Heavy-ion collisions at center-of-mass energies between 1 and 100 GeV per nucleon can be used to map the QCD phase diagram where a hypothetical critical point serves as a landmark. At these energies the net baryon density of the system can be high and critical fluctuations can become essential in the presence of the critical point, and thus simulating their dynamical evolution becomes an indispensable part of theoretical modeling. In this talk, I will first discuss the relativistic hydrodynamic description of the baryon-charged quark-gluon plasma produced in the low energy heavy-ion collisions. I will then discuss the effects caused by the baryon diffusion on the longitudinal dynamics and on the phase diagram trajectories of fluid cells at different space-time rapidities of the system, and how they are affected by critical fluctuations near the critical point.