  A Rayleigh B\'enard instability study using the energy conserving dissipative
particle dynamics method is presented here for the first time. The simulation
is performed on an ideal dissipative particle dynamics fluid in a three
dimensional domain with carefully selected parameters to make the convection
terms in the equation more dominant than the conduction ones. Beyond a critical
temperature difference a two cell pattern is observed as the dominant
structure. As the temperature is increased further, the density changes in the
system are sharp with formation of distinct high density layers close to the
cold wall. Doubling the length of the domain led to the formation of four
convection cells with the same cell diameter as before, confirming the
invariance of the pattern formation in that dimension. Changes in the height of
the domain led to cells with more uniform looking patterns. The results and
patterns seen here are qualitatively similar to previous studies performed on
rarefied gases.
