sfepy.terms.terms_diffusion module¶
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class
sfepy.terms.terms_diffusion.
AdvectDivFreeTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Advection of a scalar quantity p with the advection velocity \ul{y} given as a material parameter (a known function of space and time).
The advection velocity has to be divergence-free!
Definition: \int_{\Omega} \nabla \cdot (\ul{y} p) q = \int_{\Omega} (\underbrace{(\nabla \cdot \ul{y})}_{\equiv 0} + (\ul{y}, \nabla)) p) q
Call signature: dw_advect_div_free (material, virtual, state)
Arguments: - material : \ul{y}
- virtual : q
- virtual : p
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arg_shapes
= {'state': '1', 'material': 'D, 1', 'virtual': ('1', 'state')}¶
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arg_types
= ('material', 'virtual', 'state')¶
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name
= 'dw_advect_div_free'¶
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class
sfepy.terms.terms_diffusion.
ConvectVGradSTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Scalar gradient term with convective velocity.
Definition: \int_{\Omega} q (\ul{u} \cdot \nabla p)
Call signature: dw_convect_v_grad_s (virtual, state_v, state_s)
Arguments: - virtual : q
- state_v : \ul{u}
- state_s : p
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arg_shapes
= [{'state_s': 1, 'virtual': (1, 'state_s'), 'state_v': 'D'}]¶
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arg_types
= ('virtual', 'state_v', 'state_s')¶
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function
()¶
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name
= 'dw_convect_v_grad_s'¶
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class
sfepy.terms.terms_diffusion.
DiffusionCoupling
(name, arg_str, integral, region, **kwargs)[source]¶ Diffusion copupling term with material parameter K_{j}.
Definition: \int_{\Omega} p K_{j} \nabla_j q \mbox{ , } \int_{\Omega} q K_{j} \nabla_j p
Call signature: dw_diffusion_coupling (material, virtual, state)
(material, state, virtual)
(material, parameter_1, parameter_2)
Arguments: - material : K_{j}
- virtual : q
- state : p
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arg_shapes
= {'parameter_2': 1, 'state': 1, 'material': 'D, 1', 'parameter_1': 1, 'virtual': (1, 'state')}¶
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arg_types
= (('material', 'virtual', 'state'), ('material', 'state', 'virtual'), ('material', 'parameter_1', 'parameter_2'))¶
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modes
= ('weak0', 'weak1', 'eval')¶
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name
= 'dw_diffusion_coupling'¶
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class
sfepy.terms.terms_diffusion.
DiffusionRTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Diffusion-like term with material parameter K_{j} (to use on the right-hand side).
Definition: \int_{\Omega} K_{j} \nabla_j q
Call signature: dw_diffusion_r (material, virtual)
Arguments: - material : K_j
- virtual : q
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arg_shapes
= {'material': 'D, 1', 'virtual': (1, None)}¶
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arg_types
= ('material', 'virtual')¶
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static
function
()¶
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name
= 'dw_diffusion_r'¶
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class
sfepy.terms.terms_diffusion.
DiffusionTerm
(name, arg_str, integral, region, **kwargs)[source]¶ General diffusion term with permeability K_{ij}. Can be evaluated. Can use derivatives.
Definition: \int_{\Omega} K_{ij} \nabla_i q \nabla_j p \mbox{ , } \int_{\Omega} K_{ij} \nabla_i \bar{p} \nabla_j r
Call signature: dw_diffusion (material, virtual, state)
(material, parameter_1, parameter_2)
Arguments 1: - material : K_{ij}
- virtual : q
- state : p
Arguments 2: - material : K_{ij}
- parameter_1 : \bar{p}
- parameter_2 : r
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arg_shapes
= {'parameter_2': 1, 'state': 1, 'material': 'D, D', 'parameter_1': 1, 'virtual': (1, 'state')}¶
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arg_types
= (('material', 'virtual', 'state'), ('material', 'parameter_1', 'parameter_2'))¶
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modes
= ('weak', 'eval')¶
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name
= 'dw_diffusion'¶
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symbolic
= {'map': {'K': 'material', 'u': 'state'}, 'expression': 'div( K * grad( u ) )'}¶
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class
sfepy.terms.terms_diffusion.
DiffusionVelocityTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Evaluate diffusion velocity.
Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.
