diff --git a/docs/source_docs/user_guide/inputs/output/monitors.rst b/docs/source_docs/user_guide/inputs/output/monitors.rst index 5ff9dd7519d6f6f8173ce7804b1a7b59267ff9d3..10181c93520809e669574dd718b645c1dc253026 100644 --- a/docs/source_docs/user_guide/inputs/output/monitors.rst +++ b/docs/source_docs/user_guide/inputs/output/monitors.rst @@ -406,16 +406,37 @@ Volume Integral .. math:: \int \phi dV = \sum_{ijk}{\phi_{ijk} \lvert V_{ijk}} \rvert +Volume-Weighted Integral + +--------------------------------------------------+ + | Eulerian::VolumeIntegral::VolumeWeightedIntegral | + +--------------------------------------------------+ + + The volume-weighted integral is computed by summing the product of the + selected field variable, phase volume fraction and cell volume. + + .. math:: \int\varepsilon \phi dV = \sum_{ijk}{\phi_{ijk} \varepsilon_{ijk} \lvert V_{ijk}} \rvert + +Volume Average + +-----------------------------------------+ + | Eulerian::VolumeIntegral::VolumeAverage | + +-----------------------------------------+ + + 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. + + .. math:: \frac{\int\phi dV}{V} = \frac{\sum_{ijk}{\phi_{ijk} \lvert V_{ijk} \rvert}}{\sum_{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. + product of the selected field variable, phase volume fraction and cell volume + by the sum of the product of the phase volume fraction and cell volumes. - .. math:: \frac{\int\phi dV}{V} = \frac{\sum_{ijk}{\phi_{ijk} \lvert V_{ijk} \rvert}}{\sum_{ijk}{\lvert V_{ijk} \rvert}} + .. math:: \frac{\int\varepsilon\phi dV}{\int\varepsilon dV} = \frac{\sum_{ijk}{\phi_{ijk} \varepsilon_{ijk} \lvert V_{ijk} \rvert}}{\sum_{ijk}{\varepsilon_{ijk} \lvert V_{ijk} \rvert}} Mass-Weighted Integral +------------------------------------------------+