generate_axisymmetric_navier_stokes_element Namespace Reference

Variables
string	mode = "c"
	Symbolic generation settings. More...
bool	divide_by_rho = True
bool	ASGS_stabilization = True
bool	add_incompressibility_error = False
bool	do_simplifications = False
string	output_filename = "axisymmetric_navier_stokes.cpp"
string	template_filename = "axisymmetric_navier_stokes_cpp_template.cpp"
string	info_msg = f"\n"
list	dim_vector = [2, 2]
list	n_nodes_vector = [3, 4]
	templatefile = open(template_filename)
	Initialize the outstring to be filled with the template .cpp file. More...
	outstring = templatefile.read()
	Replace the computed RHS and LHS in the template outstring. More...
bool	impose_partion_of_unity = False
	Define shape functions, shape function gradients and integration weight. More...
	gauss_weight = sympy.Symbol('w_gauss', positive = True)
	N
	DN
	v = DefineMatrix('v',n_nodes,dim)
	Unknown fields definition. More...
	v_n = DefineMatrix('v_n',n_nodes,dim)
	v_nn = DefineMatrix('v_nn',n_nodes,dim)
	p = DefineVector('p',n_nodes)
	mu = sympy.Symbol('mu', positive = True)
	Fluid properties. More...
	rho = sympy.Symbol('rho', positive = True)
	w = DefineMatrix('w',n_nodes,dim)
	Test functions definition. More...
	q = DefineVector('q',n_nodes)
	f = DefineMatrix('f',n_nodes,dim)
	Other data definitions. More...
	y = sympy.Symbol('y', positive = True)
	Other simbols definition. More...
	h = sympy.Symbol('h', positive = True)
	dt = sympy.Symbol('dt', positive = True)
	dyn_tau = sympy.Symbol('dyn_tau', positive = True)
	stab_c1 = sympy.Symbol('stab_c1', positive = True)
	stab_c2 = sympy.Symbol('stab_c2', positive = True)
	bdf0 = sympy.Symbol('bdf0')
	Backward differences coefficients. More...
	bdf1 = sympy.Symbol('bdf1')
	bdf2 = sympy.Symbol('bdf2')
	f_gauss = f.transpose()*N
	Data interpolation to the Gauss points. More...
	v_gauss = v.transpose()*N
	p_gauss = p.transpose()*N
	w_gauss = w.transpose()*N
	q_gauss = q.transpose()*N
	v_conv = DefineMatrix('v_conv', n_nodes, dim)
	Convective velocity definition. More...
	v_conv_gauss = v_conv.transpose()*N
float	stab_norm_a = 0.0
	Compute the stabilization parameters. More...
float	tau1 = 1.0/((rho*dyn_tau)/dt + (stab_c2*rho*stab_norm_a)/h + (stab_c1*mu)/(h*h))
	tau2 = mu + (stab_c2*rho*stab_norm_a*h)/stab_c1
tuple	accel_gauss = (bdf0*v + bdf1*v_n + bdf2*v_nn).transpose()*N
	Compute the rest of magnitudes at the Gauss points. More...
	grad_w = DfjDxi(DN,w)
	Gradients computation (fluid dynamics gradient) More...
	grad_q = DfjDxi(DN,q)
	grad_p = DfjDxi(DN,p)
	grad_v = DfjDxi(DN,v)
	grad_v_conv = DfjDxi(DN,v_conv)
tuple	galerkin_functional = rho*w_gauss[0]*f_gauss[0] - rho*w_gauss[0]*accel_gauss[0] - rho*w_gauss[0]*v_conv_gauss[1]*grad_v[1,0] - rho*w_gauss[0]*v_conv_gauss[0]*grad_v[0,0] + grad_w[0,0]*p_gauss[0] - mu*grad_w[1,0]*grad_v[1,0] - mu*grad_w[0,0]*grad_v[0,0]
	Compute galerkin functional Navier-Stokes functional. More...
tuple	vel_residual_x = rho*f_gauss[0] - rho*accel_gauss[0] - rho*v_conv_gauss[1]*grad_v[1,0] - rho*v_conv_gauss[0]*grad_v[0,0] - grad_p[0] + (mu/y)*grad_v[1,0]
	Stabilization functional terms Momentum conservation residual Note that the second order viscous stress terms are dropped since linear elements are used. More...
tuple	vel_residual_y = rho*f_gauss[1] - rho*accel_gauss[1] - rho*v_conv_gauss[1]*grad_v[1,1] - rho*v_conv_gauss[0]*grad_v[0,1] - grad_p[1] - mu*v_gauss[1]/y**2 + (mu/y)*grad_v[1,1]
	mas_residual = - v_gauss[1]/y - grad_v[1,1] - grad_v[0,0]
float	vel_subscale_x = tau1*vel_residual_x
float	vel_subscale_y = tau1*vel_residual_y
	pres_subscale = tau2*mas_residual
float	stabilization_functional = - q_gauss[0]*vel_subscale_y/y + grad_q[1]*vel_subscale_y + grad_q[0]*vel_subscale_x
tuple	functional = galerkin_functional
	Add the stabilization terms to the original residual terms. More...
	dofs = sympy.zeros(n_nodes*(dim+1), 1)
	Define DOFs and test function vectors. More...
	test_func = sympy.zeros(n_nodes*(dim+1), 1)
	aux_functional = sympy.Matrix([[functional]])
	Compute LHS and RHS. More...
	rhs = Compute_RHS(aux_functional.copy(), test_func, do_simplifications)
	rhs_out = OutputVector_CollectingFactors(gauss_weight * rhs, "rRHS", mode, assignment_op='+=')
	lhs = Compute_LHS(rhs, test_func, dofs, do_simplifications)
	lhs_out = OutputMatrix_CollectingFactors(gauss_weight * lhs, "rLHS", mode, assignment_op='+=')
	out = open(output_filename,'w')
	Write the modified template. More...

