generate_two_fluid_navier_stokes Namespace Reference

Variables
bool	do_simplifications = False
	Settings explanation DIMENSION TO COMPUTE: This symbolic generator is valid for both 2D and 3D cases. More...
string	dim_to_compute = "Both"
string	linearisation = "Picard"
bool	divide_by_rho = True
bool	ASGS_stabilization = True
string	mode = "c"
string	time_integration = "bdf2"
string	output_filename = "two_fluid_navier_stokes.cpp"
string	template_filename = "two_fluid_navier_stokes_template.cpp"
string	err_msg = "Wrong time_integration. Given \'" + time_integration + "\'. Available options are \'bdf2\' , \'alpha_method\'and \'theta_scheme\'."
list	dim_vector = [2]
	templatefile = open(template_filename)
	Read the template file. More...
	outstring = templatefile.read()
int	nnodes = 3
int	strain_size = 3
bool	impose_partion_of_unity = False
	N
	DN
	DNenr = DefineMatrix('DNenr',nnodes,dim)
	Nenr = DefineVector('Nenr',nnodes)
	v = DefineMatrix('v',nnodes,dim)
	Unknown fields definition. More...
	vn = DefineMatrix('vn',nnodes,dim)
	vnn = DefineMatrix('vnn',nnodes,dim)
	p = DefineVector('p',nnodes)
	penr = DefineVector('penr',nnodes)
	w = DefineMatrix('w',nnodes,dim)
	Test functions definition. More...
	q = DefineVector('q',nnodes)
	qenr = DefineVector('qenr' ,nnodes)
	f = DefineMatrix('f',nnodes,dim)
	Other data definitions. More...
	fn = DefineMatrix('fn',nnodes,dim)
	vmeshn = DefineMatrix('vmeshn',nnodes,dim)
	C = DefineSymmetricMatrix('C',strain_size,strain_size)
	Constitutive matrix definition. More...
	stress = DefineVector('stress',strain_size)
	Stress vector definition. More...
	dt = sympy.Symbol('dt', positive = True)
	Other simbols definition. More...
	rho = sympy.Symbol('rho', positive = True)
	nu = sympy.Symbol('nu', positive = True)
	mu = sympy.Symbol('mu', positive = True)
	tau1 = sympy.Symbol('tau1', positive = True)
	tau2 = sympy.Symbol('tau2', positive = True)
	h = sympy.Symbol('h', 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)
	volume_error_ratio = sympy.Symbol('volume_error_ratio')
	art_dyn_visc_coeff = sympy.Symbol('art_dyn_visc_coeff')
	vconv = DefineMatrix('vconv',nnodes,dim)
	Convective velocity definition. More...
	vmesh = DefineMatrix('vmesh',nnodes,dim)
	vconv_gauss = vconv.transpose()*N
float	vconv_gauss_norm = 0.0
	Compute the stabilization parameters. More...
	K_darcy = sympy.Symbol('K_darcy', positive = True)
	Data interpolation to the Gauss points. More...
	bdf0 = sympy.Symbol('bdf0')
	Backward differences coefficients. More...
	bdf1 = sympy.Symbol('bdf1')
	bdf2 = sympy.Symbol('bdf2')
tuple	acceleration = (bdf0*v +bdf1*vn + bdf2*vnn)
	v_gauss = v.transpose()*N
	f_gauss = f.transpose()*N
	max_sprectral_radius = sympy.Symbol('max_spectral_radius', positive = True)
	acceleration_alpha_method = DefineMatrix('acceleration_alpha_method',nnodes,dim)
float	alpha_m = 0.5*((3-max_sprectral_radius)/(1+max_sprectral_radius))
int	alpha_f = 1/(1+max_sprectral_radius)
float	gamma = 0.5+ alpha_m -alpha_f
int	f_alpha = fn+alpha_f*(f-fn)
	alpha method affected variables More...
int	v_alpha = vn+alpha_f*(v-vn)
tuple	acceleration_n = (v-vn)/(gamma*dt)+acceleration_alpha_method*(gamma-1)/gamma
	p_gauss = p.transpose()*N
	Data interpolation to the Gauss points. More...
	penr_gauss = penr.transpose()*Nenr
	w_gauss = w.transpose()*N
	q_gauss = q.transpose()*N
	qenr_gauss = qenr.transpose()*Nenr
tuple	accel_gauss = acceleration.transpose()*N
	grad_v = DN.transpose()*v
	Gradients computation. More...
	grad_w = DN.transpose()*w
	grad_q = DN.transpose()*q
	grad_qenr = DNenr.transpose()*qenr
	grad_p = DN.transpose()*p
	grad_penr = DNenr.transpose()*penr
	div_v = div(DN,v)
	div_v_stabilization = div(DN,v)
	div_w = div(DN,w)
	div_vconv = div(DN,vconv)
	grad_sym_v_voigt = grad_sym_voigtform(DN,v)
	grad_sym_w_voigt = grad_sym_voigtform(DN,w)
tuple	convective_term = (vconv_gauss.transpose()*grad_v)
tuple	rv_galerkin = rho*w_gauss.transpose()*f_gauss - rho*w_gauss.transpose()*accel_gauss - rho*w_gauss.transpose()*convective_term.transpose() - grad_sym_w_voigt.transpose()*stress + div_w*p_gauss
	Galerkin Functional. More...
tuple	vel_residual = rho*f_gauss - rho*accel_gauss - rho*convective_term.transpose() - grad_p
	mas_residual = -div_v_stabilization[0,0]+volume_error_ratio
tuple	vel_subscale = tau1*vel_residual
	mas_subscale = tau2*mas_residual
tuple	rv_stab = grad_q.transpose()*vel_subscale
tuple	rv = rv_galerkin + rv_stab
	Add the stabilization terms to the original residual terms. More...
	dofs = sympy.zeros(nnodes*(dim+1), 1)
	Define DOFs and test function vectors. More...
	testfunc = sympy.zeros(nnodes*(dim+1), 1)
	rhs = Compute_RHS(rv.copy(), testfunc, do_simplifications)
	Compute LHS and RHS For the RHS computation one wants the residual of the previous iteration (residual based formulation). More...
	rhs_out = OutputVector_CollectingFactors(rhs, "rhs", mode)
	lhs = Compute_LHS(rhs, testfunc, dofs, do_simplifications)
	lhs_out = OutputMatrix_CollectingFactors(lhs, "lhs", mode)
	vel_residual_enr = rho*f_gauss - rho*(accel_gauss + convective_term.transpose()) - grad_p - grad_penr
	K V x = b + rhs_eV H Kee penr = rhs_ee. More...
	vel_subscale_enr = vel_residual_enr * tau1
	rv_galerkin_enriched = div_w*penr_gauss
	rv_stab_enriched = grad_qenr.transpose()*vel_subscale_enr
	rv_enriched = rv_galerkin_enriched
	dofs_enr = sympy.zeros(nnodes,1)
	Add the stabilization terms to the original residual terms. More...
	testfunc_enr = sympy.zeros(nnodes,1)
	rhs_eV
	K V x = b + rhs_eV H Kee penr = rhs_ee. More...
	V
	rhs_ee
	H
	Kee
	V_out = OutputMatrix_CollectingFactors(V,"V",mode)
	H_out = OutputMatrix_CollectingFactors(H,"H",mode)
	Kee_out = OutputMatrix_CollectingFactors(Kee,"Kee",mode)
	rhs_ee_out = OutputVector_CollectingFactors(rhs_ee,"rhs_ee",mode)
tuple	vel_residual_norm = vel_residual.norm()
	grad_v_norm = grad_v.norm()
float	artificial_mu = 0.5*h*art_dyn_visc_coeff*(vel_residual_norm/grad_v_norm)
	grad_v_norm_out = OutputScalar(grad_v_norm, "grad_v_norm", mode)
	artificial_mu_out = OutputScalar(artificial_mu, "artificial_mu", mode)
	out = open(output_filename,'w')

