def setup_aero(self):
"""
Specific method to add the necessary components to the problem for an
aerodynamic problem.
"""
# Set the problem name if the user doesn't
if 'prob_name' not in self.prob_dict.keys():
self.prob_dict['prob_name'] = 'aero'
# Create the base root-level group
root = Group()
# Create the problem and assign the root group
self.prob = Problem()
self.prob.root = root
# Loop over each surface in the surfaces list
for surface in self.surfaces:
# Get the surface name and create a group to contain components
# only for this surface
name = surface['name']
tmp_group = Group()
# Add independent variables that do not belong to a specific component
indep_vars = [('twist_cp', numpy.zeros(surface['num_twist'])),
('dihedral', surface['dihedral']),
('sweep', surface['sweep']),
('span', surface['span']),
('taper', surface['taper']),
('disp', numpy.zeros((surface['num_y'], 6)))]
# Obtain the Jacobian to interpolate the data from the b-spline
# control points
jac_twist = get_bspline_mtx(surface['num_twist'], surface['num_y'])
# Add aero components to the surface-specific group
tmp_group.add('indep_vars',
IndepVarComp(indep_vars),
promotes=['*'])
tmp_group.add('twist_bsp',
Bspline('twist_cp', 'twist', jac_twist),
promotes=['*'])
tmp_group.add('mesh', GeometryMesh(surface), promotes=['*'])
tmp_group.add('def_mesh',
TransferDisplacements(surface),
promotes=['*'])
tmp_group.add('vlmgeom', VLMGeometry(surface), promotes=['*'])
# Add tmp_group to the problem as the name of the surface.
# Note that is a group and performance group for each
# individual surface.
name_orig = name.strip('_')
name = name_orig
exec(name + ' = tmp_group')
exec('root.add("' + name + '", ' + name + ', promotes=[])')
# Add a performance group for each surface
name = name_orig + '_perf'
exec('root.add("' + name + '", ' + 'VLMFunctionals(surface)' +
', promotes=["v", "alpha", "M", "Re", "rho"])')
# Add problem information as an independent variables component
prob_vars = [('v', self.prob_dict['v']),
('alpha', self.prob_dict['alpha']),
('M', self.prob_dict['M']), ('Re', self.prob_dict['Re']),
('rho', self.prob_dict['rho'])]
root.add('prob_vars', IndepVarComp(prob_vars), promotes=['*'])
# Add a single 'aero_states' component that solves for the circulations
# and forces from all the surfaces.
# While other components only depends on a single surface,
# this component requires information from all surfaces because
# each surface interacts with the others.
root.add('aero_states',
VLMStates(self.surfaces, self.prob_dict),
promotes=['circulations', 'v', 'alpha', 'rho'])
# Explicitly connect parameters from each surface's group and the common
# 'aero_states' group.
# This is necessary because the VLMStates component requires information
# from each surface, but this information is stored within each
# surface's group.
for surface in self.surfaces:
name = surface['name']
# Perform the connections with the modified names within the
# 'aero_states' group.
root.connect(name[:-1] + '.def_mesh',
'aero_states.' + name + 'def_mesh')
root.connect(name[:-1] + '.b_pts', 'aero_states.' + name + 'b_pts')
root.connect(name[:-1] + '.c_pts', 'aero_states.' + name + 'c_pts')
root.connect(name[:-1] + '.normals',
'aero_states.' + name + 'normals')
# Connect the results from 'aero_states' to the performance groups
root.connect('aero_states.' + name + 'sec_forces',
name + 'perf' + '.sec_forces')
# Connect S_ref for performance calcs
root.connect(name[:-1] + '.S_ref', name + 'perf' + '.S_ref')
# Actually set up the problem
self.setup_prob()
def setup_aerostruct(self):
"""
Specific method to add the necessary components to the problem for an
aerostructural problem.
