  Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic particle method
which allows to select the level of resolution at which a fluid is simulated.
The numerical integration of its equations of motion still suffers from the
lack of numerical schemes satisfying all the desired properties: energy
conservation, parallelizability and stability. The similarities between SDPD
and Dissipative Particle Dynamics with Energy conservation (DPDE), which is
another coarse-grained model, enable the adaptation of recent numerical schemes
developed for DPDE to the SDPD setting. In this article, we introduce a
Metropolis step in the integration of the fluctuation/dissipation part of SDPD
to improve its stability.