Variable Documentation

accel_gauss

tuple generate_two_fluid_navier_stokes.accel_gauss = acceleration.transpose()*N

acceleration

float generate_two_fluid_navier_stokes.acceleration = (bdf0*v +bdf1*vn + bdf2*vnn)

acceleration_alpha_method

generate_two_fluid_navier_stokes.acceleration_alpha_method = DefineMatrix('acceleration_alpha_method',nnodes,dim)

acceleration_n

tuple generate_two_fluid_navier_stokes.acceleration_n = (v-vn)/(gamma*dt)+acceleration_alpha_method*(gamma-1)/gamma

alpha_f

int generate_two_fluid_navier_stokes.alpha_f = 1/(1+max_sprectral_radius)

alpha_m

float generate_two_fluid_navier_stokes.alpha_m = 0.5*((3-max_sprectral_radius)/(1+max_sprectral_radius))

art_dyn_visc_coeff

generate_two_fluid_navier_stokes.art_dyn_visc_coeff = sympy.Symbol('art_dyn_visc_coeff')

artificial_mu

float generate_two_fluid_navier_stokes.artificial_mu = 0.5*h*art_dyn_visc_coeff*(vel_residual_norm/grad_v_norm)

artificial_mu_out

generate_two_fluid_navier_stokes.artificial_mu_out = OutputScalar(artificial_mu, "artificial_mu", mode)