"""
# Set the problem name if the user doesn't
if 'prob_name' not in self.prob_dict.keys():
self.prob_dict['prob_name'] = 'aerostruct'
# Create the base root-level group
root = Group()
coupled = Group()
# Create the problem and assign the root group
self.prob = Problem()
self.prob.root = root
# Loop over each surface in the surfaces list
for surface in self.surfaces:
# Get the surface name and create a group to contain components
# only for this surface
name = surface['name']
tmp_group = Group()
# Add independent variables that do not belong to a specific component
indep_vars = [
('twist_cp', numpy.zeros(surface['num_twist'])),
('thickness_cp', numpy.ones(surface['num_thickness']) *
numpy.max(surface['t'])), ('r', surface['r']),
('dihedral', surface['dihedral']), ('sweep', surface['sweep']),
('span', surface['span']), ('taper', surface['taper'])
]
# Obtain the Jacobians to interpolate the data from the b-spline
# control points
jac_twist = get_bspline_mtx(surface['num_twist'], surface['num_y'])
jac_thickness = get_bspline_mtx(surface['num_thickness'],
surface['num_y'] - 1)
# Add components to include in the surface's group
tmp_group.add('indep_vars',
IndepVarComp(indep_vars),
promotes=['*'])
tmp_group.add('twist_bsp',
Bspline('twist_cp', 'twist', jac_twist),
promotes=['*'])
tmp_group.add('thickness_bsp',
Bspline('thickness_cp', 'thickness', jac_thickness),
promotes=['*'])
tmp_group.add('tube', MaterialsTube(surface), promotes=['*'])
# Add tmp_group to the problem with the name of the surface.
name_orig = name
name = name[:-1]
exec(name + ' = tmp_group')
exec('root.add("' + name + '", ' + name + ', promotes=[])')
# Add components to the 'coupled' group for each surface.
# The 'coupled' group must contain all components and parameters
# needed to converge the aerostructural system.
tmp_group = Group()
tmp_group.add('mesh', GeometryMesh(surface), promotes=['*'])
tmp_group.add('def_mesh',
TransferDisplacements(surface),
promotes=['*'])
tmp_group.add('aero_geom', VLMGeometry(surface), promotes=['*'])
tmp_group.add('struct_states',
SpatialBeamStates(surface),
promotes=['*'])
tmp_group.struct_states.ln_solver = LinearGaussSeidel()
name = name_orig
exec(name + ' = tmp_group')
exec('coupled.add("' + name[:-1] + '", ' + name + ', promotes=[])')
# Add a loads component to the coupled group
exec('coupled.add("' + name_orig + 'loads' + '", ' +
'TransferLoads(surface)' + ', promotes=[])')
# Add a performance group which evaluates the data after solving
# the coupled system
tmp_group = Group()
tmp_group.add('struct_funcs',
SpatialBeamFunctionals(surface),
promotes=['*'])
tmp_group.add('aero_funcs',
VLMFunctionals(surface),
promotes=['*'])
name = name_orig + 'perf'
exec(name + ' = tmp_group')
exec('root.add("' + name + '", ' + name +
', promotes=["rho", "v", "alpha", "Re", "M"])')
# Add a single 'aero_states' component for the whole system within the
# coupled group.
coupled.add('aero_states',
VLMStates(self.surfaces, self.prob_dict),
promotes=['v', 'alpha', 'rho'])
# Explicitly connect parameters from each surface's group and the common
# 'aero_states' group.
for surface in self.surfaces:
name = surface['name']
# Perform the connections with the modified names within the
# 'aero_states' group.
root.connect('coupled.' + name[:-1] + '.def_mesh',
'coupled.aero_states.' + name + 'def_mesh')
root.connect('coupled.' + name[:-1] + '.b_pts',
'coupled.aero_states.' + name + 'b_pts')
root.connect('coupled.' + name[:-1] + '.c_pts',
'coupled.aero_states.' + name + 'c_pts')
root.connect('coupled.' + name[:-1] + '.normals',
'coupled.aero_states.' + name + 'normals')
# Connect the results from 'aero_states' to the performance groups
root.connect('coupled.aero_states.' + name + 'sec_forces',
name + 'perf' + '.sec_forces')
# Connect the results from 'coupled' to the performance groups
root.connect('coupled.' + name[:-1] + '.def_mesh',
'coupled.' + name + 'loads.def_mesh')
root.connect('coupled.aero_states.' + name + 'sec_forces',
'coupled.' + name + 'loads.sec_forces')
root.connect('coupled.' + name + 'loads.loads',
name + 'perf.loads')
