Inlet-Outlet - Boundary Condition

Inlet-Outlet - Boundary Condition   Description

Inlet-Outlet is an example of a mixed boundary condition that switches between Zero Gradient when the fluid flows out of the domain, and Fixed Value, when the fluid is flowing into the domain.

This boundary condition permits fluid to either enter or exit the domain, depending on local flow conditions. It is particularly useful in situations where the flow direction at the boundary may change, such as with recirculating flows or in cases of bidirectional flow.

The Inlet-Outlet condition is commonly applied to scalar fields (except \(p\)) at boundaries considered to be outlets. It can also be used with a vector field, such as velocity to prevent reverse flow. This helps to prevent numerical instability caused by unexpected inflow.

This boundary condition can also be used for scalar fields (temperature, concentration) in conjugation with a pressure inlet when the flow direction is not known in advance.

Inlet-Outlet - Boundary Condition   Understanding Inlet-Outlet

Inlet-Outlet - Graphical Representation

Red velocity profile illustrates outlet conditions where a part of the flow exits the domain while another part experiences inflow. When the Inlet-Outlet is applied (green curve), the velocity profile changes. The segment of the profile where inflow occurs is switched to Fixed Value = 0 to ensure stability and no reverse flow.

The Inlet-Outlet calculates the flux at each boundary face and determines whether it should function as an inlet or an outlet based on the local flow direction. It then adjusts the flow properties accordingly by switching between Zero Gradient and Fixed Value.

Inlet-Outlet Boundary Condition
Figure 1. Inlet-Outlet Boundary Condition

Inlet-Outlet Governing Equations

The Inlet-Outlet belongs to the class of mixed boundary conditions - a combination of two boundary conditions: Fixed Value and Fixed Gradient. The general form of the mixed boundary condition can be described as:

\[\phi_f = w \cdot \phi_{ref} + (1-w) \cdot (\phi_P + g_{ref}|d|)\]
  • \(\phi_f\) is the face value enforced by the boundary condition
  • \(w\) is the weight factor that determines the blend between Fixed Value and Fixed Gradient
  • \(\phi_{ref}\) is a user-specified reference value
  • \(\phi_P\) is the cell value at the cell center
  • \(g_{ref}\) is the user-specified gradient at the boundary
  • \(d\) is the distance between the cell centroid and the boundary cell face (see: Figure 2)

The Inlet-Outlet can be expressed as a special case of the mixed boundary condition. In this case, the weight factor operates between two values:
- 0 when the flow is out of the domain
- 1 when the flow is into the domain.

Also, the reference gradient value is constrained to always be zero: \(g_{ref} = 0\)

In the case of Inlet-Outlet, the mixed boundary condition simplifies to:

\[\phi_f = w \cdot \phi_b + (1-w) \cdot \phi_P\]

For the outflow, \(w=0\), the face value will reduce to: \(\phi_f = \phi_P\)
and Inlet-Outlet works as exactly as Zero Gradient.

For the inlet, \(w=1\), the face value is expressed as: \(\phi_f = \phi_b\)
The face value \(\phi_f\) will be equal to the specified value as in Fixed Value.

In other words, we can say the Inlet-Outlet boundary condition "advects" cell center value to the boundary when the fluid exits the domain, or it "advects" a specified reference value from the outside world when the flow is reversed.

How Does Inlet-Outlet Boundary Condition Work?
Figure 2. How Does Inlet-Outlet Boundary Condition Work?

When setting the outlet boundary condition for the velocity field, it is common practice to use the Inlet-Outlet condition with a fixed value of zero velocity. This approach helps to prevent reverse flows.

Inlet-Outlet - Boundary Condition   Application & Physical Interpretation

The Inlet-Outlet is designed to efficiently handle flow at boundaries where the direction of flow can potentially reverse, making it particularly suitable for domains where inflow and outflow conditions are not strictly predefined. This boundary condition is adaptive, meaning it changes its behavior based on the local flow conditions at the boundary. Below are a few examples demonstrating how this boundary condition can be used and how to correctly interpret its meaning.

