Interface

The Interface statistics provide time-dependent data associated with the fluid–fluid interface in simulations involving a free surface or two-fluid configuration. The name of this file is Interface.txt. The data is written as a time series, with each row corresponding to a simulation time. The output file is updated at the Statistics Output Write Interval.

The reported quantities include spatial statistics (minimum, mean, and maximum) of velocity, strain rate, energy dissipation rate (EDR), and custom variables, as well as the total interfacial area. Velocity quantities are reported both in the stationary frame (Velocity) and in a frame accounting for domain motion (Absolute Velocity).

The reported quantities fall into several categories:

• Geometric Metrics: Surface area describes the total interface area.

• Kinematic Metrics: Velocity (relative) and absolute velocity (accounting for domain motion) describe the motion of the fluid at the interface.

• Turbulence and Dissipation Metrics: Energy dissipation rate characterizes turbulence intensity at the interface.

• Deformation Metrics: Strain rate describes the local rate of deformation along the interface.

• Scalar and Custom Variable Metrics: Custom variables provide additional user-defined or model-linked quantities evaluated on the interface.

• Extrema and Statistical Metrics: Maximum, mean, and minimum values describe the range and distribution of quantities over the interface surface.

Statistics Table

The index table below shows the statistics that can appear in the Interface output file. Within this table, each statistic corresponds to a column in the output table that evolves with the time column.

Statistics	Units	Details	When Appears
Time	s	simulation time
Absolute Velocity Max	m/s	spatial max of fluid velocity magnitude accounting for domain movement
Absolute Velocity Mean	m/s	spatial mean of fluid velocity magnitude accounting for domain movement
Absolute Velocity Min	m/s	spatial min of fluid velocity magnitude accounting for domain movement
Area	m^2	total surface area
Custom Variable Max	[dynamic]	spatial max of custom variable value
Custom Variable Mean	[dynamic]	spatial mean of custom variable value
Custom Variable Min	[dynamic]	spatial min of custom variable value
EDR Max	W/kg	spatial max of energy dissipation rate including both resolved and unresolved components
EDR Mean	W/kg	spatial mean of energy dissipation rate including both resolved and unresolved components
EDR Min	W/kg	spatial min of energy dissipation rate including both resolved and unresolved components
Strain Rate Max	1/s	spatial max of strain rate magnitude
Strain Rate Mean	1/s	spatial mean of strain rate magnitude
Strain Rate Min	1/s	spatial min of strain rate magnitude
Velocity Max	m/s	spatial max of fluid velocity magnitude
Velocity Mean	m/s	spatial mean of fluid velocity magnitude
Velocity Min	m/s	spatial min of fluid velocity magnitude

Usage and Applications

Interface statistics are computed as spatial reductions over the interface surface, providing minimum, mean, and maximum values of key flow quantities. These are derived from the underlying field variables sampled on the interface, analogous to plane and probe outputs where quantities are evaluated over a defined manifold.

The mean value of any scalar quantity \(ϕ\) (e.g., velocity magnitude, strain rate, EDR, or a custom variable) over the interface is given by the area-average

\[\langle \phi \rangle = \frac{1}{A} \int_A \phi(\mathbf{x}, t) \, dA,\]

where \(A\) is the total interface area and \(ϕ(x,t)\) is the local field value at the interface.

The minimum and maximum values are defined as

\[\phi_{\min} = \min_{\mathbf{x} \in A} \phi(\mathbf{x}, t), \quad \phi_{\max} = \max_{\mathbf{x} \in A} \phi(\mathbf{x}, t).\]

The reported interface area is

\[A = \int_A dA.\]

The velocity statistics are based on the local fluid velocity magnitude

\[|\mathbf{u}| = \sqrt{u_x^2 + u_y^2 + u_z^2}.\]

The absolute velocity accounts for domain motion,

\[\mathbf{u}_{\text{abs}} = \mathbf{u} + \mathbf{u}_{\text{domain}}\]

and

\[|\mathbf{u}_{\text{abs}}| = \|\mathbf{u} + \mathbf{u}_{\text{domain}}.\|\]

This distinction is important in rotating or accelerating systems where relative and absolute motion differ.

The local strain rate is computed from the resolved strain-rate tensor

\[S_{ij} = \frac{1}{2} \left( \frac{\partial v_i}{\partial x_j} + \frac{\partial v_j}{\partial x_i} \right),\]

where \(v_i\) is the \(i\)-th component of the fluid velocity. This tensor represents the symmetric part of the velocity gradient and captures local fluid deformation.

The scalar strain rate magnitude is

\[\dot{\gamma} = \sqrt{S_{ij} S_{ij}},\]

which corresponds to the Frobenius norm of the strain-rate tensor.

The local energy dissipation rate (EDR) quantifies the rate at which kinetic energy is converted into thermal energy by viscous stresses

\[\varepsilon = 2 \, \nu \, S_{ij} S_{ij},\]

where \(ν\) is the kinematic viscosity.

In the interface statistics, the reported values (min, mean, max) for velocity, strain rate, EDR, and custom variables are spatial reductions of these quantities evaluated over the interface surface.