# Connect the output of the loads component with the FEM
# displacement parameter. This links the coupling within the coupled
# group that necessitates the subgroup solver.
root.connect('coupled.' + name + 'loads.loads',
'coupled.' + name[:-1] + '.loads')
# Connect aerodyamic design variables
root.connect(name[:-1] + '.dihedral',
'coupled.' + name[:-1] + '.dihedral')
root.connect(name[:-1] + '.span', 'coupled.' + name[:-1] + '.span')
root.connect(name[:-1] + '.sweep',
'coupled.' + name[:-1] + '.sweep')
root.connect(name[:-1] + '.taper',
'coupled.' + name[:-1] + '.taper')
root.connect(name[:-1] + '.twist',
'coupled.' + name[:-1] + '.twist')
# Connect structural design variables
root.connect(name[:-1] + '.A', 'coupled.' + name[:-1] + '.A')
root.connect(name[:-1] + '.Iy', 'coupled.' + name[:-1] + '.Iy')
root.connect(name[:-1] + '.Iz', 'coupled.' + name[:-1] + '.Iz')
root.connect(name[:-1] + '.J', 'coupled.' + name[:-1] + '.J')
# Connect performance calculation variables
root.connect(name[:-1] + '.r', name + 'perf.r')
root.connect(name[:-1] + '.A', name + 'perf.A')
# Connection performance functional variables
root.connect(name + 'perf.weight', 'fuelburn.' + name + 'weight')
root.connect(name + 'perf.weight', 'eq_con.' + name + 'weight')
root.connect(name + 'perf.L', 'eq_con.' + name + 'L')
root.connect(name + 'perf.CL', 'fuelburn.' + name + 'CL')
root.connect(name + 'perf.CD', 'fuelburn.' + name + 'CD')
# Connect paramters from the 'coupled' group to the performance
# group.
root.connect('coupled.' + name[:-1] + '.nodes',
name + 'perf.nodes')
root.connect('coupled.' + name[:-1] + '.disp', name + 'perf.disp')
root.connect('coupled.' + name[:-1] + '.S_ref',
name + 'perf.S_ref')
# Set solver properties for the coupled group
coupled.ln_solver = ScipyGMRES()
coupled.ln_solver.options['iprint'] = 1
coupled.ln_solver.preconditioner = LinearGaussSeidel()
coupled.aero_states.ln_solver = LinearGaussSeidel()
coupled.nl_solver = NLGaussSeidel()
coupled.nl_solver.options['iprint'] = 1
# Ensure that the groups are ordered correctly within the coupled group
# so that a system with multiple surfaces is solved corretly.
order_list = []
for surface in self.surfaces:
order_list.append(surface['name'][:-1])
order_list.append('aero_states')
for surface in self.surfaces:
order_list.append(surface['name'] + 'loads')
coupled.set_order(order_list)
# Add the coupled group to the root problem
root.add('coupled', coupled, promotes=['v', 'alpha', 'rho'])
# Add problem information as an independent variables component
prob_vars = [('v', self.prob_dict['v']),
('alpha', self.prob_dict['alpha']),
('M', self.prob_dict['M']), ('Re', self.prob_dict['Re']),
('rho', self.prob_dict['rho'])]
root.add('prob_vars', IndepVarComp(prob_vars), promotes=['*'])
# Add functionals to evaluate performance of the system.
# Note that only the interesting results are promoted here; not all
# of the parameters.
root.add('fuelburn',
FunctionalBreguetRange(self.surfaces, self.prob_dict),
promotes=['fuelburn'])
root.add('eq_con',
FunctionalEquilibrium(self.surfaces, self.prob_dict),
promotes=['eq_con', 'fuelburn'])
# Actually set up the system
self.setup_prob()
def setup_struct(self):
"""
Specific method to add the necessary components to the problem for a
structural problem.
"""
# Set the problem name if the user doesn't
if 'prob_name' not in self.prob_dict.keys():
self.prob_dict['prob_name'] = 'struct'
# Create the base root-level group
root = Group()
# Create the problem and assign the root group
self.prob = Problem()
self.prob.root = root
# Loop over each surface in the surfaces list
for surface in self.surfaces:
# Get the surface name and create a group to contain components
# only for this surface.
# This group's name is whatever the surface's name is.
# The default is 'wing'.
name = surface['name']
tmp_group = Group()
