From 77017cc5afe1c5d157749484e9c416822c030f38 Mon Sep 17 00:00:00 2001
From: "robbberto88@gmail.com" <robbberto88@gmail.com>
Date: Fri, 1 Jul 2022 15:16:14 -0400
Subject: [PATCH] add more information to the monitors inputs
---
docs/source/inputs/InputsMonitors.rst | 364 ++++++++++++++++++++++++--
1 file changed, 335 insertions(+), 29 deletions(-)
diff --git a/docs/source/inputs/InputsMonitors.rst b/docs/source/inputs/InputsMonitors.rst
index 04428ac..1370278 100644
--- a/docs/source/inputs/InputsMonitors.rst
+++ b/docs/source/inputs/InputsMonitors.rst
@@ -1,11 +1,11 @@
.. _Chap:InputsMonitors:
-Monitors
-========
+Spatial averages
+================
The following inputs must be preceded by "amr" and control whether to compute
-monitors, i.e., spatial averages, and how often to output the results.
-n is the number of monitors implicitly defined by the size of avg_region_x_w.
+spatial averages, and how often to output the results. n is the number of
+spatial averages implicitly defined by the size of avg_region_x_w.
+------------------+-----------------------------------------------------------------------+-------------+-----------+
| | Description | Type | Default |
@@ -43,11 +43,31 @@ n is the number of monitors implicitly defined by the size of avg_region_x_w.
| avg_region_z_t | Upper bound of averaging region in z-direction | n*Real | None |
+------------------+-----------------------------------------------------------------------+-------------+-----------+
+
+
+Monitors
+========
+
A Monitor is a tool for capturing data from the solver about the model.
Data (such as volume fraction, pressure, velocity, etc.) for a given
-:ref:`monitor_region` is written to a :ref:`CSV file <monitor_filename>`
-while the solver is running.
+monitor region is written to a CSV file while the solver is running.
+To define monitors, the following inputs must be preceded by "amr." prefix.
+
++--------------------+------------------------------------------------------+-------------+-----------+
+| | Description | Type | Default |
++====================+======================================================+=============+===========+
+| monitors | Names of the monitors to be computed | String | None |
++--------------------+------------------------------------------------------+-------------+-----------+
+| monitors.[monitor] | Monitor type | String | None |
++--------------------+------------------------------------------------------+-------------+-----------+
+
+.. code-block:: none
+
+ amr.monitors = my_monitor0 my_monitor1
+
+ amr.monitors.my_monitor0 = Eulerian::VolumeIntegral::MassWeightedIntegral
+ amr.monitors.my_monitor1 = Lagrangian::Average::VolumeWeightedAverage
Region Selection
@@ -55,45 +75,70 @@ Region Selection
To define a monitor, there must be a region already defined in the regions
inputs. A Monitor region is a single point, plane, or volume. Multiple regions
-cannot be combined for a monitor.
+cannot be combined for a monitor. The following inputs must be preceded by the
+"amr.monitors." prefix.
+------------------+-----------------------------------------------------------------------+-------------+-----------+
| | Description | Type | Default |
+==================+=======================================================================+=============+===========+
-| region | Define the region in which the monitor will be computed | String | None |
-+------------------+-----------------------------------------------------------------------+-------------+-----------+
-| plane | For LagrangianMonitors::FlowRate, defines the plane through which | String | None |
-| | the flow rate of the particles in the [region] will be computed | | |
+| [monitor].region | Define the region in which the monitor will be computed | String | None |
+------------------+-----------------------------------------------------------------------+-------------+-----------+
+.. code-block:: none
+
+ # regionA and regionB to be defined in the "regions" inputs section
+ amr.monitors.my_monitor0.region = regionA
+ amr.monitors.my_monitor1.region = regionB
+
Monitor Output
--------------
-The monitor data will be output to the Filename base with the extension
-``.csv``. The monitor output file is in Comma Separated Value (CSV) format. The
-first line of the file provides header information.
+The monitor data will be output to a file with name given by the input
+"plot_file", and the extension ``.csv`` is automatically added. The monitor
+output file is in Comma Separated Value (CSV) format. The first line of the file
+provides header information. The following inputs must be preceded by the
+"amr.monitors." prefix.
