generate_convection_diffusion_explicit_element Namespace Reference

Functions
def	DefineShapeFunctionsMatrix (dim, n_nodes, n_gauss)

Variables
bool	do_simplifications = False
string	dim_to_compute = "Both"
bool	stabilization = True
bool	OSS_stabilization = True
bool	dynamic_subscales = False
string	mode = "c"
list	dim_vector = [2]
string	template_filename = "d_convection_diffusion_explicit_cpp_template.cpp"
	templatefile = open(template_filename)
	outstring = templatefile.read()
string	output_filename = "d_convection_diffusion_explicit.cpp"
string	err_msg = "Wrong template_filename provided. Must be (template --> output):\n"
int	nnodes = 3
int	ngauss = 3
	DN = DefineMatrix('DN', nnodes, dim)
def	mat_N = DefineShapeFunctionsMatrix(dim, nnodes, ngauss)
	phi = DefineVector('phi',nnodes)
	phi_old = DefineVector('phi_old',nnodes)
	phi_subscale_gauss = DefineVector('phi_subscale_gauss',ngauss)
	phi_acceleration_old = DefineVector('phi_acceleration_old',nnodes)
	w = DefineMatrix('w',nnodes,dim)
	q = DefineVector('q',nnodes)
	f = DefineVector('f',nnodes)
	alpha = Symbol('alpha',positive= True)
	v = DefineMatrix('v',nnodes,dim)
	tau = DefineVector('tau',ngauss)
	delta_time = Symbol('delta_time',positive= True)
	explicit_step_coefficient = Symbol('explicit_step_coefficient')
	prj = DefineVector('prj',nnodes)
	res_tot = Matrix(zeros(1,1))
	res_OSS_tot = Matrix(zeros(1,1))
	N = DefineVector('N', nnodes)
	f_gauss = f.transpose()*N
	Estimate variables on gauss point ##########. More...
	w_gauss = w.transpose()*N
	q_gauss = q.transpose()*N
	v_gauss = v.transpose()*N
	phi_gauss = phi.transpose()*N
	phi_old_gauss = phi_old.transpose()*N
	phi_acceleration_old_gauss = phi_acceleration_old.transpose()*N
	prj_gauss = prj.transpose()*N
	grad_w = DfjDxi(DN,w)
	grad_q = DfjDxi(DN,q)
	grad_phi = DfjDxi(DN,phi)
	grad_f = DfjDxi(DN,f)
	div_w = ones(1,1)*sum([DN[i]*w[i] for i in range (0,len(DN))])
	div_v = ones(1,1)*sum([DN[i]*v[i] for i in range (0,len(DN))])
	rhs_forcing = q_gauss.transpose() * f_gauss
	Estimate residuals on gauss point ##########. More...
	rhs_diffusion = - alpha * grad_phi.transpose() * grad_q
	rhs_convective_1 = - q_gauss * (v_gauss.transpose() * grad_phi)
	rhs_convective_2 = - q_gauss * phi_gauss * div_v
	rhs_galerkin = rhs_forcing + rhs_diffusion + rhs_convective_1 + rhs_convective_2
	rhs_stab_1_forcing = tau[i_gauss] * (v_gauss.transpose() * grad_q) * f_gauss
	Stabilization ASGS/OSS functional terms ##### ASGS/OSS Convective term. More...
	rhs_stab_1_mass = - tau[i_gauss] * (grad_q.transpose() * v_gauss) * N.transpose() * (phi-phi_old)*explicit_step_coefficient
	rhs_stab_1_convection_1 = - tau[i_gauss] * (v_gauss.transpose() * grad_q) * (v_gauss.transpose() * grad_phi)
	rhs_stab_1_convection_2 = - tau[i_gauss] * (v_gauss.transpose() * grad_q) * phi_gauss * div_v
	rhs_stab_1 = rhs_stab_1_forcing + rhs_stab_1_convection_1 + rhs_stab_1_convection_2 + rhs_stab_1_mass
	rhs_stab_1_oss = tau[i_gauss] * (v_gauss.transpose() * grad_q) * prj_gauss
	rhs_stab_1_dynamic = tau[i_gauss] * (v_gauss.transpose() * grad_q) * phi_subscale_gauss[i_gauss]/delta_time
	rhs_stab_2_forcing = - tau[i_gauss] * q_gauss.transpose() * f_gauss
	rhs_stab_2_mass = tau[i_gauss] * q_gauss.transpose() * N.transpose() * (phi-phi_old)*explicit_step_coefficient
	rhs_stab_2_convection_1 = tau[i_gauss] * q_gauss * (v_gauss.transpose() * grad_phi)
	rhs_stab_2_convection_2 = tau[i_gauss] * q_gauss * phi_gauss * div_v
	rhs_stab_2_diffusion = tau[i_gauss] * alpha * grad_phi.transpose() * grad_q
	rhs_stab_2_subgrid_old = - tau[i_gauss] * q_gauss.transpose() * phi_subscale_gauss[i_gauss]
	rhs_stab_2_mass_subgrid_old = q_gauss.transpose() * phi_subscale_gauss[i_gauss] / delta_time
	rhs_stab_2 = rhs_stab_2_forcing + rhs_stab_2_mass + rhs_stab_2_convection_1 + rhs_stab_2_convection_2 + rhs_stab_2_diffusion + rhs_stab_2_subgrid_old + rhs_stab_2_mass_subgrid_old
	rhs_stab_2_oss = - tau[i_gauss] * q_gauss.transpose() * prj_gauss
	rhs_stabilization = rhs_stab_1
	lhs_OSS_forcing = - q_gauss.transpose() * f_gauss
	OSS step ##### with lhs we refer to the fact we take the strong equation on the left side. More...
	lhs_OSS_mass = q_gauss.transpose() * (N.transpose() * (phi-phi_old)*explicit_step_coefficient)
	lhs_OSS_mass_subscale = - q_gauss.transpose() * (phi_subscale_gauss[i_gauss]/delta_time)
	lhs_OSS_diffusion = alpha * grad_phi.transpose() * grad_q
	lhs_OSS_convective_1 = q_gauss * (v_gauss.transpose() * grad_phi)
	lhs_OSS_convective_2 = q_gauss * phi_gauss * div_v
	res_OSS = lhs_OSS_forcing + lhs_OSS_mass + lhs_OSS_diffusion + lhs_OSS_convective_1 + lhs_OSS_convective_2
	res = rhs_galerkin + rhs_stabilization
	dofs = Matrix( zeros(nnodes*(1), 1) )
	testfunc = Matrix( zeros(nnodes*(1), 1) )
	rhs = Compute_RHS(res_tot.copy(), testfunc, do_simplifications)
	rhs_out = OutputVector_CollectingFactors(rhs, "rhs", mode)
string	to_substitute = 'DN(' + str(i_node) + ',' + str(j_dim) + ')'
string	substituted_value = 'DN_DX_' + str(i_node) + '_' + str(j_dim)
	out = open(output_filename,'w')

