non-isothermal

Model that adds an energy equation (thermal equilibrium) to another porous medium flow model. More...

Description

The implicit non-isothermal model.

This model implements a generic energy balance for single and multi-phase transport problems. Currently the non-isothermal model can be used on top of the 1p2c, 2p, 2p2c and 3p3c models. Comparison to simple analytical solutions for pure convective and conductive problems are found in the 1p2c test. Also refer to this test for details on how to activate the non-isothermal model.

For the energy balance, local thermal equilibrium is assumed. This results in one energy conservation equation for the porous solid matrix and the fluids,

\begin{align*} \phi \frac{\partial \sum_\alpha \varrho_\alpha S_\alpha (u_\alpha - \mathbf{g}\cdot\mathbf{x})}{\partial t} & + \frac{\partial \left((\left( 1 - \phi \right) \varrho_s c_s T\right)}{\partial t} - \sum_\alpha \nabla \cdot \left\{ \varrho_\alpha (h_\alpha - \mathbf{g}\cdot\mathbf{x}) \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left( \nabla p_\alpha - \varrho_\alpha \mathbf{g} \right) \right\} \\ & - \nabla \cdot \left(\lambda_{pm} \nabla T \right) - q^h = 0, \end{align*}

where:

• \( \phi \) is the porosity of the porous medium,
• \( S_\alpha \) represents the saturation of phase \( \alpha \),
• \( \rho_\alpha \) is the mass density of phase \( \alpha \),
• \( h_\alpha \) is the specific enthalpy of phase \( \alpha \),
• \( u_\alpha \) is the specific internal energy of phase \( \alpha \),
• \( \lambda_{pm}\) is the effective heat conductivity in the porous medium,
• \( T \) is the temperature,
• \( \rho_s \) is the mass density of the solid phase,
• \( c_s \) is the heat capacity of the solid,
• \( k_{r\alpha} \) is the relative permeability of phase \( \alpha \),
• \( \mu_\alpha \) is the dynamic viscosity of phase \( \alpha \),
• \( \mathbf{K} \) is the intrinsic permeability tensor,
• \( p_\alpha \) is the pressure of phase \( \alpha \),
• \( \mathbf{g} \) is the gravitational acceleration vector,
• \( q^h \) is a source or sink term.

The gravitational potential is approximated by \(\psi \approx \mathbf{g}\cdot\mathbf{x}\) with \( \mathbf{g} = -\nabla\psi\) and where \(\mathbf{x}\) is the position in space. The approximation is exact in case the gravitation vector is constant in space. The implementation via the gravitational potential in the formulation above also assumes that the gravitional potential is independent of time. This formulation is incorrect otherwise.

Files
file	porousmediumflow/nonisothermal/indices.hh
	Defines the indices used by the non-isothermal two-phase two-component model.
file	porousmediumflow/nonisothermal/iofields.hh
	Adds I/O fields specific to non-isothermal models.
file	porousmediumflow/nonisothermal/localresidual.hh
	Element-wise calculation of the local residual for non-isothermal fully implicit models. See NIModel for the detailed description.
file	porousmediumflow/nonisothermal/model.hh
	The implicit non-isothermal model.
file	porousmediumflow/nonisothermal/volumevariables.hh
	Base class for the model specific class which provides access to all volume averaged quantities.

Classes
struct	Dumux::EnergyIndices< IsothermalIndices, numEq >
	Indices for the non-isothermal two-phase two-component model. More...
class	Dumux::EnergyIOFields< IsothermalIOFields >
	Adds I/O fields specific to non-isothermal models. More...
class	Dumux::EnergyIOFields< void >
	Adds I/O fields specific to non-isothermal models. More...
class	Dumux::EnergyLocalResidualImplementation< TypeTag, false >
	Element-wise calculation of the energy residual for isothermal problems. More...
class	Dumux::EnergyLocalResidualImplementation< TypeTag, true >
	Element-wise calculation of the energy residual for non-isothermal problems. More...
struct	Dumux::PorousMediumFlowNIModelTraits< IsothermalT, TDM >
	Specifies a number properties of non-isothermal porous medium flow models based on the specifics of a given isothermal model. More...
class	Dumux::EnergyVolumeVariablesImplementation< IsothermalTraits, Impl, false >
	The isothermal base class. More...

Typedefs
template<class IsothermalTraits , class Impl >
using	Dumux::EnergyVolumeVariables = EnergyVolumeVariablesImplementation< IsothermalTraits, Impl, IsothermalTraits::ModelTraits::enableEnergyBalance()>
	Base class for the model specific class which provides access to all volume averaged quantities. More...

Typedef Documentation

EnergyVolumeVariables

template<class IsothermalTraits , class Impl >

using Dumux::EnergyVolumeVariables = typedef EnergyVolumeVariablesImplementation<IsothermalTraits,Impl, IsothermalTraits::ModelTraits::enableEnergyBalance()>

The volume variables base class is specialized for isothermal and non-isothermal models.