-+------------------+-----------------------------------------------------------------------+-------------+-----------+
-| | Description | Type | Default |
-+==================+=======================================================================+=============+===========+
-| plot_file | Define the name of the plotfile where monitor output will be saved | String | None |
-+------------------+-----------------------------------------------------------------------+-------------+-----------+
-| plot_int | Define the timestep frequency for saving monitored data to file | Int | -1 |
-+------------------+-----------------------------------------------------------------------+-------------+-----------+
-| plot_per_approx | Define the approximated simulation time at which saving monitored | Real | 0 |
-| | data | | |
-+------------------+-----------------------------------------------------------------------+-------------+-----------+
++----------------------------+-------------------------------------------------------------+-------------+-----------+
+| | Description | Type | Default |
++============================+=============================================================+=============+===========+
+| [monitor].plot_file | Define the name of the plotfile where monitor output will | String | None |
+| | be saved | | |
++----------------------------+-------------------------------------------------------------+-------------+-----------+
+| [monitor].plot_int | Define the timestep frequency for saving monitored data to | Int | -1 |
+| | file | | |
++----------------------------+-------------------------------------------------------------+-------------+-----------+
+| [monitor].plot_per_approx | Define the approximated simulation time at which saving | Real | 0 |
+| | monitored data | | |
++----------------------------+-------------------------------------------------------------+-------------+-----------+
+
+.. code-block:: none
+
+ amr.monitors.my_monitor0.plot_file = monitor0_output
+ amr.monitors.my_monitor0.plot_int = 10
+
+ amr.monitors.my_monitor1.plot_file = monitor1_output
+ amr.monitors.my_monitor1.plot_per_approx = 0.01
Monitor Variables
-----------------
-+------------------+-----------------------------------------------------------------------+-------------+-----------+
-| | Description | Type | Default |
-+==================+=======================================================================+=============+===========+
-| variables | Define which variables are to be monitored by this monitor | String | None |
-+------------------+-----------------------------------------------------------------------+-------------+-----------+
+The variables to be monitored can be specified in the inputs by including the
+following input preceded by the "amr.monitors." prefix.
+
++---------------------+--------------------------------------------------------------------+-------------+-----------+
+| | Description | Type | Default |
++=====================+====================================================================+=============+===========+
+| [monitor].variables | Define which variables are to be monitored by this monitor | String | None |
++---------------------+--------------------------------------------------------------------+-------------+-----------+
+
+.. code-block:: none
+
+ amr.monitors.my_monitor0.variables = T_g vel_g p_g gp_y X_gk
+
+ amr.monitors.my_monitor1.variables = density drag_y T_s txfr_vel_x
Eulerian Monitors
@@ -119,6 +164,72 @@ Symbol Description
:math:`V_{ijk}` Volume of indexed cell
========================= =========================================
+The following table lists all the fluid phase variables that can be monitored:
+
++--------------------------+-----------------------------------------------------------------------------------------+
+| | Description |
++==========================+=========================================================================================+
+| ep_g | fluid volume fraction |
++--------------------------+-----------------------------------------------------------------------------------------+
+| p_g | fluid pressure |
++--------------------------+-----------------------------------------------------------------------------------------+
+| ro_g | fluid density |
++--------------------------+-----------------------------------------------------------------------------------------+
+| trac | tracer |
++--------------------------+-----------------------------------------------------------------------------------------+
+| vel_g | fluid velocity |
+| | (all the three components of the velocity) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| vel_g_[x/y/z] | x, y, or z component of the fluid velocity |
++--------------------------+-----------------------------------------------------------------------------------------+
+| gp | fluid pressure gradient |
+| | (all the three components of the gradient) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| gp_[x/y/z] | x, y, or z component of the fluid pressure gradient |
++--------------------------+-----------------------------------------------------------------------------------------+
+| T_g | fluid temperature |
++--------------------------+-----------------------------------------------------------------------------------------+