Function Documentation

DefineShapeFunctionsMatrix()

def generate_convection_diffusion_explicit_element.DefineShapeFunctionsMatrix	(		dim,
			n_nodes,
			n_gauss
	)

Variable Documentation

alpha

generate_convection_diffusion_explicit_element.alpha = Symbol('alpha',positive= True)

delta_time

generate_convection_diffusion_explicit_element.delta_time = Symbol('delta_time',positive= True)

dim_to_compute

string generate_convection_diffusion_explicit_element.dim_to_compute = "Both"

dim_vector

list generate_convection_diffusion_explicit_element.dim_vector = [2]

div_v

generate_convection_diffusion_explicit_element.div_v = ones(1,1)*sum([DN[i]*v[i] for i in range (0,len(DN))])

div_w

generate_convection_diffusion_explicit_element.div_w = ones(1,1)*sum([DN[i]*w[i] for i in range (0,len(DN))])

DN

generate_convection_diffusion_explicit_element.DN = DefineMatrix('DN', nnodes, dim)

do_simplifications

bool generate_convection_diffusion_explicit_element.do_simplifications = False

dofs

generate_convection_diffusion_explicit_element.dofs = Matrix( zeros(nnodes*(1), 1) )

dynamic_subscales

bool generate_convection_diffusion_explicit_element.dynamic_subscales = False

err_msg

string generate_convection_diffusion_explicit_element.err_msg = "Wrong template_filename provided. Must be (template --> output):\n"

explicit_step_coefficient

generate_convection_diffusion_explicit_element.explicit_step_coefficient = Symbol('explicit_step_coefficient')

f

generate_convection_diffusion_explicit_element.f = DefineVector('f',nnodes)

f_gauss

generate_convection_diffusion_explicit_element.f_gauss = f.transpose()*N

Estimate variables on gauss point ##########.