Variable Documentation

accel_gauss

tuple generate_axisymmetric_navier_stokes_element.accel_gauss = (bdf0*v + bdf1*v_n + bdf2*v_nn).transpose()*N

Compute the rest of magnitudes at the Gauss points.

add_incompressibility_error

bool generate_axisymmetric_navier_stokes_element.add_incompressibility_error = False

ASGS_stabilization

bool generate_axisymmetric_navier_stokes_element.ASGS_stabilization = True

aux_functional

generate_axisymmetric_navier_stokes_element.aux_functional = sympy.Matrix([[functional]])

Compute LHS and RHS.

bdf0

generate_axisymmetric_navier_stokes_element.bdf0 = sympy.Symbol('bdf0')

Backward differences coefficients.

bdf1

generate_axisymmetric_navier_stokes_element.bdf1 = sympy.Symbol('bdf1')

bdf2

generate_axisymmetric_navier_stokes_element.bdf2 = sympy.Symbol('bdf2')

dim_vector

list generate_axisymmetric_navier_stokes_element.dim_vector = [2, 2]

divide_by_rho

bool generate_axisymmetric_navier_stokes_element.divide_by_rho = True

DN

generate_axisymmetric_navier_stokes_element.DN

do_simplifications

bool generate_axisymmetric_navier_stokes_element.do_simplifications = False

dofs

generate_axisymmetric_navier_stokes_element.dofs = sympy.zeros(n_nodes*(dim+1), 1)

Define DOFs and test function vectors.

dt

generate_axisymmetric_navier_stokes_element.dt = sympy.Symbol('dt', positive = True)

dyn_tau

generate_axisymmetric_navier_stokes_element.dyn_tau = sympy.Symbol('dyn_tau', positive = True)

f

generate_axisymmetric_navier_stokes_element.f = DefineMatrix('f',n_nodes,dim)

Other data definitions.