+| h_g | fluid enthalpy |
++--------------------------+-----------------------------------------------------------------------------------------+
+| X_gk | fluid species mass fractions (monitor all the fluid species) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| X_gk_[species] | fluid "species" mass fraction (only species "species" is monitored) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| vort | fluid vorticity |
+| | (all the three components of the vorticity) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| vort[x/y/z] | x, y, or z component of the fluid vorticity |
++--------------------------+-----------------------------------------------------------------------------------------+
+| txfr_velocity | interphase velocity transferred to the fluid |
+| | (all the three components of the velocity) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| txfr_vel_[x/y/z] | x, y, or z component of the interphase velocity transferred to the fluid |
++--------------------------+-----------------------------------------------------------------------------------------+
+| txfr_beta | drag coefficient |
++--------------------------+-----------------------------------------------------------------------------------------+
+| txfr_gammaTp | convection coefficient multiplied by the solids temperature |
++--------------------------+-----------------------------------------------------------------------------------------+
+| txfr_gamma | convection coefficient |
++--------------------------+-----------------------------------------------------------------------------------------+
+| chem_txfr_X_gk | rate of mass transferred to the fluid phase due to heterogeneous chemical reactions |
+| | (monitor all the fluid species) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| chem_txfr_X_gk_[species] | fluid "species" rate of mass transferred due to heterogeneous chemical reactions |
+| | (only species "species" is monitored) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| chem_txfr_velocity | rate of velocity transferred to the fluid phase due to heterogeneous chemical reactions |
+| | (all the three components of the velocity) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| chem_txfr_vel_[x/y/z] | x, y, or z component of the rate of velocity transferred due to heterogeneous reactions |
++--------------------------+-----------------------------------------------------------------------------------------+
+| chem_txfr_h | rate of enthalpy transferred to the fluid phase due to heterogeneous chemical reactions |
++--------------------------+-----------------------------------------------------------------------------------------+
+| divtau | divergence of the viscous stress tensor |
+| | (all the three components) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| divtau_[x/y/z] | x, y, or z component of the divergence of the viscous stress tensor |
++--------------------------+-----------------------------------------------------------------------------------------+
+
Point Region
~~~~~~~~~~~~
@@ -127,6 +238,10 @@ For a point region, the monitor data value is simply the value of the variable
at that point:
Value
+ ============================
+ Eulerian::PointRegion::Value
+ ============================
+
Returns the value of the field quantity in the selected region.
.. math:: \phi_{ijk}
@@ -138,28 +253,58 @@ Area or Volume Region
The following monitor types are valid for area and volume regions:
Sum
+ ===========================
+ Eulerian::AreaRegion::Sum
+ ---------------------------
+ Eulerian::VolumeRegion::Sum
+ ===========================
+
The sum is computed by summing all values of the field quantity in the
selected region.
.. math:: \sum_{ijk}\phi_{ijk}
Min
+ ===========================
+ Eulerian::AreaRegion::Min
+ ---------------------------
+ Eulerian::VolumeRegion::Min
+ ===========================
+
Minimum value of the field quantity in the selected region.
.. math:: \min_{ijk} \phi_{ijk}
Max
+ ===========================
+ Eulerian::AreaRegion::Max
+ ---------------------------
+ Eulerian::VolumeRegion::Max
+ ===========================
+
Maximum value of the field quantity in the selected region.
.. math:: \max_{ijk} \phi_{ijk}
Average
+ ===============================
+ Eulerian::AreaRegion::Average
+ -------------------------------
+ Eulerian::VolumeRegion::Average
+ ===============================
+
Average value of the field quantity in the selected region where :math:`N` is
the total number of observations (cells) in the selected region.
.. math:: \phi_0 = \frac{\sum_{ijk} \phi_{ijk}}{N}
Standard Deviation
+ =========================================
+ Eulerian::AreaRegion::StandardDeviation
+ -----------------------------------------
+ Eulerian::VolumeRegion::StandardDeviation
+ =========================================
+
The standard deviation of the field quantity in the selected region where
:math:`\phi_0` is the average of the variable in the selected region.
@@ -172,12 +317,20 @@ Surface Integrals
The following types are only valid for area regions:
Area
+ ===============================
+ Eulerian::SurfaceIntegral::Area
+ ===============================
+
Area of selected region is computed by summing the areas of the facets that
define the surface.