surface['r'] = surface['r'] / 5
surface['t'] = surface['r'] / 20
# Add independent variables that do not belong to a specific component.
# Note that these are the only ones necessary for structual-only
# analysis and optimization.
indep_vars = [
('thickness_cp', numpy.ones(surface['num_thickness']) *
numpy.max(surface['t'])), ('r', surface['r']),
('loads', surface['loads'])
]
# Obtain the Jacobians to interpolate the data from the b-spline
# control points
jac_twist = get_bspline_mtx(surface['num_twist'], surface['num_y'])
jac_thickness = get_bspline_mtx(surface['num_thickness'],
surface['num_y'] - 1)
# Add structural components to the surface-specific group
tmp_group.add('indep_vars',
IndepVarComp(indep_vars),
promotes=['*'])
tmp_group.add('twist_bsp',
Bspline('twist_cp', 'twist', jac_twist),
promotes=['*'])
tmp_group.add('thickness_bsp',
Bspline('thickness_cp', 'thickness', jac_thickness),
promotes=['*'])
tmp_group.add('mesh', GeometryMesh(surface), promotes=['*'])
tmp_group.add('tube', MaterialsTube(surface), promotes=['*'])
tmp_group.add('struct_states',
SpatialBeamStates(surface),
promotes=['*'])
tmp_group.add('struct_funcs',
SpatialBeamFunctionals(surface),
promotes=['*'])
# Add tmp_group to the problem with the name of the surface.
# The default is 'wing'.
nm = name
name = name[:-1]
exec(name + ' = tmp_group')
exec('root.add("' + name + '", ' + name + ', promotes=[])')
# Actually set up the problem
self.setup_prob()
def struct(loads, params):
# Unpack variables
mesh = params.get('mesh')
num_x = params.get('num_x')
num_y = params.get('num_y')
span = params.get('span')
twist_cp = params.get('twist_cp')
thickness_cp = params.get('thickness_cp')
v = params.get('v')
alpha = params.get('alpha')
rho = params.get('rho')
r = params.get('r')
t = params.get('t')
aero_ind = params.get('aero_ind')
fem_ind = params.get('fem_ind')
num_thickness = params.get('num_thickness')
num_twist = params.get('num_twist')
sweep = params.get('sweep')
taper = params.get('taper')
disp = params.get('disp')
dihedral = params.get('dihedral')
E = params.get('E')
G = params.get('G')
stress = params.get('stress')
mrho = params.get('mrho')
tot_n_fem = params.get('tot_n_fem')
num_surf = params.get('num_surf')
jac_twist = params.get('jac_twist')
jac_thickness = params.get('jac_thickness')
check = params.get('check')
out_stream = params.get('out_stream')
# Define the design variables
des_vars = [
('twist_cp', twist_cp),
('thickness_cp', thickness_cp),
('r', r),
# ('dihedral', dihedral),
# ('sweep', sweep),
# ('span', span),
# ('taper', taper),
# ('v', v),
# ('alpha', alpha),
# ('rho', rho),
# ('disp', disp),
('loads', loads)
]
root = Group()
root.add(
'des_vars',
IndepVarComp(des_vars),
# promotes=['thickness_cp','r','loads'])
promotes=['*'])
# root.add('twist_bsp', # What is this doing?
# Bspline('twist_cp', 'twist', jac_twist),
# promotes=['*'])
root.add('twist_bsp',
Bspline('twist_cp', 'twist', jac_twist),
promotes=['*'])
root.add(
'thickness_bsp', # What is this doing?
Bspline('thickness_cp', 'thickness', jac_thickness),
# promotes=['thickness'])
promotes=['*'])
root.add('mesh', GeometryMesh(mesh, aero_ind), promotes=['*'])
root.add(
'tube',
MaterialsTube(fem_ind),
# promotes=['r','thickness','A','Iy','Iz','J'])
promotes=['*'])
root.add(
'spatialbeamstates',
SpatialBeamStates(aero_ind, fem_ind, E, G),
# promotes=[
# 'mesh', # ComputeNodes
# 'A','Iy','Iz','J','loads', # SpatialBeamFEM
# 'disp' # SpatialBeamDisp
# ])
promotes=['*'])
root.add(
'transferdisp',
TransferDisplacements(aero_ind, fem_ind),
# promotes=['mesh','disp','def_mesh'])
promotes=['*'])
prob = Problem()
prob.root = root
prob.setup(check=check, out_stream=out_stream)
prob.run()
return prob['def_mesh'] # Output the def_mesh matrix
('v', v),
('alpha', alpha),
('rho', rho),
('r', r),
('t', t),
('aero_ind', aero_ind)
]