ASGS_stabilization

bool generate_two_fluid_navier_stokes.ASGS_stabilization = True

bdf0

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

Backward differences coefficients.

bdf1

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

bdf2

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

C

generate_two_fluid_navier_stokes.C = DefineSymmetricMatrix('C',strain_size,strain_size)

Constitutive matrix definition.

convective_term

tuple generate_two_fluid_navier_stokes.convective_term = (vconv_gauss.transpose()*grad_v)

dim_to_compute

string generate_two_fluid_navier_stokes.dim_to_compute = "Both"

dim_vector

list generate_two_fluid_navier_stokes.dim_vector = [2]

div_v

generate_two_fluid_navier_stokes.div_v = div(DN,v)

div_v_stabilization

generate_two_fluid_navier_stokes.div_v_stabilization = div(DN,v)

div_vconv

generate_two_fluid_navier_stokes.div_vconv = div(DN,vconv)

div_w

generate_two_fluid_navier_stokes.div_w = div(DN,w)

divide_by_rho

bool generate_two_fluid_navier_stokes.divide_by_rho = True

DN

generate_two_fluid_navier_stokes.DN

DNenr

generate_two_fluid_navier_stokes.DNenr = DefineMatrix('DNenr',nnodes,dim)

do_simplifications

bool generate_two_fluid_navier_stokes.do_simplifications = False

Settings explanation DIMENSION TO COMPUTE: This symbolic generator is valid for both 2D and 3D cases.

Since the element has been programed with a dimension template in Kratos, it is advised to set the dim_to_compute flag as "Both". In this case the generated .cpp file will contain both 2D and 3D implementations. LINEARISATION SETTINGS: FullNR considers the convective velocity as "v-vmesh", hence v is taken into account in the derivation of the LHS and RHS. Picard (a.k.a. QuasiNR) considers the convective velocity as "a", thus it is considered as a constant in the derivation of the LHS and RHS. DIVIDE BY RHO: If set to true, divides the mass conservation equation by rho in order to have a better conditioned matrix. Otherwise the original form is kept.

Symbolic generation settings

dofs

generate_two_fluid_navier_stokes.dofs = sympy.zeros(nnodes*(dim+1), 1)

Define DOFs and test function vectors.

dofs_enr

generate_two_fluid_navier_stokes.dofs_enr = sympy.zeros(nnodes,1)

Add the stabilization terms to the original residual terms.

dt

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

Other simbols definition.

dyn_tau

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

err_msg

string generate_two_fluid_navier_stokes.err_msg = "Wrong time_integration. Given \'" + time_integration + "\'. Available options are \'bdf2\' , \'alpha_method\'and \'theta_scheme\'."

f

generate_two_fluid_navier_stokes.f = DefineMatrix('f',nnodes,dim)

Other data definitions.

f_alpha

int generate_two_fluid_navier_stokes.f_alpha = fn+alpha_f*(f-fn)

alpha method affected variables

f_gauss

int generate_two_fluid_navier_stokes.f_gauss = f.transpose()*N

fn

generate_two_fluid_navier_stokes.fn = DefineMatrix('fn',nnodes,dim)

gamma

float generate_two_fluid_navier_stokes.gamma = 0.5+ alpha_m -alpha_f

grad_p

generate_two_fluid_navier_stokes.grad_p = DN.transpose()*p

grad_penr

generate_two_fluid_navier_stokes.grad_penr = DNenr.transpose()*penr

grad_q

generate_two_fluid_navier_stokes.grad_q = DN.transpose()*q

grad_qenr

generate_two_fluid_navier_stokes.grad_qenr = DNenr.transpose()*qenr

grad_sym_v_voigt

generate_two_fluid_navier_stokes.grad_sym_v_voigt = grad_sym_voigtform(DN,v)

grad_sym_w_voigt

generate_two_fluid_navier_stokes.grad_sym_w_voigt = grad_sym_voigtform(DN,w)

grad_v

int generate_two_fluid_navier_stokes.grad_v = DN.transpose()*v

Gradients computation.