.. math:: \int dA = \sum_{ijk} \lvert A_{ijk} \rvert
Area-Weighted Average
+ ==============================================
+ Eulerian::SurfaceIntegral::AreaWeightedAverage
+ ==============================================
+
The area-weighted average is computed by dividing the summation of the
product of the selected variable and facet area by the total area of the
region.
@@ -185,6 +338,10 @@ Area-Weighted Average
.. math:: \frac{\int\phi dA}{A} = \frac{\sum_{ijk}{\phi_{ijk} \lvert A_{ijk} \rvert}}{\sum_{ijk}{\lvert A_{ijk} \rvert}}
Flow Rate
+ ===================================
+ Eulerian::SurfaceIntegral::FlowRate
+ ===================================
+
The flow rate of a field variable through a surface is computed by summing
the product of the phase volume fraction, density, the selected field
variable, phase velocity normal to the facet :math:`v_n`, and the facet area.
@@ -192,6 +349,10 @@ Flow Rate
.. math:: \int\varepsilon\rho\phi{v_n}dA = \sum_{ijk}\varepsilon_{ijk}\rho_{ijk}\phi_{ijk} {v}_{n,ijk} \lvert A_{ijk} \rvert
Mass Flow Rate
+ =======================================
+ Eulerian::SurfaceIntegral::MassFlowRate
+ =======================================
+
The mass flow rate through a surface is computed by summing the product of
the phase volume fraction, density, phase velocity normal to the facet
:math:`v_n`, and the facet area.
@@ -199,6 +360,10 @@ Mass Flow Rate
.. math:: \int\varepsilon\rho{v_n} dA = \sum_{ijk}\varepsilon_{ijk}\rho_{ijk}{v}_{n,ijk} \lvert A_{ijk} \rvert
Mass-Weighted Average
+ ==============================================
+ Eulerian::SurfaceIntegral::MassWeightedAverage
+ ==============================================
+
The mass flow rate through a surface is computed by summing the product of
the phase volume fraction, density, phase velocity normal to the facet, and
the facet area.
@@ -206,6 +371,10 @@ Mass-Weighted Average
.. math:: \frac{\int\varepsilon\rho\phi{v_n}dA}{\int\varepsilon\rho{v_n}dA} = \frac{\sum_{ijk}\varepsilon_{ijk}\rho_{ijk}\phi_{ijk} {v}_{n,ijk} \lvert A_{ijk} \rvert}{\sum_{ijk}\varepsilon_{ijk}\rho_{ijk} {v}_{n,ijk} \lvert A_{ijk} \rvert}
Volume Flow Rate
+ =========================================
+ Eulerian::SurfaceIntegral::VolumeFlowRate
+ =========================================
+
The volume flow rate through a surface is computed by summing the product of
the phase volume fraction, phase velocity normal to the facet :math:`v_n`,
and the facet area.
@@ -219,18 +388,30 @@ Volume Integrals
The following types are only valid for volume regions:
Volume
+ ================================
+ Eulerian::VolumeIntegral::Volume
+ ================================
+
The volume is computed by summing all of the cell volumes in the selected
region.
.. math:: \int dV = \sum_{ijk}{ \lvert V_{ijk}} \rvert
Volume Integral
+ ========================================
+ Eulerian::VolumeIntegral::VolumeIntegral
+ ========================================
+
The volume integral is computed by summing the product of the selected field
variable and the cell volume.
.. math:: \int \phi dV = \sum_{ijk}{\phi_{ijk} \lvert V_{ijk}} \rvert
Volume-Weighted Average
+ ===============================================
+ Eulerian::VolumeIntegral::VolumeWeightedAverage
+ ===============================================
+
The volume-weighted average is computed by dividing the summation of the
product of the selected field variable and cell volume by the sum of the cell
volumes.
@@ -238,12 +419,20 @@ Volume-Weighted Average
.. math:: \frac{\int\phi dV}{V} = \frac{\sum_{ijk}{\phi_{ijk} \lvert V_{ijk} \rvert}}{\sum_{ijk}{\lvert V_{ijk} \rvert}}
Mass-Weighted Integral
+ ==============================================
+ Eulerian::VolumeIntegral::MassWeightedIntegral
+ ==============================================
+
The mass-weighted integral is computed by summing the product of phase volume
fraction, density, selected field variable, and cell volume.