f_gauss

generate_axisymmetric_navier_stokes_element.f_gauss = f.transpose()*N

Data interpolation to the Gauss points.

functional

tuple generate_axisymmetric_navier_stokes_element.functional = galerkin_functional

Add the stabilization terms to the original residual terms.

galerkin_functional

tuple generate_axisymmetric_navier_stokes_element.galerkin_functional = rho*w_gauss[0]*f_gauss[0] - rho*w_gauss[0]*accel_gauss[0] - rho*w_gauss[0]*v_conv_gauss[1]*grad_v[1,0] - rho*w_gauss[0]*v_conv_gauss[0]*grad_v[0,0] + grad_w[0,0]*p_gauss[0] - mu*grad_w[1,0]*grad_v[1,0] - mu*grad_w[0,0]*grad_v[0,0]

Compute galerkin functional Navier-Stokes functional.

gauss_weight

generate_axisymmetric_navier_stokes_element.gauss_weight = sympy.Symbol('w_gauss', positive = True)

grad_p

generate_axisymmetric_navier_stokes_element.grad_p = DfjDxi(DN,p)

grad_q

generate_axisymmetric_navier_stokes_element.grad_q = DfjDxi(DN,q)

grad_v

generate_axisymmetric_navier_stokes_element.grad_v = DfjDxi(DN,v)

grad_v_conv

generate_axisymmetric_navier_stokes_element.grad_v_conv = DfjDxi(DN,v_conv)

grad_w

generate_axisymmetric_navier_stokes_element.grad_w = DfjDxi(DN,w)

Gradients computation (fluid dynamics gradient)

h

generate_axisymmetric_navier_stokes_element.h = sympy.Symbol('h', positive = True)

impose_partion_of_unity

bool generate_axisymmetric_navier_stokes_element.impose_partion_of_unity = False

Define shape functions, shape function gradients and integration weight.

info_msg

string generate_axisymmetric_navier_stokes_element.info_msg = f"\n"

lhs

generate_axisymmetric_navier_stokes_element.lhs = Compute_LHS(rhs, test_func, dofs, do_simplifications)

lhs_out

generate_axisymmetric_navier_stokes_element.lhs_out = OutputMatrix_CollectingFactors(gauss_weight * lhs, "rLHS", mode, assignment_op='+=')

mas_residual

generate_axisymmetric_navier_stokes_element.mas_residual = - v_gauss[1]/y - grad_v[1,1] - grad_v[0,0]

mode

string generate_axisymmetric_navier_stokes_element.mode = "c"

Symbolic generation settings.

mu

generate_axisymmetric_navier_stokes_element.mu = sympy.Symbol('mu', positive = True)

Fluid properties.

N

generate_axisymmetric_navier_stokes_element.N

n_nodes_vector

list generate_axisymmetric_navier_stokes_element.n_nodes_vector = [3, 4]

out

generate_axisymmetric_navier_stokes_element.out = open(output_filename,'w')

Write the modified template.

output_filename

string generate_axisymmetric_navier_stokes_element.output_filename = "axisymmetric_navier_stokes.cpp"

outstring

generate_axisymmetric_navier_stokes_element.outstring = templatefile.read()

Replace the computed RHS and LHS in the template outstring.

p

generate_axisymmetric_navier_stokes_element.p = DefineVector('p',n_nodes)

p_gauss

generate_axisymmetric_navier_stokes_element.p_gauss = p.transpose()*N

pres_subscale

generate_axisymmetric_navier_stokes_element.pres_subscale = tau2*mas_residual

q

generate_axisymmetric_navier_stokes_element.q = DefineVector('q',n_nodes)

q_gauss

generate_axisymmetric_navier_stokes_element.q_gauss = q.transpose()*N

rho

generate_axisymmetric_navier_stokes_element.rho = sympy.Symbol('rho', positive = True)

