How can I verify that I filled my multimaterial Euler mesh correctly? (Verify proper mass/volume was filled)

There are a couple of ways to accomplish this:

1) The Euler cells can be partially filled. Hence, to review this, one can plot a contour of material fraction.
If "Plots > Material Location" is used to plot the material (e.g., TNT in air), cells partially-filled may not appear (cells will either show all or no material). Click the arrow beside the "Material Location" to open the dialog window of material plot settings, then click "Smooth multi-material". Now the partially-filled cells will show every material inside the cells.

2) During solution, the mass and volume of filled material (e.g., TNT in air) will be printed in the .prt file. (For example, use "Output > Print > Start Cycle" and set to 1 to print information for cycle #1)

Because multimaterial Euler cells can be partially filled, one does not need a very fine mesh to capture the fill accurately.

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