sfepy.terms.terms_navier_stokes module¶

class sfepy.terms.terms_navier_stokes.ConvectTerm(name, arg_str, integral, region, **kwargs)[source]¶

Nonlinear convective term.

Definition:

$\int_{\Omega} ((\ul{u} \cdot \nabla) \ul{u}) \cdot \ul{v}$

Call signature:

dw_convect

(virtual, state)

Arguments:

virtual : $\ul{v}$
state : $\ul{u}$

arg_shapes = {'state': 'D', 'virtual': ('D', 'state')}¶

arg_types = ('virtual', 'state')¶

static function(out, grad, state, cmap, is_diff)¶

get_fargs(virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_convect'¶

class sfepy.terms.terms_navier_stokes.DivGradTerm(name, arg_str, integral, region, **kwargs)[source]¶

Diffusion term.

Definition:

$\int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u} \mbox{ , } \int_{\Omega} \nabla \ul{v} : \nabla \ul{u}$

Call signature:

dw_div_grad	`(opt_material, virtual, state)`
	`(opt_material, parameter_1, parameter_2)`

Arguments:

material: $\nu$ (viscosity, optional)
virtualparameter_1: $\ul{v}$
state/parameter_2: $\ul{u}$

arg_shapes = [{'opt_material': '1, 1', 'parameter_1': 'D', 'parameter_2': 'D', 'state': 'D', 'virtual': ('D', 'state')}, {'opt_material': None}]¶

arg_types = (('opt_material', 'virtual', 'state'), ('opt_material', 'parameter_1', 'parameter_2'))¶

d_div_grad(out, grad1, grad2, mat, vg, fmode)[source]¶

static function(out, grad, viscosity, cmap_v, cmap_s, is_diff)¶

get_eval_shape(mat, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(mat, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

modes = ('weak', 'eval')¶

name = 'dw_div_grad'¶

set_arg_types()[source]¶

class sfepy.terms.terms_navier_stokes.DivOperatorTerm(name, arg_str, integral, region, **kwargs)[source]¶

Weighted divergence term of a test function.

Definition:

$\int_{\Omega} \nabla \cdot \ul{v} \mbox { or } \int_{\Omega} c \nabla \cdot \ul{v}$

Call signature:

dw_div

(opt_material, virtual)

Arguments:

material : $c$ (optional)
virtual : $\ul{v}$

arg_shapes = [{'opt_material': '1, 1', 'virtual': ('D', None)}, {'opt_material': None}]¶

arg_types = ('opt_material', 'virtual')¶

static function(out, mat, vg)[source]¶

get_fargs(mat, virtual, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_div'¶

class sfepy.terms.terms_navier_stokes.DivTerm(name, arg_str, integral, region, **kwargs)[source]¶

Evaluate divergence of a vector field.

Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.

Definition:

$\int_{\cal{D}} \nabla \cdot \ul{u} \mbox { , } \int_{\cal{D}} c \nabla \cdot \ul{u}$

Call signature:

ev_div

(opt_material, parameter)

Arguments:

parameter : $\ul{u}$

arg_shapes = [{'opt_material': '1, 1', 'parameter': 'D'}, {'opt_material': None}]¶

arg_types = ('opt_material', 'parameter')¶

static function(out, mat, div, vg, fmode)[source]¶

get_eval_shape(mat, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(mat, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

integration = ('cell', 'facet_extra')¶

name = 'ev_div'¶

class sfepy.terms.terms_navier_stokes.GradDivStabilizationTerm(name, arg_str, integral, region, **kwargs)[source]¶

Grad-div stabilization term ( $\gamma$ is a global stabilization parameter).

Definition:

$\gamma \int_{\Omega} (\nabla\cdot\ul{u}) \cdot (\nabla\cdot\ul{v})$

Call signature:

dw_st_grad_div

(material, virtual, state)

Arguments:

material : $\gamma$
virtual : $\ul{v}$
state : $\ul{u}$

arg_shapes = {'material': '1, 1', 'state': 'D', 'virtual': ('D', 'state')}¶

arg_types = ('material', 'virtual', 'state')¶

static function(out, div, coef, cmap, is_diff)¶

get_fargs(gamma, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_st_grad_div'¶

class sfepy.terms.terms_navier_stokes.GradTerm(name, arg_str, integral, region, **kwargs)[source]¶

Evaluate gradient of a scalar or vector field.

Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.