grad_v_norm

generate_two_fluid_navier_stokes.grad_v_norm = grad_v.norm()

grad_v_norm_out

generate_two_fluid_navier_stokes.grad_v_norm_out = OutputScalar(grad_v_norm, "grad_v_norm", mode)

grad_w

generate_two_fluid_navier_stokes.grad_w = DN.transpose()*w

h

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

H

generate_two_fluid_navier_stokes.H

H_out

generate_two_fluid_navier_stokes.H_out = OutputMatrix_CollectingFactors(H,"H",mode)

impose_partion_of_unity

bool generate_two_fluid_navier_stokes.impose_partion_of_unity = False

K_darcy

generate_two_fluid_navier_stokes.K_darcy = sympy.Symbol('K_darcy', positive = True)

Data interpolation to the Gauss points.

Kee

generate_two_fluid_navier_stokes.Kee

Kee_out

generate_two_fluid_navier_stokes.Kee_out = OutputMatrix_CollectingFactors(Kee,"Kee",mode)

lhs

generate_two_fluid_navier_stokes.lhs = Compute_LHS(rhs, testfunc, dofs, do_simplifications)

lhs_out

generate_two_fluid_navier_stokes.lhs_out = OutputMatrix_CollectingFactors(lhs, "lhs", mode)

linearisation

string generate_two_fluid_navier_stokes.linearisation = "Picard"

mas_residual

generate_two_fluid_navier_stokes.mas_residual = -div_v_stabilization[0,0]+volume_error_ratio

mas_subscale

generate_two_fluid_navier_stokes.mas_subscale = tau2*mas_residual

max_sprectral_radius

generate_two_fluid_navier_stokes.max_sprectral_radius = sympy.Symbol('max_spectral_radius', positive = True)

mode

string generate_two_fluid_navier_stokes.mode = "c"

mu

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

N

generate_two_fluid_navier_stokes.N

Nenr

generate_two_fluid_navier_stokes.Nenr = DefineVector('Nenr',nnodes)

nnodes

int generate_two_fluid_navier_stokes.nnodes = 3

nu

generate_two_fluid_navier_stokes.nu = sympy.Symbol('nu', positive = True)

out

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

output_filename

string generate_two_fluid_navier_stokes.output_filename = "two_fluid_navier_stokes.cpp"

outstring

generate_two_fluid_navier_stokes.outstring = templatefile.read()

p

generate_two_fluid_navier_stokes.p = DefineVector('p',nnodes)

p_gauss

generate_two_fluid_navier_stokes.p_gauss = p.transpose()*N

Data interpolation to the Gauss points.

penr

generate_two_fluid_navier_stokes.penr = DefineVector('penr',nnodes)

penr_gauss

generate_two_fluid_navier_stokes.penr_gauss = penr.transpose()*Nenr

q

generate_two_fluid_navier_stokes.q = DefineVector('q',nnodes)

q_gauss

generate_two_fluid_navier_stokes.q_gauss = q.transpose()*N

qenr

generate_two_fluid_navier_stokes.qenr = DefineVector('qenr' ,nnodes)

qenr_gauss

generate_two_fluid_navier_stokes.qenr_gauss = qenr.transpose()*Nenr

rho

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

rhs

generate_two_fluid_navier_stokes.rhs = Compute_RHS(rv.copy(), testfunc, do_simplifications)

Compute LHS and RHS For the RHS computation one wants the residual of the previous iteration (residual based formulation).

By this reason the stress is included as a symbolic variable, which is assumed to be passed as an argument from the previous iteration database.

rhs_ee

generate_two_fluid_navier_stokes.rhs_ee

rhs_ee_out

generate_two_fluid_navier_stokes.rhs_ee_out = OutputVector_CollectingFactors(rhs_ee,"rhs_ee",mode)

rhs_eV

generate_two_fluid_navier_stokes.rhs_eV

K V x = b + rhs_eV H Kee penr = rhs_ee.

rhs_out

generate_two_fluid_navier_stokes.rhs_out = OutputVector_CollectingFactors(rhs, "rhs", mode)

rv

tuple generate_two_fluid_navier_stokes.rv = rv_galerkin + rv_stab

Add the stabilization terms to the original residual terms.