.. math:: \int \varepsilon\rho\phi dV = \sum_{ijk}\varepsilon_{ijk}\rho_{ijk}\phi_{ijk} \lvert V_{ijk}\rvert
Mass-Weighted Average
+ =============================================
+ Eulerian::VolumeIntegral::MassWeightedAverage
+ =============================================
+
The mass-weighted average is computed by dividing the sum of the product of
phase volume fraction, density, selected field variable, and cell volume by
the summation of the product of the phase volume fraction, density, and cell
@@ -256,6 +445,16 @@ Mass-Weighted Average
Lagrangian Monitors
-------------------
++------------------+-----------------------------------------------------------------------+-------------+-----------+
+| | Description | Type | Default |
++==================+=======================================================================+=============+===========+
+| region | Define the region in which the monitor will be computed | String | None |
++------------------+-----------------------------------------------------------------------+-------------+-----------+
+| plane | For LagrangianMonitors::FlowRate, defines the plane through which | String | None |
+| | the flow rate of the particles in the [region] will be computed | | |
++------------------+-----------------------------------------------------------------------+-------------+-----------+
+
+
There are different types of monitors available. A monitor type applies an
operator (for example a sum, an area integral or a volume integral) to the
variable. The dimensionality of the region determines which operators can be
@@ -277,6 +476,73 @@ Symbol Description
.. [#] *The statistical weight is one for DEM simulations.*
+The following table lists all the solids phase variables that can be monitored:
+
++--------------------------+-----------------------------------------------------------------------------------------+
+| | Description |
++==========================+=========================================================================================+
+| position | particles position (all the three components) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| pos_[x/y/z] | x, y, or z component of the particles position |
++--------------------------+-----------------------------------------------------------------------------------------+
+| id | particles id |
++--------------------------+-----------------------------------------------------------------------------------------+
+| cpu | particles cpu |
++--------------------------+-----------------------------------------------------------------------------------------+
+| radius | particles radius |
++--------------------------+-----------------------------------------------------------------------------------------+
+| volume | particles volume |
++--------------------------+-----------------------------------------------------------------------------------------+
+| mass | particles mass |
++--------------------------+-----------------------------------------------------------------------------------------+
+| density | particles density |
++--------------------------+-----------------------------------------------------------------------------------------+
+| oneOverI | particles inverse of momentum of inertia |
++--------------------------+-----------------------------------------------------------------------------------------+
+| velocity | particles velocity (all the three components) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| vel_[x/y/z] | x, y, or z component of the particles velocity |
++--------------------------+-----------------------------------------------------------------------------------------+
+| omega | particles angular velocity (all the three components) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| omega_[x/y/z] | x, y, or z component of the particles angular velocity |
++--------------------------+-----------------------------------------------------------------------------------------+
+| statwt | particles statistical weight |
++--------------------------+-----------------------------------------------------------------------------------------+
+| dragcoeff | particles drag coefficient |
++--------------------------+-----------------------------------------------------------------------------------------+
+| drag | particles drag (all the three components) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| drag_[x/y/z] | x, y, or z component of the particles drag |
++--------------------------+-----------------------------------------------------------------------------------------+
+| cp_s | particles specific heat coefficient |
++--------------------------+-----------------------------------------------------------------------------------------+
+| T_s | particles temperature |
++--------------------------+-----------------------------------------------------------------------------------------+
+| convection | particles convective heat transfer |
++--------------------------+-----------------------------------------------------------------------------------------+
+| phase | particles phase |
++--------------------------+-----------------------------------------------------------------------------------------+
+| state | particles state |
++--------------------------+-----------------------------------------------------------------------------------------+
+| X_sn | particles species mass fractions (for all the solids species) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| X_sn_[species] | solids "species" mass fraction (only species "species" is monitored) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| txfr_velocity | rate of velocity transferred to the fluid phase due to heterogeneous chemical reactions |
+| | (all the three components) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| txfr_vel_[x/y/z] | x, y, or z components of the transferred velocity due to heterogeneous reactions |
++--------------------------+-----------------------------------------------------------------------------------------+
+| txfr_h | rate of enthalpy transferred due to heterogeneous chemical reactions |
++--------------------------+-----------------------------------------------------------------------------------------+
+| txfr_X_sn | rate of mass transferred due to heterogeneous chemical reactions (for all the species) |
++--------------------------+-----------------------------------------------------------------------------------------+
+| txfr_X_sn_[species] | solids "species" rate of transfer due to heterogeneous reactions (only species |
+| | "species" is monitored) |
++--------------------------+-----------------------------------------------------------------------------------------+
+
+
General particle properties
~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -286,18 +552,30 @@ plane are used in evaluating the average.