Definition:

$\int_{\cal{D}} \nabla p \mbox{ or } \int_{\cal{D}} \nabla \ul{u}\\ \int_{\cal{D}} c \nabla p \mbox{ or } \int_{\cal{D}} c \nabla \ul{u}$

Call signature:

ev_grad

(opt_material, parameter)

Arguments:

parameter : $p$ or $\ul{u}$

arg_shapes = [{'opt_material': '1, 1', 'parameter': 'N'}, {'opt_material': None}]¶

arg_types = ('opt_material', 'parameter')¶

static function(out, mat, grad, vg, fmode)[source]¶

get_eval_shape(mat, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(mat, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

integration = ('cell', 'facet_extra')¶

name = 'ev_grad'¶

class sfepy.terms.terms_navier_stokes.LinearConvect2Term(name, arg_str, integral, region, **kwargs)[source]¶

Linearized convective term with the convection velocity given as a material parameter.

Definition:

$\int_{\Omega} ((\ul{c} \cdot \nabla) \ul{u}) \cdot \ul{v}$

$((\ul{c} \cdot \nabla) \ul{u})|_{qp}$

Call signature:

dw_lin_convect2

(material, virtual, state)

Arguments:

material : $\ul{c}$
virtual : $\ul{v}$
state : $\ul{u}$

arg_shapes = {'material': 'D, 1', 'state': 'D', 'virtual': ('D', 'state')}¶

arg_types = ('material', 'virtual', 'state')¶

static function(out, grad, state_b, cmap, is_diff)¶

get_fargs(material, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_lin_convect2'¶

class sfepy.terms.terms_navier_stokes.LinearConvectTerm(name, arg_str, integral, region, **kwargs)[source]¶

Linearized convective term.

Definition:

$\int_{\Omega} ((\ul{w} \cdot \nabla) \ul{u}) \cdot \ul{v}$

$((\ul{w} \cdot \nabla) \ul{u})|_{qp}$

Call signature:

dw_lin_convect

(virtual, parameter, state)

Arguments:

virtual : $\ul{v}$
parameter : $\ul{w}$
state : $\ul{u}$

arg_shapes = {'parameter': 'D', 'state': 'D', 'virtual': ('D', 'state')}¶

arg_types = ('virtual', 'parameter', 'state')¶

static function(out, grad, state_b, cmap, is_diff)¶

get_fargs(virtual, parameter, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_lin_convect'¶

class sfepy.terms.terms_navier_stokes.PSPGCStabilizationTerm(name, arg_str, integral, region, **kwargs)[source]¶

PSPG stabilization term, convective part ( $\tau$ is a local stabilization parameter).

Definition:

$\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ ((\ul{b} \cdot \nabla) \ul{u}) \cdot \nabla q$

Call signature:

dw_st_pspg_c

(material, virtual, parameter, state)

Arguments:

material : $\tau_K$
virtual : $q$
parameter : $\ul{b}$
state : $\ul{u}$

arg_shapes = {'material': '1, 1', 'parameter': 'D', 'state': 'D', 'virtual': (1, None)}¶

arg_types = ('material', 'virtual', 'parameter', 'state')¶

static function(out, state_b, state_u, coef, cmap_p, cmap_u, conn, is_diff)¶

get_fargs(tau, virtual, parameter, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_st_pspg_c'¶

class sfepy.terms.terms_navier_stokes.PSPGPStabilizationTerm(name, arg_str, integral, region, **kwargs)[source]¶

PSPG stabilization term, pressure part ( $\tau$ is a local stabilization parameter), alias to Laplace term dw_laplace.

Definition:

$\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ \nabla p \cdot \nabla q$

Call signature:

dw_st_pspg_p	`(opt_material, virtual, state)`
	`(opt_material, parameter_1, parameter_2)`

Arguments:

material : $\tau_K$
virtual : $q$
state : $p$

name = 'dw_st_pspg_p'¶

class sfepy.terms.terms_navier_stokes.SUPGCStabilizationTerm(name, arg_str, integral, region, **kwargs)[source]¶

SUPG stabilization term, convective part ( $\delta$ is a local stabilization parameter).

Definition:

$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ ((\ul{b} \cdot \nabla) \ul{u})\cdot ((\ul{b} \cdot \nabla) \ul{v})$

Call signature:

dw_st_supg_c

(material, virtual, parameter, state)

Arguments:

material : $\delta_K$
virtual : $\ul{v}$
parameter : $\ul{b}$
state : $\ul{u}$

arg_shapes = {'material': '1, 1', 'parameter': 'D', 'state': 'D', 'virtual': ('D', 'state')}¶

arg_types = ('material', 'virtual', 'parameter', 'state')¶

static function(out, state_b, state_u, coef, cmap, conn, is_diff)¶

get_fargs(delta, virtual, parameter, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_st_supg_c'¶

class sfepy.terms.terms_navier_stokes.SUPGPStabilizationTerm(name, arg_str, integral, region, **kwargs)[source]¶

SUPG stabilization term, pressure part ( $\delta$ is a local stabilization parameter).