grad_f

generate_convection_diffusion_explicit_element.grad_f = DfjDxi(DN,f)

grad_phi

generate_convection_diffusion_explicit_element.grad_phi = DfjDxi(DN,phi)

grad_q

generate_convection_diffusion_explicit_element.grad_q = DfjDxi(DN,q)

grad_w

generate_convection_diffusion_explicit_element.grad_w = DfjDxi(DN,w)

lhs_OSS_convective_1

generate_convection_diffusion_explicit_element.lhs_OSS_convective_1 = q_gauss * (v_gauss.transpose() * grad_phi)

lhs_OSS_convective_2

generate_convection_diffusion_explicit_element.lhs_OSS_convective_2 = q_gauss * phi_gauss * div_v

lhs_OSS_diffusion

generate_convection_diffusion_explicit_element.lhs_OSS_diffusion = alpha * grad_phi.transpose() * grad_q

lhs_OSS_forcing

generate_convection_diffusion_explicit_element.lhs_OSS_forcing = - q_gauss.transpose() * f_gauss

OSS step ##### with lhs we refer to the fact we take the strong equation on the left side.

lhs_OSS_mass

generate_convection_diffusion_explicit_element.lhs_OSS_mass = q_gauss.transpose() * (N.transpose() * (phi-phi_old)*explicit_step_coefficient)

lhs_OSS_mass_subscale

generate_convection_diffusion_explicit_element.lhs_OSS_mass_subscale = - q_gauss.transpose() * (phi_subscale_gauss[i_gauss]/delta_time)

mat_N

def generate_convection_diffusion_explicit_element.mat_N = DefineShapeFunctionsMatrix(dim, nnodes, ngauss)

mode

string generate_convection_diffusion_explicit_element.mode = "c"

N

generate_convection_diffusion_explicit_element.N = DefineVector('N', nnodes)

ngauss

int generate_convection_diffusion_explicit_element.ngauss = 3

nnodes

int generate_convection_diffusion_explicit_element.nnodes = 3

OSS_stabilization

bool generate_convection_diffusion_explicit_element.OSS_stabilization = True

out

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

output_filename

string generate_convection_diffusion_explicit_element.output_filename = "d_convection_diffusion_explicit.cpp"

outstring

generate_convection_diffusion_explicit_element.outstring = templatefile.read()

phi

generate_convection_diffusion_explicit_element.phi = DefineVector('phi',nnodes)

phi_acceleration_old

generate_convection_diffusion_explicit_element.phi_acceleration_old = DefineVector('phi_acceleration_old',nnodes)

phi_acceleration_old_gauss

generate_convection_diffusion_explicit_element.phi_acceleration_old_gauss = phi_acceleration_old.transpose()*N

phi_gauss

generate_convection_diffusion_explicit_element.phi_gauss = phi.transpose()*N

phi_old

generate_convection_diffusion_explicit_element.phi_old = DefineVector('phi_old',nnodes)

phi_old_gauss

generate_convection_diffusion_explicit_element.phi_old_gauss = phi_old.transpose()*N

phi_subscale_gauss

generate_convection_diffusion_explicit_element.phi_subscale_gauss = DefineVector('phi_subscale_gauss',ngauss)

prj

generate_convection_diffusion_explicit_element.prj = DefineVector('prj',nnodes)

prj_gauss

generate_convection_diffusion_explicit_element.prj_gauss = prj.transpose()*N

q

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

q_gauss

generate_convection_diffusion_explicit_element.q_gauss = q.transpose()*N

res

generate_convection_diffusion_explicit_element.res = rhs_galerkin + rhs_stabilization

res_OSS

generate_convection_diffusion_explicit_element.res_OSS = lhs_OSS_forcing + lhs_OSS_mass + lhs_OSS_diffusion + lhs_OSS_convective_1 + lhs_OSS_convective_2

res_OSS_tot

generate_convection_diffusion_explicit_element.res_OSS_tot = Matrix(zeros(1,1))

res_tot

generate_convection_diffusion_explicit_element.res_tot = Matrix(zeros(1,1))

rhs

generate_convection_diffusion_explicit_element.rhs = Compute_RHS(res_tot.copy(), testfunc, do_simplifications)

rhs_convective_1

generate_convection_diffusion_explicit_element.rhs_convective_1 = - q_gauss * (v_gauss.transpose() * grad_phi)

rhs_convective_2

generate_convection_diffusion_explicit_element.rhs_convective_2 = - q_gauss * phi_gauss * div_v

rhs_diffusion

generate_convection_diffusion_explicit_element.rhs_diffusion = - alpha * grad_phi.transpose() * grad_q

rhs_forcing

generate_convection_diffusion_explicit_element.rhs_forcing = q_gauss.transpose() * f_gauss

Estimate residuals on gauss point ##########.

