[FXC-4940] Add surface integral output (#58)

* add surface integral output

* added toctree to tools

Author: piotrkluba

docs/02.simulation-setup/04.output/02.outputs-list/20.surface-integral-output.md

@@ -0,0 +1,79 @@
+(surface-integral-output)=
+# Surface Integral Output
+
+*Surface Integral Output computes surface integrals of custom user variables on selected surfaces and can optionally report moving statistics over time.*
+
+---
+
+## **Available Options**
+
+| *Option* | *Description* | *Applicable* |
+|----------|---------------|--------------|
+| **Output fields** | Custom user variables to integrate over the assigned surfaces | always |
+| **Statistics function** | Optional moving statistic applied to the integrated values | always |
+| **Moving window size** | Window size for moving statistics (in output data points) | when **Statistics function** is not `None` |
+| **Start step** | Step at which to start statistics calculation | when **Statistics function** is not `None` |
+| **Assigned surfaces** | Surfaces used for the integral | always |
+
+---
+
+## **Detailed Descriptions**
+
+### **Output fields**
+
+*The custom user variables to integrate over the selected surfaces.*
+
+- **Required** (at least one field must be selected)
+- **Allowed fields:** Custom user variables only
+- **Example:** `PressureForce`, `HingeTorqueZ`
+>**Note:** Surface Integral Output only accepts custom user variables. Define them in [Variable Settings](../../../05.tools/02.variable-settings.md) (Custom variables tab).
+
+### **Statistics function**
+
+*Optional moving statistic applied to the integrated values. When set to `None`, raw integral values are reported.*
+
+- **Default:** `None`
+- **Options:**
+  - `None` - No statistics processing
+  - `Mean` - Moving average
+  - `Min` - Minimum in the window
+  - `Max` - Maximum in the window
+  - `Standard deviation` - Sample standard deviation (Bessel's correction)
+  - `Deviation` - Range (maximum minus minimum) in the window
+
+### **Moving window size**
+
+*The number of output data points used in the moving statistics window.*
+
+- **Default:** `10`
+- **Minimum value:** `2`
+>**Note:** For steady simulations, the solver typically outputs a data point every 10 pseudo steps. For unsteady simulations, it outputs every physical step.
+
+### **Start step**
+
+*The number of steps to skip before statistics calculation begins.*
+
+- **Default:** `0`
+>**Note:** For steady simulations, this value is rounded up to the nearest multiple of 10 (based on output cadence).
+
+### **Assigned surfaces**
+
+*The surfaces on which the integral is computed.*
+
+- **Required:** Yes (at least one surface must be selected)
+- **Supported surface types:**
+  - Simulation surfaces (mesh boundaries)
+  - Imported sample surfaces
+>**Notes:**
+> - Import sample surfaces in the Entities browser before selecting them. See [Sample Surfaces](../../../04.entities-browser/10.sample-surfaces.md).
+> - Do not mix simulation surfaces and imported sample surfaces in a single Surface Integral Output. Create separate outputs if you need both.
+
+---
+
+## **Use Cases**
+
+Surface Integral Output is useful for:
+
+- Computing hinge torques, forces, or moments defined as custom variables
+- Integrating heat flux or other derived quantities over selected surfaces
+- Monitoring integrated quantities with moving statistics during transient simulations

docs/02.simulation-setup/04.output/02.outputs-list/README.md

@@ -17,6 +17,7 @@
 | **[Probe Outputs](./07.probe-outputs.md)** | Flow field data monitoring during simulation | Tracking convergence and flow properties |
 | **[Time-averaging Probe Outputs](./08.time-averaging-probe-outputs.md)** | Time-averaged monitoring data | Statistical monitoring data |
 | **[Surface Probe Output](./09.surface-probe-outputs.md)** | Flow field data at specific points projected onto surfaces | Point-specific surface data |
+| **[Surface Integral Output](./20.surface-integral-output.md)** | Surface integral of custom user variables on selected surfaces | Integrated forces, torques, and custom derived quantities |
 | **[Isosurface Output](./11.isosurface-output.md)** | Flow field data on surfaces of constant variable value | Visualization of vortices, shock waves |
 | **[Time-averaging Isosurface Output](./12.time-averaging-isosurface-output.md)** | Time-averaged flow field data on surfaces of constant variable value | Statistical analysis of vortices, shock waves |
 | **[Aeroacoustic Output](./13.aeroacoustic-output.md)** | Data for aeroacoustic analysis at observer positions | Noise prediction and analysis |
@@ -124,7 +125,7 @@ Each output type has specific configuration options. For detailed documentation
 
 ### **Custom Variables**
 
-User defined expressions with dimensions. By default, the following expressions are available:
+User defined expressions with dimensions. Create and manage these in [Variable Settings](../../../05.tools/02.variable-settings.md). By default, the following expressions are available:
 
 | Variable Name                         | Expression                                      |
 |--------------------------------------|-------------------------------------------------|
@@ -176,6 +177,7 @@ User defined expressions with dimensions. By default, the following expressions
 ./08.time-averaging-probe-outputs.md
 ./09.surface-probe-outputs.md
 ./10.surface-slice-output.md
+./20.surface-integral-output.md
 ./11.isosurface-output.md
 ./12.time-averaging-isosurface-output.md
 ./13.aeroacoustic-output.md

docs/02.simulation-setup/04.output/README.md

@@ -32,6 +32,7 @@
 - **[Time-averaging Probe Outputs](./02.outputs-list/08.time-averaging-probe-outputs.md)** - Time-averaged monitoring data
 - **[Surface Probe Output](./02.outputs-list/09.surface-probe-outputs.md)** - Flow field data at specific points projected onto surfaces
 - **[Surface Slice Output](./02.outputs-list/10.surface-slice-output.md)** - Flow field data on slices of surfaces
+- **[Surface Integral Output](./02.outputs-list/20.surface-integral-output.md)** - Surface integral of custom user variables on selected surfaces
 - **[Isosurface Output](./02.outputs-list/11.isosurface-output.md)** - Flow field data on surfaces of constant variable value
 - **[Time-averaging Isosurface Output](./02.outputs-list/12.time-averaging-isosurface-output.md)** - Time-averaged flow field data on surfaces of constant variable value
 - **[Aeroacoustic Output](./02.outputs-list/13.aeroacoustic-output.md)** - Data for aeroacoustic analysis at observer positions

docs/05.tools/README.md

@@ -9,3 +9,13 @@ This section covers the available tools in the Flow360 webUI:
 - [Surface Mesh Diagnostics](./03.surface-mesh-diagnostics.md) - Analyze surface mesh quality
 - [Volume Mesh Diagnostics](./04.volume-mesh-diagnostics.md) - Inspect volume mesh quality through slices
 - [Mesh Statistics Panel](./05.mesh-statistics-panel.md) - View detailed mesh statistics
+
+```{toctree}
+:hidden:
+:maxdepth: 2
+./01.probing.md
+./02.variable-settings.md
+./03.surface-mesh-diagnostics.md
+./04.volume-mesh-diagnostics.md
+./05.mesh-statistics-panel.md
+```