############################################################
# These are your components, put them in the correct groups.
# indep_vars_comp, tube_comp, and weiss_func_comp have been
# done for you as examples
############################################################
indep_vars_comp = IndepVarComp(indep_vars)
twist_comp = Bspline('twist_cp', 'twist', jac_twist)
thickness_comp = Bspline('thickness_cp', 'thickness', jac_thickness)
tube_comp = MaterialsTube(fem_ind)
mesh_comp = GeometryMesh(mesh, aero_ind)
spatialbeamstates_comp = SpatialBeamStates(aero_ind, fem_ind, E, G)
def_mesh_comp = TransferDisplacements(aero_ind, fem_ind)
vlmstates_comp = VLMStates(aero_ind)
loads_comp = TransferLoads(aero_ind, fem_ind)
vlmfuncs_comp = VLMFunctionals(aero_ind, CL0, CD0)
spatialbeamfuncs_comp = SpatialBeamFunctionals(aero_ind, fem_ind, E, G, stress, mrho)
fuelburn_comp = FunctionalBreguetRange(W0, CT, a, R, M, aero_ind)
eq_con_comp = FunctionalEquilibrium(W0, aero_ind)
############################################################
def setup_aerostruct(self):
"""
Specific method to add the necessary components to the problem for an
aerostructural problem.
"""
# Set the problem name if the user doesn't
if 'prob_name' not in self.prob_dict.keys():
self.prob_dict['prob_name'] = 'aerostruct'
# Create the base root-level group
root = Group()
coupled = Group()
# Create the problem and assign the root group
self.prob = Problem()
self.prob.root = root
# Loop over each surface in the surfaces list
for surface in self.surfaces:
# Get the surface name and create a group to contain components
# only for this surface
name = surface['name']
tmp_group = Group()
# Add independent variables that do not belong to a specific component
indep_vars = [
(name + 'twist_cp', numpy.zeros(surface['num_twist'])),
(name + 'thickness_cp', numpy.ones(surface['num_thickness']) *
numpy.max(surface['t'])), (name + 'r', surface['r']),
(name + 'dihedral', surface['dihedral']),
(name + 'sweep', surface['sweep']),
(name + 'span', surface['span']),
(name + 'taper', surface['taper'])
]
# Obtain the Jacobians to interpolate the data from the b-spline
# control points
jac_twist = get_bspline_mtx(surface['num_twist'], surface['num_y'])
jac_thickness = get_bspline_mtx(surface['num_thickness'],
surface['num_y'] - 1)
# Add components to include in the '_pre_solve' group
tmp_group.add('indep_vars',
IndepVarComp(indep_vars),
promotes=['*'])
tmp_group.add('twist_bsp',
Bspline(name + 'twist_cp', name + 'twist',
jac_twist),
promotes=['*'])
tmp_group.add('thickness_bsp',
Bspline(name + 'thickness_cp', name + 'thickness',
jac_thickness),
promotes=['*'])
tmp_group.add('tube', MaterialsTube(surface), promotes=['*'])
# Add tmp_group to the problem with the name of the surface and
# '_pre_solve' appended.
name_orig = name #.strip('_')
name = name + 'pre_solve'
exec(name + ' = tmp_group')
exec('root.add("' + name + '", ' + name + ', promotes=["*"])')
# Add components to the 'coupled' group for each surface
tmp_group = Group()
tmp_group.add('mesh', GeometryMesh(surface), promotes=['*'])
tmp_group.add('def_mesh',
TransferDisplacements(surface),
promotes=['*'])
tmp_group.add('vlmgeom', VLMGeometry(surface), promotes=['*'])
tmp_group.add('spatialbeamstates',
SpatialBeamStates(surface),
promotes=['*'])
tmp_group.spatialbeamstates.ln_solver = LinearGaussSeidel()
name = name_orig + 'group'
exec(name + ' = tmp_group')
exec('coupled.add("' + name + '", ' + name + ', promotes=["*"])')
# Add a loads component to the coupled group
exec('coupled.add("' + name_orig + 'loads' + '", ' +
'TransferLoads(surface)' + ', promotes=["*"])')
# Add a '_post_solve' group which evaluates the data after solving
# the coupled system
tmp_group = Group()
tmp_group.add('spatialbeamfuncs',
SpatialBeamFunctionals(surface),
promotes=['*'])
tmp_group.add('vlmfuncs', VLMFunctionals(surface), promotes=['*'])
name = name_orig + 'post_solve'
exec(name + ' = tmp_group')
exec('root.add("' + name + '", ' + name + ', promotes=["*"])')