Galerkin functional terms #####

rhs_galerkin

generate_convection_diffusion_explicit_element.rhs_galerkin = rhs_forcing + rhs_diffusion + rhs_convective_1 + rhs_convective_2

rhs_out

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

rhs_stab_1

generate_convection_diffusion_explicit_element.rhs_stab_1 = rhs_stab_1_forcing + rhs_stab_1_convection_1 + rhs_stab_1_convection_2 + rhs_stab_1_mass

rhs_stab_1_convection_1

generate_convection_diffusion_explicit_element.rhs_stab_1_convection_1 = - tau[i_gauss] * (v_gauss.transpose() * grad_q) * (v_gauss.transpose() * grad_phi)

rhs_stab_1_convection_2

generate_convection_diffusion_explicit_element.rhs_stab_1_convection_2 = - tau[i_gauss] * (v_gauss.transpose() * grad_q) * phi_gauss * div_v

rhs_stab_1_dynamic

generate_convection_diffusion_explicit_element.rhs_stab_1_dynamic = tau[i_gauss] * (v_gauss.transpose() * grad_q) * phi_subscale_gauss[i_gauss]/delta_time

rhs_stab_1_forcing

generate_convection_diffusion_explicit_element.rhs_stab_1_forcing = tau[i_gauss] * (v_gauss.transpose() * grad_q) * f_gauss

Stabilization ASGS/OSS functional terms ##### ASGS/OSS Convective term.

rhs_stab_1_mass

generate_convection_diffusion_explicit_element.rhs_stab_1_mass = - tau[i_gauss] * (grad_q.transpose() * v_gauss) * N.transpose() * (phi-phi_old)*explicit_step_coefficient

rhs_stab_1_oss

generate_convection_diffusion_explicit_element.rhs_stab_1_oss = tau[i_gauss] * (v_gauss.transpose() * grad_q) * prj_gauss

rhs_stab_2

generate_convection_diffusion_explicit_element.rhs_stab_2 = rhs_stab_2_forcing + rhs_stab_2_mass + rhs_stab_2_convection_1 + rhs_stab_2_convection_2 + rhs_stab_2_diffusion + rhs_stab_2_subgrid_old + rhs_stab_2_mass_subgrid_old

rhs_stab_2_convection_1

generate_convection_diffusion_explicit_element.rhs_stab_2_convection_1 = tau[i_gauss] * q_gauss * (v_gauss.transpose() * grad_phi)

rhs_stab_2_convection_2

generate_convection_diffusion_explicit_element.rhs_stab_2_convection_2 = tau[i_gauss] * q_gauss * phi_gauss * div_v

rhs_stab_2_diffusion

generate_convection_diffusion_explicit_element.rhs_stab_2_diffusion = tau[i_gauss] * alpha * grad_phi.transpose() * grad_q

rhs_stab_2_forcing

generate_convection_diffusion_explicit_element.rhs_stab_2_forcing = - tau[i_gauss] * q_gauss.transpose() * f_gauss

rhs_stab_2_mass

generate_convection_diffusion_explicit_element.rhs_stab_2_mass = tau[i_gauss] * q_gauss.transpose() * N.transpose() * (phi-phi_old)*explicit_step_coefficient

rhs_stab_2_mass_subgrid_old

generate_convection_diffusion_explicit_element.rhs_stab_2_mass_subgrid_old = q_gauss.transpose() * phi_subscale_gauss[i_gauss] / delta_time

rhs_stab_2_oss

generate_convection_diffusion_explicit_element.rhs_stab_2_oss = - tau[i_gauss] * q_gauss.transpose() * prj_gauss

rhs_stab_2_subgrid_old

generate_convection_diffusion_explicit_element.rhs_stab_2_subgrid_old = - tau[i_gauss] * q_gauss.transpose() * phi_subscale_gauss[i_gauss]

rhs_stabilization

generate_convection_diffusion_explicit_element.rhs_stabilization = rhs_stab_1

stabilization

bool generate_convection_diffusion_explicit_element.stabilization = True

substituted_value

string generate_convection_diffusion_explicit_element.substituted_value = 'DN_DX_' + str(i_node) + '_' + str(j_dim)

tau

generate_convection_diffusion_explicit_element.tau = DefineVector('tau',ngauss)

template_filename

string generate_convection_diffusion_explicit_element.template_filename = "d_convection_diffusion_explicit_cpp_template.cpp"

templatefile

generate_convection_diffusion_explicit_element.templatefile = open(template_filename)

testfunc

generate_convection_diffusion_explicit_element.testfunc = Matrix( zeros(nnodes*(1), 1) )

to_substitute

string generate_convection_diffusion_explicit_element.to_substitute = 'DN(' + str(i_node) + ',' + str(j_dim) + ')'

v

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

v_gauss

generate_convection_diffusion_explicit_element.v_gauss = v.transpose()*N

w

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

w_gauss

generate_convection_diffusion_explicit_element.w_gauss = w.transpose()*N