Table 1.

Balance equations and boundary conditions

Balance equationsNodal variables (unknowns)Physical laws and constitutive propertiesBoundary conditions
Mass balance of liquid: liquid water and air dissolved in water (H balance)PlDarcy's lawPressures/fluxes/meteorological factors
Fick's law
Henry's law
Psychrometric law
Ideal gas law
Retention curve
Conductivity functions
Diffusion/dispersion coefficients
Mass balance of gas: water vapour and air (G balance)Pg
Internal energy balance (T balance)TFourier's lawTemperatures/fluxes
 Thermal conductivity
 Density variation with T
Momentum balance (M balance)uSoil constitutive model and corresponding parametersDisplacements/forces