Sum
+ ================================
+ Lagrangian::GeneralProperty::Sum
+ ================================
+
The sum of particle property, :math:`\phi_p` in the selected region is
calculated using the following expression.
.. math:: \sum_p w_p \phi_p
Min
+ ================================
+ Lagrangian::GeneralProperty::Min
+ ================================
+
The minimum value of particle property :math:`phi_p` is the selected region
is obtained using the following expression.
.. math:: \min_p \phi_p
Max
+ ================================
+ Lagrangian::GeneralProperty::Max
+ ================================
+
The maximum value of particle property :math:`phi_p` is the selected region
is obtained using the following expression.
@@ -313,6 +591,10 @@ in evaluating the average.
Average
+ =====================================
+ Lagrangian::AveragedProperty::Average
+ =====================================
+
The average value of particle property, :math:`\phi_p` in the selected region
is calculated using the following expression. For DEM simulations, the
statistical weight of a particle, :math:`w_p`, is one such that the sum of
@@ -321,6 +603,10 @@ Average
.. math:: \bar{\phi} = \frac{\sum_p w_p \phi_p}{\sum_p w_p}
Standard Deviation
+ ===============================================
+ Lagrangian::AveragedProperty::StandardDeviation
+ ===============================================
+
The standard deviation of particle property, :math:`phi_p` in the selected
region is calculated using the following expression. :math:`\bar{\phi}` is
the averaged variable in the selected region.
@@ -328,12 +614,20 @@ Standard Deviation
.. math:: \sigma_{\phi} = \sqrt{\frac{ \sum_p w_p (\phi_p-\bar{\phi})^2 }{\sum_p w_p}}
Mass-weighted average
+ =================================================
+ Lagrangian::AveragedProperty::MassWeightedAverage
+ =================================================
+
Mass-weighted average value of particle property, :math:`\phi_p` in the
selected region is calculated using the following expression.
.. math:: \bar{\phi}_m = \frac{\sum_{p} w_p m_p \phi_p}{\sum_p w_p m_p }
Volume-weighted average
+ ===================================================
+ Lagrangian::AveragedProperty::VolumeWeightedAverage
+ ===================================================
+
Volume-weighted average value of particle property, :math:`\phi_p` in the
selected region is calculated using the following expression.
@@ -357,6 +651,10 @@ and
Flow rate
+ ==============================
+ Lagrangian::FlowRate::FlowRate
+ ==============================
+
The net flow rate of a general particle property :math:`\phi_p` is computed
by summing the properties of the set of particles projected to have crossed
the flow plane, :math:`\Gamma`.
@@ -364,6 +662,10 @@ Flow rate
.. math:: \sum_{p \in \Gamma} w_p \phi_p \frac{v_p}{\left| v_p \right|}
Mass-weighted flow rate
+ ==========================================
+ Lagrangian::FlowRate::MassWeightedFlowRate
+ ==========================================
+
The net mass-weighted flow rate is the sum of the general particle property
:math:`\phi_p` multiplied by the particle mass, :math:`m_p` of the set of
particles projected to have crossed the flow plane, :math:`\Gamma`.
@@ -371,6 +673,10 @@ Mass-weighted flow rate
.. math:: \sum_{p \in \Gamma} w_p m_p \phi_p \frac{v_p}{\left| v_p \right|}
Volume-weighted flow rate
+ ============================================
+ Lagrangian::FlowRate::VolumeWeightedFlowRate
+ ============================================
+
The net volume-weighted flow rate is the sum of the general particle property
:math:`\phi_p` multiplied by the particle volume, :math:`V_p` of the set of
particles projected to have crossed the flow plane, :math:`\Gamma`.
--
GitLab