text: Hydrodynamic theories describe liquids in terms of space- and time-dependent macroscopic fields, such as density, velocity, and temperature. These fields obey partial differential equations, which can be linear or nonlinear. Hydrodynamic theories are more general than equilibrium thermodynamic descriptions, which assume that liquids are approximately homogeneous and time-independent. The Navier-Stokes equations are a well-known example: they are partial differential equations giving the time evolution of density, velocity, and temperature of a viscous fluid. There are numerous methods for numerically solving the Navier-Stokes equations and its variants.