Integration over arbitrary volume
 

Hi everyone,

I am simulating the aerodynamic flow over an aircraft flying at high subsonic. I want to perform 3D (volume) and 2D (surface) integrals of some specific variables (definition of which is not relevant to this post). Only half the plane has been simulated with a mesh of almost 11 million cells (mesh depicted in the following images, where the circular shape corresponds to the simmetry plane). The mesh is multiblock, FE - Brick in Tecplot.
Attachment 81108 Attachment 81111

The issue is that I do not want to integrate over the whole volume but just over a specific range. Imagine, for instance, a rectangular control volume around the aircraft that only extends up to two aircraft lengths:

Attachment 81114

2D surface integrals do not seem problematic. I can create slices at arbitrary X, Y or Z locations, which correspond to the "faces" of the rectangular control volume, and perform the integrals once the slices have been "extracted". Tecplot allows me to select, for example, a specific X location where I place my slice and I assume that it interpolates the variables at that plane.

However, I cannot select the specific X,Y and Z range in which I want to perform the volume integrals. I've tried with "Value Blanking", but the consequent volume is dependent on the cell distribution. In the image below, the values have been blanked with the idea of obtaining a rectangular shape similar to the depicted above. Thus, I cannot, for instance, place the outer boundary of the volume at an arbitrary Xmax perpendicular to freestream velocity.
Attachment 81115

An alternative approach I've tried is to interpolate the data from the initial fluid volume (using the inverse-distance interpolation method) onto the rectangular domain. The idea is to generate an ordered zone where I can perform the integrals. However, this method seems extremelly computationally expensive, particularly because it does not allow me to generate a finer mesh towards the surface of the airplane.

How can I then perform 3D volume integrals over specific volumes inside the fluid domain? Any ideas/suggestions will be appreciated.

Thank you for your time.

You have described the best options for doing as you want there really isn't any other method. Although Linear Interpolation will likely be slightly faster than inverse distance.

Thank you for your answer! :)

If that is the case, ins't interpolating a really inefficient method? After all, I only want the integration volume to have a specific shape (e.g. rectangular shape). All the flow field data inside the integration volume does not need to be modified/interpolated. In other words, only the data at the boundaries needs to be interpolated to adapt to the defined shape. This would mean that perhaps only less than 1% of the total cells within the volume would be interpolated, saving a huge amount of computing resources.

The surface integrals at the boundaries are properly defined, as tecplot interpolates the data at a exact location when you create a slice. However, it does not work the same way for 3D integrals, for which you cannot define the exact limits of integration (at least for an unordered mesh). I was wondering if there is any approach that allows you to do this.

How are you defining the rectangular shape? You may be able to define a zone which is surfaces of the rectangle thus only interpolate to those.

It may be easier to do this via email or a phone call, give support@tecplot.com an email and we will see what we can do.