In some cases where there are challenging gradients in the density,
particularly associated with highly compressible flows, it can be
helpful or indeed essential to include some diffusivity to the continuity
equation, although there is no such physical process.
In the \textsc{Pencil Code} we have three forms of such diffusivities: a bulk
diffusion with
coefficient \texttt{diffrho}, which acts proportional to the Laplacian of
density, a shock diffusion with coefficient \texttt{diffrho\_shock}, which acts
proportional to the product of the flow convergence and the Laplacian of
density, and hyper-diffusion with coefficient \texttt{diffrho\_hyper3}, which
acts proportional to the cubic Laplacian of density ($\partial^6/\partial
x^6 + \partial^6/\partial y^6 +\partial^6/\partial z^6$).

These apply an effective mass sink in the system, so to conserve momentum
and/or energy, appropriate corrections can be applied to the momentum
and/or energy equations, which is enabled by setting the flag
\texttt{lmassdiff\_fix} to \texttt{.true.}\,.
By default this has been set to \texttt{.false.} in the \textsc{Pencil Code}.
However, experiments with the shock tube tests (Sod 1978)\footnote{
Sod, G. A. (1978). ``A Survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws''.
\textit{J. Comput. Phys.} \textbf{27}, 1-–31
(\url{https://doi.org/10.1016/0021-9991(78)90023-2}).} reported in Gent et al.\ (2020),
\url{http://doi.org/10.1080/03091929.2019.1634705}, indicate that 
simulations without the flag set \texttt{.true.} yield less accurate solutions.
It would therefore be more appropriate to make the default \texttt{.true.}\,.
This evidently creates some numerical crashes when used in some
simulations with high Mach particle flows, so a 2022 change to the
default without consultation was recently reverted on request.
Now that we have time to consider the matter collectively, I propose
that we change the default to \texttt{.true.} and explicitly set 
it in those reference samples to \texttt{.false.} which require it so.
A warning about the choice should be printed to alert the user about
its significance whenever they select mass diffusion.
The effect of the switch was not reported in the cited article, but
given its subsequent impact on users of the code I propose in the near
future to prepare a more comprehensive study of these effects, based on
the Sod (1978) solutions.

Because the application of the mass diffusion fix has been found to cause
numerical crashes when applied to mass hyper-diffusion, the fix is only
effective for Laplacian and shock diffusion.
I would also add that I have found mass hyper-diffusion to be prone to
density holes including negative density when solving for linear 
(non-logarithmic) density.
Note, that the \textsc{Pencil Code} is not a conservative code (in its default
configuration) and when solving for highly compressible flows, using the
linear rather than the logarithmic form of the continuity equation has also
been found to be more conservative.