Definition:

$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ \nabla p\cdot ((\ul{b} \cdot \nabla) \ul{v})$

Call signature:

dw_st_supg_p

(material, virtual, parameter, state)

Arguments:

material : $\delta_K$
virtual : $\ul{v}$
parameter : $\ul{b}$
state : $p$

arg_shapes = {'material': '1, 1', 'parameter': 'D', 'state': 1, 'virtual': ('D', None)}¶

arg_types = ('material', 'virtual', 'parameter', 'state')¶

static function(out, state_b, grad_p, coef, cmap_u, cmap_p, is_diff)¶

get_fargs(delta, virtual, parameter, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_st_supg_p'¶

class sfepy.terms.terms_navier_stokes.StokesTerm(name, arg_str, integral, region, **kwargs)[source]¶

Stokes problem coupling term. Corresponds to weak forms of gradient and divergence terms. Can be evaluated.

Definition:

$\int_{\Omega} p\ \nabla \cdot \ul{v} \mbox{ , } \int_{\Omega} q\ \nabla \cdot \ul{u}\\ \mbox{ or } \int_{\Omega} c\ p\ \nabla \cdot \ul{v} \mbox{ , } \int_{\Omega} c\ q\ \nabla \cdot \ul{u}$

Call signature:

dw_stokes	`(opt_material, virtual, state)`
	`(opt_material, state, virtual)`
	`(opt_material, parameter_v, parameter_s)`

Arguments 1:

material: $c$ (optional)
virtual/parameter_v: $\ul{v}$
state/parameter_s: $p$

Arguments 2:

material : $c$ (optional)
state : $\ul{u}$
virtual : $q$

arg_shapes = [{'opt_material': '1, 1', 'parameter_s': 1, 'parameter_v': 'D', 'state/div': 'D', 'state/grad': 1, 'virtual/div': (1, None), 'virtual/grad': ('D', None)}, {'opt_material': None}]¶

arg_types = (('opt_material', 'virtual', 'state'), ('opt_material', 'state', 'virtual'), ('opt_material', 'parameter_v', 'parameter_s'))¶

static d_eval(out, coef, vec_qp, div, vvg)[source]¶

get_eval_shape(coef, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(coef, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

modes = ('grad', 'div', 'eval')¶

name = 'dw_stokes'¶

set_arg_types()[source]¶

class sfepy.terms.terms_navier_stokes.StokesWaveDivTerm(name, arg_str, integral, region, **kwargs)[source]¶

Stokes dispersion term with the wave vector $\ul{\kappa}$ and the divergence operator.

Definition:

$\int_{\Omega} (\ul{\kappa} \cdot \ul{v}) (\nabla \cdot \ul{u}) \;, \int_{\Omega} (\ul{\kappa} \cdot \ul{u}) (\nabla \cdot \ul{v})$

Call signature:

dw_stokes_wave_div	`(material, virtual, state)`
	`(material, state, virtual)`

Arguments 1:

material : $\ul{\kappa}$
virtual : $\ul{v}$
state : $\ul{u}$

Arguments 2:

material : $\ul{\kappa}$
state : $\ul{u}$
virtual : $\ul{v}$

arg_shapes = {'material': '.: D', 'state': 'D', 'virtual': ('D', 'state')}¶

arg_types = (('material', 'virtual', 'state'), ('material', 'state', 'virtual'))¶

static function(out, out_qp, geo, fmode)[source]¶

geometries = ['2_3', '2_4', '3_4', '3_8']¶

get_fargs(kappa, kvar, dvar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

modes = ('kd', 'dk')¶

name = 'dw_stokes_wave_div'¶

class sfepy.terms.terms_navier_stokes.StokesWaveTerm(name, arg_str, integral, region, **kwargs)[source]¶

Stokes dispersion term with the wave vector $\ul{\kappa}$ .

Definition:

$\int_{\Omega} (\ul{\kappa} \cdot \ul{v}) (\ul{\kappa} \cdot \ul{u})$

Call signature:

dw_stokes_wave

(material, virtual, state)

Arguments:

material : $\ul{\kappa}$
virtual : $\ul{v}$
statee : $\ul{u}$

arg_shapes = {'material': '.: D', 'state': 'D', 'virtual': ('D', 'state')}¶

arg_types = ('material', 'virtual', 'state')¶

static function(out, out_qp, geo, fmode)[source]¶

geometries = ['2_3', '2_4', '3_4', '3_8']¶

get_fargs(kappa, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_stokes_wave'¶