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!
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\int_{\Omega} \nabla \cdot (\ul{y} p) q = \int_{\Omega} (\underbrace{(\nabla \cdot \ul{y})}_{\equiv 0} + (\ul{y}, \nabla)) p) q
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dw_advect_div_free | (material, virtual, state) |
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Scalar gradient term with convective velocity.
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\int_{\Omega} q (\ul{u} \cdot \nabla p)
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dw_convect_v_grad_s | (virtual, state_v, state_s) |
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Diffusion copupling term with material parameter K_{j}.
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\int_{\Omega} p K_{j} \nabla_j q \mbox{ , } \int_{\Omega} q K_{j} \nabla_j p
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dw_diffusion_coupling | (material, virtual, state) |
(material, state, virtual) | |
(material, parameter_1, parameter_2) |
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Diffusion-like term with material parameter K_{j} (to use on the right-hand side).
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\int_{\Omega} K_{j} \nabla_j q
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dw_diffusion_r | (material, virtual) |
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General diffusion term with permeability K_{ij}. Can be evaluated. Can use derivatives.
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\int_{\Omega} K_{ij} \nabla_i q \nabla_j p \mbox{ , } \int_{\Omega} K_{ij} \nabla_i \bar{p} \nabla_j r
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dw_diffusion | (material, virtual, state) |
(material, parameter_1, parameter_2) |
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Evaluate diffusion velocity.
Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.
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- \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}
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ev_diffusion_velocity | (material, parameter) |
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Laplace term with c coefficient. Can be evaluated. Can use derivatives.
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\int_{\Omega} c \nabla q \cdot \nabla p \mbox{ , } \int_{\Omega} c \nabla \bar{p} \cdot \nabla r
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dw_laplace | (opt_material, virtual, state) |
(opt_material, parameter_1, parameter_2) |
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Diffusion sensitivity analysis term.
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\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]
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d_sd_diffusion | (material, parameter_q, parameter_p, parameter_v) |
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Surface flux operator term.
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\int_{\Gamma} q \ul{n} \cdot \ull{K} \cdot \nabla p
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dw_surface_flux | (opt_material, virtual, state) |
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Surface flux term.
Supports ‘eval’, ‘el_eval’ and ‘el_avg’ evaluation modes.
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\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}
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d_surface_flux | (material, parameter) |
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