# Add a single 'VLMStates' component for the whole system
coupled.add('vlmstates',
VLMStates(self.surfaces, self.prob_dict),
promotes=['*'])
# Set solver properties for the coupled group
coupled.ln_solver = ScipyGMRES()
coupled.ln_solver.options['iprint'] = 1
coupled.ln_solver.preconditioner = LinearGaussSeidel()
coupled.vlmstates.ln_solver = LinearGaussSeidel()
coupled.nl_solver = NLGaussSeidel()
coupled.nl_solver.options['iprint'] = 1
# Ensure that the groups are ordered correctly within the coupled group
order_list = []
for surface in self.surfaces:
order_list.append(surface['name'] + 'group')
order_list.append('vlmstates')
for surface in self.surfaces:
order_list.append(surface['name'] + 'loads')
coupled.set_order(order_list)
# Add the coupled group to the root problem
root.add('coupled', coupled, promotes=['*'])
# Add problem information as an independent variables component
prob_vars = [('v', self.prob_dict['v']),
('alpha', self.prob_dict['alpha']),
('M', self.prob_dict['M']), ('Re', self.prob_dict['Re']),
('rho', self.prob_dict['rho'])]
root.add('prob_vars', IndepVarComp(prob_vars), promotes=['*'])
# Add functionals to evaluate performance of the system
root.add('fuelburn',
FunctionalBreguetRange(self.surfaces, self.prob_dict),
promotes=['*'])
root.add('eq_con',
FunctionalEquilibrium(self.surfaces, self.prob_dict),
promotes=['*'])
self.setup_prob()
def setup_aero(self):
"""
Specific method to add the necessary components to the problem for an
aerodynamic problem.
"""
# Set the problem name if the user doesn't
if 'prob_name' not in self.prob_dict.keys():
self.prob_dict['prob_name'] = 'aero'
# Create the base root-level group
root = Group()
# Create the problem and assign the root group
self.prob = Problem()
self.prob.root = root
# Loop over each surface in the surfaces list
for surface in self.surfaces:
# Get the surface name and create a group to contain components
# only for this surface
name = surface['name']
tmp_group = Group()
# Add independent variables that do not belong to a specific component
indep_vars = [(name + 'twist_cp',
numpy.zeros(surface['num_twist'])),
(name + 'dihedral', surface['dihedral']),
(name + 'sweep', surface['sweep']),
(name + 'span', surface['span']),
(name + 'taper', surface['taper']),
(name + 'disp', numpy.zeros((surface['num_y'], 6)))]
# Obtain the Jacobian to interpolate the data from the b-spline
# control points
jac_twist = get_bspline_mtx(surface['num_twist'], surface['num_y'])
# Add aero components to the surface-specific group
tmp_group.add('indep_vars',
IndepVarComp(indep_vars),
promotes=['*'])
tmp_group.add('twist_bsp',
Bspline(name + 'twist_cp', name + 'twist',
jac_twist),
promotes=['*'])
tmp_group.add('mesh', GeometryMesh(surface), promotes=['*'])
tmp_group.add('def_mesh',
TransferDisplacements(surface),
promotes=['*'])
tmp_group.add('vlmgeom', VLMGeometry(surface), promotes=['*'])
# Add tmp_group to the problem with the name of the surface and
# '_pre_solve' appended.
# Note that is a '_pre_solve' and '_post_solve' group for each
# individual surface.
name_orig = name.strip('_')
name = name_orig + '_pre_solve'
exec(name + ' = tmp_group')
exec('root.add("' + name + '", ' + name + ', promotes=["*"])')
# Add a '_post_solve' group
name = name_orig + '_post_solve'
exec('root.add("' + name + '", ' + 'VLMFunctionals(surface)' +
', promotes=["*"])')
# Add problem information as an independent variables component
prob_vars = [('v', self.prob_dict['v']),
('alpha', self.prob_dict['alpha']),
('M', self.prob_dict['M']), ('Re', self.prob_dict['Re']),
('rho', self.prob_dict['rho'])]
root.add('prob_vars', IndepVarComp(prob_vars), promotes=['*'])
# Add a single 'VLMStates' component that solves for the circulations
# and forces from all the surfaces.
# While other components only depends on a single surface,
# this component requires information from all surfaces because
# each surface interacts with the others.
root.add('vlmstates',
VLMStates(self.surfaces, self.prob_dict),
promotes=['*'])
self.setup_prob()