  One of the primary goals of nuclear physics is studying the phase diagram of
Quantum Chromodynamics, where a hypothetical critical point serves as a
landmark. A systematic model-data comparison of heavy-ion collisions at
center-of-mass energies between 1 and 100 GeV per nucleon is essential for
locating the critical point and the phase boundary between the deconfined
quark-gluon plasma and the confined hadron resonance gas. 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. Simulating their
dynamical evolution thus becomes an indispensable part of theoretical modeling.
In this thesis we first present the (3+1)-dimensional relativistic hydrodynamic
code BEShydro, which solves the equations of motion of second-order
Denicol-Niemi-Molnar-Rischke theory, including bulk and shear viscous
components as well as baryon diffusion current. We then study 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 dynamics near the critical point.
We finally explore the evolution of non-hydrodynamic slow processes describing
long wavelength critical fluctuations near the critical point, by extending the
conventional hydrodynamic description by coupling it to additional explicitly
evolving slow modes, and their back-reaction to the bulk matter properties.
