static_inlet))
ro_inlet = pressure_static_inlet / rgas / temp_static_inlet
# Get the grid!
grid_parameters = create_grid(nu, nv, nw)
point_x = grid_parameters[0]
point_y = grid_parameters[1]
point_z = grid_parameters[2]
# Initial guess!
for j in range(0, nv):
for i in range(0, nu):
ro[j,i,0] = 1.2
ro_vel_x[j,i,0] = 100 * (i * 1.0)/(nu * 1.0)
ro_vel_y[j,i,0] = 0.0
pressure[j,i,0] = 100000 * (0.9 + 0.1 * (i * 1.0)/(nu * 1.0))
enthalpy_stag[j,i,0] = 300000
ro_energy[j,i,0] = pressure[j,i,0] / (gamma - 1.0)
for j in range(0, nv):
for i in range(0, nu-1):
dx = point_x[jmid, i+1, 0] - point_x[jmid, i, 0]
dy = point_y[jmid, i+1, 0] - point_y[jmid, i, 0]
ds = np.sqrt(dx*dx + dy*dy)
vel_local = vel_inlet + (vel_exit - vel_inlet)* (1.0 * (i-1.0)/(nu - 1.0) )
ro_local = ro_inlet + (ro_exit - ro_inlet)* (1.0 * (i-1.0)/(nu - 1.0) )
temp_local = temp_static_inlet + (temp_static_exit - temp_static_inlet)* (1.0 * (i-1.0)/(nu - 1.0) )
velx = vel_local * dx / ds
vely = vel_local * dy / ds
ro_vel_x[j,i,0] = ro_local * velx
ro_vel_y[j,i,0] = ro_local * vely
ro[j,i,0] = ro_local
ro_energy[j,i,0] = ro_local * (cv * temp_local + 0.5 * vel_local * vel_local)
ro_vel_x[j,nu-1,0] = ro_vel_x[j,nu-2,0]
ro_vel_y[j,nu-1,0] = ro_vel_y[j,nu-2,0]
ro[j,nu-1,0] = ro[j,nu-2,0]
ro_energy[j,nu-1,0] = ro_energy[j,nu-2,0]
#-------------------------------------------------------------------------
#
# Output initial flow solution with grid
#
#-------------------------------------------------------------------------
gridToVTK("./initial_flow", point_x, point_y, point_z, pointData={"pressure": pressure, "density": ro, "density-velx": ro_vel_x })
#-------------------------------------------------------------------------
#
# Setting primary & secondary flow variables
#
#-------------------------------------------------------------------------
primary_variables = {}
secondary_variables = {}
primary_variables[0] = ro
primary_variables[1] = ro_vel_x
primary_variables[2] = ro_vel_y
primary_variables[3] = ro_energy
secondary_variables[0] = vel_x
secondary_variables[1] = vel_y
secondary_variables[2] = pressure
secondary_variables[3] = enthalpy_stag
#-------------------------------------------------------------------------
#
# Setting the fluxes
#
#-------------------------------------------------------------------------
fluxes = {}
fluxes[0] = flux_i_mass
fluxes[1] = flux_j_mass
fluxes[2] = flux_i_xmom
fluxes[3] = flux_j_xmom
fluxes[4] = flux_i_ymom
fluxes[5] = flux_j_ymom
fluxes[6] = flux_i_enthalpy
fluxes[7] = flux_j_enthalpy
fluxes[8] = flow
secondary_variables = set_other_variables(primary_variables, secondary_variables, boundary_conditions, grid_parameters)
return primary_variables, secondary_variables, fluxes, boundary_conditions, grid_parameters