Definition: - \int_{\Omega} K_{ij} \nabla_j \bar{p}
\mbox{vector for } K \from \Ical_h: - \int_{T_K} K_{ij} \nabla_j \bar{p} / \int_{T_K} 1
- K_{ij} \nabla_j \bar{p}
Call signature: ev_diffusion_velocity (material, parameter)
Arguments: - material : K_{ij}
- parameter : \bar{p}
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arg_shapes
= {'material': 'D, D', 'parameter': 1}¶
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arg_types
= ('material', 'parameter')¶
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name
= 'ev_diffusion_velocity'¶
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class
sfepy.terms.terms_diffusion.
LaplaceTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Laplace term with c coefficient. Can be evaluated. Can use derivatives.
Definition: \int_{\Omega} c \nabla q \cdot \nabla p \mbox{ , } \int_{\Omega} c \nabla \bar{p} \cdot \nabla r
Call signature: dw_laplace (opt_material, virtual, state)
(opt_material, parameter_1, parameter_2)
Arguments 1: - material : c
- virtual : q
- state : p
Arguments 2: - material : c
- parameter_1 : \bar{p}
- parameter_2 : r
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arg_shapes
= [{'opt_material': '1, 1', 'state': 1, 'parameter_1': 1, 'virtual': (1, 'state'), 'parameter_2': 1}, {'opt_material': None}]¶
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arg_types
= (('opt_material', 'virtual', 'state'), ('opt_material', 'parameter_1', 'parameter_2'))¶
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modes
= ('weak', 'eval')¶
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name
= 'dw_laplace'¶
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symbolic
= {'map': {'c': 'opt_material', 'u': 'state'}, 'expression': 'c * div( grad( u ) )'}¶
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class
sfepy.terms.terms_diffusion.
SDDiffusionTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Diffusion sensitivity analysis term.
Definition: \int_{\Omega} \left[ (\dvg \ul{\Vcal}) K_{ij} \nabla_i q\, \nabla_j p - K_{ij} (\nabla_j \ul{\Vcal} \nabla q) \nabla_i p - K_{ij} \nabla_j q (\nabla_i \ul{\Vcal} \nabla p)\right]
Call signature: d_sd_diffusion (material, parameter_q, parameter_p, parameter_v)
Arguments: - material: K_{ij}
- parameter_q: q
- parameter_p: p
- parameter_v: \ul{\Vcal}
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arg_shapes
= {'parameter_q': 1, 'material': 'D, D', 'parameter_v': 'D', 'parameter_p': 1}¶
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arg_types
= ('material', 'parameter_q', 'parameter_p', 'parameter_v')¶
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static
function
()¶
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get_eval_shape
(mat, parameter_q, parameter_p, parameter_v, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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get_fargs
(mat, parameter_q, parameter_p, parameter_v, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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name
= 'd_sd_diffusion'¶
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class
sfepy.terms.terms_diffusion.
SurfaceFluxOperatorTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Surface flux operator term.
Definition: \int_{\Gamma} q \ul{n} \cdot \ull{K} \cdot \nabla p
Call signature: dw_surface_flux (opt_material, virtual, state)
Arguments: - material : \ull{K}
- virtual : q
- state : p
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arg_shapes
= [{'opt_material': 'D, D', 'state': 1, 'virtual': (1, 'state')}, {'opt_material': None}]¶
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arg_types
= ('opt_material', 'virtual', 'state')¶
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function
()¶
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integration
= 'surface_extra'¶
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name
= 'dw_surface_flux'¶
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class
sfepy.terms.terms_diffusion.
SurfaceFluxTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Surface flux term.
Supports ‘eval’, ‘el_eval’ and ‘el_avg’ evaluation modes.
Definition: \int_{\Gamma} \ul{n} \cdot K_{ij} \nabla_j \bar{p}
\mbox{vector for } K \from \Ical_h: \int_{T_K} \ul{n} \cdot K_{ij} \nabla_j \bar{p}\ / \int_{T_K} 1
\mbox{vector for } K \from \Ical_h: \int_{T_K} \ul{n} \cdot K_{ij} \nabla_j \bar{p}
Call signature: d_surface_flux (material, parameter)
Arguments: - material: \ul{K}
- parameter: \bar{p},
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arg_shapes
= {'material': 'D, D', 'parameter': 1}¶
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arg_types
= ('material', 'parameter')¶
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static
function
()¶
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integration
= 'surface_extra'¶
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name
= 'd_surface_flux'¶