rhs

generate_axisymmetric_navier_stokes_element.rhs = Compute_RHS(aux_functional.copy(), test_func, do_simplifications)

rhs_out

generate_axisymmetric_navier_stokes_element.rhs_out = OutputVector_CollectingFactors(gauss_weight * rhs, "rRHS", mode, assignment_op='+=')

stab_c1

generate_axisymmetric_navier_stokes_element.stab_c1 = sympy.Symbol('stab_c1', positive = True)

stab_c2

generate_axisymmetric_navier_stokes_element.stab_c2 = sympy.Symbol('stab_c2', positive = True)

stab_norm_a

generate_axisymmetric_navier_stokes_element.stab_norm_a = 0.0

Compute the stabilization parameters.

stabilization_functional

float generate_axisymmetric_navier_stokes_element.stabilization_functional = - q_gauss[0]*vel_subscale_y/y + grad_q[1]*vel_subscale_y + grad_q[0]*vel_subscale_x

tau1

float generate_axisymmetric_navier_stokes_element.tau1 = 1.0/((rho*dyn_tau)/dt + (stab_c2*rho*stab_norm_a)/h + (stab_c1*mu)/(h*h))

tau2

generate_axisymmetric_navier_stokes_element.tau2 = mu + (stab_c2*rho*stab_norm_a*h)/stab_c1

template_filename

string generate_axisymmetric_navier_stokes_element.template_filename = "axisymmetric_navier_stokes_cpp_template.cpp"

templatefile

generate_axisymmetric_navier_stokes_element.templatefile = open(template_filename)

Initialize the outstring to be filled with the template .cpp file.

test_func

generate_axisymmetric_navier_stokes_element.test_func = sympy.zeros(n_nodes*(dim+1), 1)

v

generate_axisymmetric_navier_stokes_element.v = DefineMatrix('v',n_nodes,dim)

Unknown fields definition.

v_conv

generate_axisymmetric_navier_stokes_element.v_conv = DefineMatrix('v_conv', n_nodes, dim)

Convective velocity definition.

v_conv_gauss

generate_axisymmetric_navier_stokes_element.v_conv_gauss = v_conv.transpose()*N

v_gauss

generate_axisymmetric_navier_stokes_element.v_gauss = v.transpose()*N

v_n

generate_axisymmetric_navier_stokes_element.v_n = DefineMatrix('v_n',n_nodes,dim)

v_nn

generate_axisymmetric_navier_stokes_element.v_nn = DefineMatrix('v_nn',n_nodes,dim)

vel_residual_x

tuple generate_axisymmetric_navier_stokes_element.vel_residual_x = rho*f_gauss[0] - rho*accel_gauss[0] - rho*v_conv_gauss[1]*grad_v[1,0] - rho*v_conv_gauss[0]*grad_v[0,0] - grad_p[0] + (mu/y)*grad_v[1,0]

Stabilization functional terms Momentum conservation residual Note that the second order viscous stress terms are dropped since linear elements are used.

vel_residual_y

tuple generate_axisymmetric_navier_stokes_element.vel_residual_y = rho*f_gauss[1] - rho*accel_gauss[1] - rho*v_conv_gauss[1]*grad_v[1,1] - rho*v_conv_gauss[0]*grad_v[0,1] - grad_p[1] - mu*v_gauss[1]/y**2 + (mu/y)*grad_v[1,1]

vel_subscale_x

float generate_axisymmetric_navier_stokes_element.vel_subscale_x = tau1*vel_residual_x

vel_subscale_y

float generate_axisymmetric_navier_stokes_element.vel_subscale_y = tau1*vel_residual_y

w

generate_axisymmetric_navier_stokes_element.w = DefineMatrix('w',n_nodes,dim)

Test functions definition.

w_gauss

generate_axisymmetric_navier_stokes_element.w_gauss = w.transpose()*N

y

generate_axisymmetric_navier_stokes_element.y = sympy.Symbol('y', positive = True)

Other simbols definition.