rv_enriched

generate_two_fluid_navier_stokes.rv_enriched = rv_galerkin_enriched

rv_galerkin

tuple generate_two_fluid_navier_stokes.rv_galerkin = rho*w_gauss.transpose()*f_gauss - rho*w_gauss.transpose()*accel_gauss - rho*w_gauss.transpose()*convective_term.transpose() - grad_sym_w_voigt.transpose()*stress + div_w*p_gauss

Galerkin Functional.

rv_galerkin_enriched

generate_two_fluid_navier_stokes.rv_galerkin_enriched = div_w*penr_gauss

rv_stab

tuple generate_two_fluid_navier_stokes.rv_stab = grad_q.transpose()*vel_subscale

rv_stab_enriched

generate_two_fluid_navier_stokes.rv_stab_enriched = grad_qenr.transpose()*vel_subscale_enr

stab_c1

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

stab_c2

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

strain_size

int generate_two_fluid_navier_stokes.strain_size = 3

stress

generate_two_fluid_navier_stokes.stress = DefineVector('stress',strain_size)

Stress vector definition.

tau1

float generate_two_fluid_navier_stokes.tau1 = sympy.Symbol('tau1', positive = True)

tau2

generate_two_fluid_navier_stokes.tau2 = sympy.Symbol('tau2', positive = True)

template_filename

string generate_two_fluid_navier_stokes.template_filename = "two_fluid_navier_stokes_template.cpp"

templatefile

generate_two_fluid_navier_stokes.templatefile = open(template_filename)

Read the template file.

testfunc

generate_two_fluid_navier_stokes.testfunc = sympy.zeros(nnodes*(dim+1), 1)

testfunc_enr

generate_two_fluid_navier_stokes.testfunc_enr = sympy.zeros(nnodes,1)

time_integration

string generate_two_fluid_navier_stokes.time_integration = "bdf2"

v

generate_two_fluid_navier_stokes.v = DefineMatrix('v',nnodes,dim)

Unknown fields definition.

V

generate_two_fluid_navier_stokes.V

v_alpha

int generate_two_fluid_navier_stokes.v_alpha = vn+alpha_f*(v-vn)

v_gauss

int generate_two_fluid_navier_stokes.v_gauss = v.transpose()*N

V_out

generate_two_fluid_navier_stokes.V_out = OutputMatrix_CollectingFactors(V,"V",mode)

vconv

generate_two_fluid_navier_stokes.vconv = DefineMatrix('vconv',nnodes,dim)

Convective velocity definition.

vconv_gauss

generate_two_fluid_navier_stokes.vconv_gauss = vconv.transpose()*N

vconv_gauss_norm

generate_two_fluid_navier_stokes.vconv_gauss_norm = 0.0

Compute the stabilization parameters.

vel_residual

tuple generate_two_fluid_navier_stokes.vel_residual = rho*f_gauss - rho*accel_gauss - rho*convective_term.transpose() - grad_p

vel_residual_enr

generate_two_fluid_navier_stokes.vel_residual_enr = rho*f_gauss - rho*(accel_gauss + convective_term.transpose()) - grad_p - grad_penr

K V x = b + rhs_eV H Kee penr = rhs_ee.

vel_residual_norm

tuple generate_two_fluid_navier_stokes.vel_residual_norm = vel_residual.norm()

vel_subscale

tuple generate_two_fluid_navier_stokes.vel_subscale = tau1*vel_residual

vel_subscale_enr

generate_two_fluid_navier_stokes.vel_subscale_enr = vel_residual_enr * tau1

vmesh

generate_two_fluid_navier_stokes.vmesh = DefineMatrix('vmesh',nnodes,dim)

vmeshn

generate_two_fluid_navier_stokes.vmeshn = DefineMatrix('vmeshn',nnodes,dim)

vn

generate_two_fluid_navier_stokes.vn = DefineMatrix('vn',nnodes,dim)

vnn

generate_two_fluid_navier_stokes.vnn = DefineMatrix('vnn',nnodes,dim)

volume_error_ratio

generate_two_fluid_navier_stokes.volume_error_ratio = sympy.Symbol('volume_error_ratio')

w

generate_two_fluid_navier_stokes.w = DefineMatrix('w',nnodes,dim)

Test functions definition.

w_gauss

generate_two_fluid_navier_stokes.w_gauss = w.transpose()*N