Mass-Transport Boundary Conditions - Overview

By default, all model boundaries in FEFLOW are assumed to be impermeable for mass flux, i.e., no mass can flow into the model or out of the model. Exceptions are flow boundary conditions where water enters or leaves the model without the specification of a mass transport boundary condition. Their handling depends on whether the convective or divergence form of the transport equation is used. At boundaries that are not assumed as impermeable, boundary conditions have to be specifically set. Boundary conditions can be placed both at outer model borders and inside the model.

Boundary conditions are defined on a nodal basis. However, some of them (Mass-flux and Mass-transfer boundary conditions) have to be applied to more than one node to be fully functional.

The following four types of boundary conditions for mass transport are available in FEFLOW. All of them can be used as time-constant or in combination with a time series. The application of all the boundary conditions can be constrained by additional physical constraints (constraint conditions).

 

Symbol	Boundary Condition	Short Description	Examples
	Mass-concentration BC	Fixed solute concentration (1st kind/Dirichlet boundary condition)	Well-known background concentration at inflowing boundary Contaminant source leading to a known concentration in groundwater
	Mass-flux BC	Fixed mass flux across a model boundary (2nd kind/Neumann boundary condition)	Concentration of a solute in groundwater recharge
	Mass-transfer BC	Fixed reference concentration with additional transfer rate (3rd kind/Cauchy boundary condition)	Contaminant leaking from a high-concentration source
	Mass nodal sink/source BC	Fixed removal/adding of mass at a single node	Nodal sink or source of a contaminant

For defining boundary conditions, inflows are considered as negative, outflows as positive.

FEFLOW only allows one type of mass transport boundary condition to be set at a node. Inputting another type of boundary condition will erase the previously defined condition.

Mass Transport Constraints - Overview

The application of all boundary conditions in FEFLOW can be constrained by physical limits. The combination of boundary conditions and time-constant or time-varying constraint conditions allows the representation of a broad variety of specific boundary properties. Examples in contaminant transport include sea water boundaries and rate-limited fixed concentration boundaries.

Most constraint conditions are complimentary constraints, i.e. boundary conditions of a concentration type (fixed concentration, transfer) can be constrained by a minimum and maximum mass flux, boundary conditions of a mass flux type (mass flux, well) can be constrained by a minimum and maximum concentration.

For all mass transport boundary conditions, an additional head constraint is available.

 

For defining constraint conditions, inflows are considered as positive, outflows as negative. Thus a constraint conditions of maximum mass flux = 0 g/d means that no inflow of mass is allowed at the corresponding boundary condition.