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OGS
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OGS
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Global assembler for the monolithic scheme of the non-isothermal Richards flow.
Governing equations without vapor diffusion
The energy balance equation is given by
\[ (\rho c_p)^{eff}\dot T - \nabla (\mathbf{k}_T^{eff} \nabla T)+\rho^l c_p^l \nabla T \cdot \mathbf{v}^l = Q_T \]
with \(T\) the temperature, \((\rho c_p)^{eff}\) the effective volumetric heat capacity, \(\mathbf{k}_T^{eff} \) the effective thermal conductivity, \(\rho^l\) the density of liquid, \(c_p^l\) the specific heat capacity of liquid, \(\mathbf{v}^l\) the liquid velocity, and \(Q_T\) the point heat source. The effective volumetric heat can be considered as a composite of the contributions of solid phase and the liquid phase as
\[ (\rho c_p)^{eff} = (1-\phi) \rho^s c_p^s + S^l \phi \rho^l c_p^l \]
with \(\phi\) the porosity, \(S^l\) the liquid saturation, \(\rho^s \) the solid density, and \(c_p^s\) the specific heat capacity of solid. Similarly, the effective thermal conductivity is given by
\[ \mathbf{k}_T^{eff} = (1-\phi) \mathbf{k}_T^s + S^l \phi k_T^l \mathbf I \]
where \(\mathbf{k}_T^s\) is the thermal conductivity tensor of solid, \( k_T^l\) is the thermal conductivity of liquid, and \(\mathbf I\) is the identity tensor.
The mass balance equation is given by
\begin{eqnarray*} \left(S^l\beta - \phi\frac{\partial S}{\partial p_c}\right) \rho^l\dot p - S \left( \frac{\partial \rho^l}{\partial T} +\rho^l(\alpha_B -S) \alpha_T^s \right)\dot T\\ +\nabla (\rho^l \mathbf{v}^l) + S \alpha_B \rho^l \nabla \cdot \dot {\mathbf u}= Q_H \end{eqnarray*}
where \(p\) is the pore pressure, \(p_c\) is the capillary pressure, which is \(-p\) under the single phase assumption, \(\beta\) is a composite coefficient by the liquid compressibility and solid compressibility, \(\alpha_B\) is the Biot's constant, \(\alpha_T^s\) is the linear thermal expansivity of solid, \(Q_H\) is the point source or sink term, \(H(S-1)\) is the Heaviside function, and \( \mathbf u\) is the displacement. While this process does not contain a fully mechanical coupling, simplfied expressions can be given to approximate the latter term under certain stress conditions. The liquid velocity \(\mathbf{v}^l\) is described by the Darcy's law as
\[ \mathbf{v}^l=-\frac{{\mathbf k} k_{ref}}{\mu} (\nabla p - \rho^l \mathbf g) \]
with \({\mathbf k}\) the intrinsic permeability, \(k_{ref}\) the relative permeability, \(\mathbf g\) the gravitational force.
Note: This list has been automatically extracted from OGS's benchmark tests (ctests). Therefore it might not be exhaustive, but it should give users a good overview about which properties they can/have to use with this process. Probably most of the properties occurring in this list are mandatory.
The list might contain different property <type>s for some property <name> to illustrate different possibilities the users have.
<type> [case] AqueousLiquid<type> [case] Gas<type> [case] Solid<name> density<type> [case] Constant<name> density<type> [case] Function<name> density<type> [case] Linear<name> density<type> [case] WaterVapourDensity<name> diffusion<type> [case] VapourDiffusionFEBEX<name> poissons_ratio<type> [case] Constant<name> poissons_ratio<type> [case] Parameter<name> specific_heat_capacity<type> [case] Constant<name> specific_latent_heat<type> [case] LinearWaterVapourLatentHeat<name> storage<type> [case] Constant<name> storage_contribution<type> [case] Constant<name> thermal_conductivity<type> [case] Constant<name> thermal_diffusion_enhancement_factor <type> [case] Constant<name> thermal_expansivity<type> [case] Constant<name> thermal_expansivity_contribution<type> [case] Constant<name> thermal_osmosis_coefficient<type> [case] Constant<name> viscosity<type> [case] Constant<name> viscosity<type> [case] Curve<name> youngs_modulus<type> [case] Constant<name> youngs_modulus<type> [case] Parameter<name> biot_coefficient<type> [case] Constant<name> bishops_effective_stress<type> [case] BishopsPowerLaw<name> bishops_effective_stress<type> [case] BishopsSaturationCutoff<name> permeability<type> [case] Constant<name> permeability<type> [case] Parameter<name> porosity<type> [case] Constant<name> relative_permeability<type> [case] Constant<name> relative_permeability<type> [case] Curve<name> relative_permeability<type> [case] RelativePermeabilityVanGenuchten<name> saturation<type> [case] Constant<name> saturation<type> [case] Curve<name> saturation<type> [case] SaturationVanGenuchten<name> thermal_conductivity<type> [case] Curve<name> thermal_conductivity<type> [case] EffectiveThermalConductivityPorosityMixing<name> thermal_conductivity<type> [case] Parameter<name> thermal_longitudinal_dispersivity<type> [case] Constant<name> thermal_transversal_dispersivity<type> [case] Constant<name> tortuosity<type> [case] ConstantNo additional info.
1.12.0