Inlet-Outlet in Aerodynamics applications

Example applications: car, aircraft aerodynamics, wind tunnel experiment

This problem can be solved by using simpleFoam (solver). The velocity boundary condition at the outlet can be defined as Inlet-Outlet. This is critical because, in the wake of the motorbike (or any other object), flow regions might experience reverse flow due to vortices or turbulent eddies.

Example Boundary Conditions set for Aerodynamics applications



Fixed Flux Pressure

Example usage of Inlet-Outlet for Aerodynamics applications in SimFlow

Dam Break

Simulation of free surface flow with a Volume of Fluid approach, analyzing the multiphase immiscible flow of water and air through a dam.

Inlet-Outlet in VoF (Volume of Fluid) applications

Example applications: free surface flows, ship hull calculations, sloshing, ship hydrodynamics, wave impact on structures

For flows with distinctive interphase between two fluids, like water and air (Volume of Fluid method used in interFoam (solver)) Inlet-Outlet for a volume fraction \(\alpha\) can be applied for so-called atmospheric boundaries of the domain, above the free surface. It will allow in this situation, air entrainment into the domain.

Example Boundary Conditions set for VoF applications
PhysicsVelocityPressurePhases \(\alpha\)

Pressure Outlet

Pressure Inlet-Outlet Velocity

Fixed Value


Inlet-Outlet in Heat Transfer applications

Example applications: room ventilation, room heating, electronic cooling, atmospheric flows

Buoyancy-driven flows with heat exchange can be simulated in the buoyantPimpleFoam (solver). The Inlet-Outlet for temperature T can be applied to the outlet out of the domain - to specify the fluid temperature in case of the backflows/reverse. It can also be used for temperature at the inlet when pressure condition is used, and we expect that the flow direction can change.

Example Boundary Conditions set for Heat Transfer applications
PhysicsPressureVelocityThermal - T

Pressure Outlet

Fixed Value

Pressure Inlet-Outlet Velocity


Inlet-Outlet in Species Transport applications

Example applications: industrial furnaces, jet engines, chemical process industry (chemically reacting foams)

The reactingParcelFoam (solver) can be applied for chemically reacting flows that involve heat transfer and multiphase particles modeling. In this application, the Inlet-Outlet defines, for example, the gas composition at the outlet in case of reverse flow.

Example Boundary Conditions set for Species Transport applications

Pressure Outlet

Fixed Value

Pressure Inlet-Outlet Velocity


Example usage of Inlet-Outlet for Species Transport applications in SimFlow

Gas & Pollutant Dispersion

Simulation of carbon dioxide and ash particles released from a chimney into the atmosphere and investigating their dispersion in flowing air using species transport and Lagrangian particle simulation.

Inlet-Outlet - Boundary Condition   How to apply Inlet-Outlet in SimFlow

The definition of boundary conditions in SimFlow is both simple and intuitive. To specify the Inlet-Outlet boundary condition, the user must navigate to the Boundary Conditions panel, select the appropriate boundary, and choose the correct option from the drop-down menu.

Inlet Value needs to be specified by the user. This value is used when the boundary works as an inlet - when reverse flow appears.

Inlet-Outlet definition in SimFlow
Figure 3. Inlet-Outlet definition in SimFlow

Inlet-Outlet - Boundary Condition   Inlet-Outlet - Alternatives

In this section, we propose boundary conditions that are alternative to Inlet-Outlet. While they may fulfill similar purposes, they might be better suited for a specific application and provide a better approximation of physical world conditions.

Inlet-Outlet - Alternatives
Boundary ConditionDescription

Zero Gradient

belongs to the Neumann boundary conditions, sets the normal gradient of any variable to zero

Pressure Inlet-Outlet Velocity

allows velocity to adjust at the outlet to satisfy mass balance in the fluid domain.


works contrary to Inlet-Outlet, applies a fixed value when the flow is directed out of the domain and a zero-gradient condition when the flow is directed into the domain