sfepy.terms.termsNavierStokes module¶

class sfepy.terms.termsNavierStokes.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')¶

function()¶

geometries = ['3_4', '3_8']¶

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

name = 'dw_convect'¶

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

Diffusion term.

Definition :

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

Call signature:

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

Arguments 1:	material : $\nu$ (viscosity, optional) virtual : $\ul{v}$ state : $\ul{u}$
Arguments 2:	material : $\nu$ (viscosity, optional) parameter_1 : $\ul{u}$ parameter_2 : $\ul{w}$

arg_shapes = {'opt_material': '1, 1', 'state': 'D', 'parameter_1': 'D', 'virtual': ('D', 'state'), 'parameter_2': 'D'}¶

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

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

function()¶

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.termsNavierStokes.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.termsNavierStokes.DivTerm(name, arg_str, integral, region, **kwargs)[source]¶

Evaluate divergence of a vector field.

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

Definition :

$\int_{\Omega} \nabla \cdot \ul{u}$

$\mbox{vector for } K \from \Ical_h: \int_{T_K} \nabla \cdot \ul{u} / \int_{T_K} 1$

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

Call signature:

ev_div (parameter)

Arguments :	parameter : $\ul{u}$

arg_shapes = {'parameter': 'D'}¶

arg_types = ('parameter',)¶

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

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

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

name = 'ev_div'¶

class sfepy.terms.termsNavierStokes.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 = {'state': 'D', 'material': '1, 1', 'virtual': ('D', 'state')}¶

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

function()¶

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

name = 'dw_st_grad_div'¶

class sfepy.terms.termsNavierStokes.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 :

$\int_{\Omega} \nabla p \mbox{ or } \int_{\Omega} \nabla \ul{w}$

$\mbox{vector for } K \from \Ical_h: \int_{T_K} \nabla p / \int_{T_K} 1 \mbox{ or } \int_{T_K} \nabla \ul{w} / \int_{T_K} 1$

$(\nabla p)|_{qp} \mbox{ or } \nabla \ul{w}|_{qp}$

Call signature:

ev_grad (parameter)

Arguments :	parameter : $p$ or $\ul{w}$

arg_shapes = [{'parameter': 1}, {'parameter': 'D'}]¶

arg_types = ('parameter',)¶

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

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

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

name = 'ev_grad'¶

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

Linearized convective term.

Definition :

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

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

Call signature:

dw_lin_convect (virtual, parameter, state)

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

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

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

function()¶

geometries = ['3_4', '3_8']¶

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

name = 'dw_lin_convect'¶

class sfepy.terms.termsNavierStokes.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 = {'state': 'D', 'material': '1, 1', 'parameter': 'D', 'virtual': (1, None)}¶

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

function()¶

geometries = ['3_4', '3_8']¶

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

name = 'dw_st_pspg_c'¶

class sfepy.terms.termsNavierStokes.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.termsNavierStokes.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 = {'state': 'D', 'material': '1, 1', 'parameter': 'D', 'virtual': ('D', 'state')}¶

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

function()¶

geometries = ['3_4', '3_8']¶

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

name = 'dw_st_supg_c'¶

class sfepy.terms.termsNavierStokes.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 = {'state': 1, 'material': '1, 1', 'parameter': 'D', 'virtual': ('D', None)}¶

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

function()¶

geometries = ['3_4', '3_8']¶

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

name = 'dw_st_supg_p'¶

class sfepy.terms.termsNavierStokes.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 : $\ul{v}$ state : $p$
Arguments 2:	material : $c$ (optional) state : $\ul{u}$ virtual : $q$
Arguments 3:	material : $c$ (optional) parameter_v : $\ul{u}$ parameter_s : $p$

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

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