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There are well designed, open source software packages for scientific visualization. … In particular, there is the VTK toolkit, and the two major contenders for scientific visualization -- Visit and Paraview -- are both built on top of it. …

I'd venture the guess that most people in computational science use either Visit or Paraview for flow visualizations. These are simply the two most widely used programs I use. It's true that there is …

Both paraview and visit support data formats that allow you to write whatever data you have on each processor of a parallel computation into one file per processor and then later visualize all the fil …

I don't have a particularly good approach, but I'd copy the 'phi' field from one VTK file into the other and name it 'phiprime' or something. In both Paraview and Visit, you have the option of definin …

You could output your data in one of the widely used file formats, for example VTK, and then use either VisIt or Paraview to visualize. These programs are used a lot for visualizing PDE solutions and …

I don't think there is a good argument to write a converter -- whatever it produces has the same information content as the existing VTK files you already have, and the usual visualization programs can …

New versions of VTK support what you are asking for, and new versions of Paraview can also display this. The current version of Visit can not yet, though, at the time of writing this. The trick is fi …

The only other drawback I am aware of is that some visualization programs can't follow interfaces between cells that don't share vertices when doing streamlines, though today they seem to have become better …

I agree that using the same color scale is generally good practice. Not doing so is confusing. Now, as you note, there are cases where this doesn't leave very much information in each picture. In such …

In practice, you rarely need data in visualization files that's more accurate than, say, 3 valid digits. In that case, ASCII is -- maybe surprisingly -- often more compact than binary form. …

This is actually a standard modeling problem if you consider the medium that flows through the network to be incompressible (e.g., liquids, or gases at low velocity). Then, you formulate everything in …

Programs like Visit and Paraview can do "volume rendering", which is what you show in your figure. You just need to export the data you have in a format that either of these programs can read.

The way this is done in the deal.II library (http://www.dealii.org; disclaimer: this is a project I am affiliated with) is that we describe an unstructured data set of 3d points and then create cells …

You need to look up the VTK file format here: https://vtk.org/wp-content/uploads/2015/04/file-formats.pdf It's not very difficult, you'd just write a single cell for each node of your quad tree. The …

20 MB data files are really not very large any more, on machines like yours. I would expect Mathematica to be able to read it in under a few seconds, and to be able to do an FFT in a few seconds to ma …