FluidDynamic

FLUIDDYNAMIC, commonly referred to as fluid dynamics, is the branch of physics and engineering that studies the motion of liquids and gases and the forces that cause or result from that motion. It covers the behavior of fluids in a wide range of scales, from microfluidic devices to atmospheric and oceanic flows.

Its governing equations are rooted in conservation laws. The continuity equation expresses conservation of mass: ∂ρ/∂t + div(ρu) = 0. The momentum equation, often written as ρ Du/Dt = -grad p + div τ + f, represents Newton's second law for a fluid. For Newtonian fluids, the viscous stress tensor τ is μ(∇u + ∇u^T) − λ(div u)I; in the incompressible limit with constant density, div u = 0 and τ = μ ∇u. The inviscid (ideal) case leads to the Euler equations.

Key concepts include the Reynolds number Re = ρUL/μ, which characterizes laminar versus turbulent flow, boundary layers near solid surfaces, and the distinction between compressible and incompressible flows (Mach number). Viscosity, density, and temperature influence system behavior, and non-Newtonian fluids exhibit more complex constitutive relations.

Modeling and computation rely on experiments, analytical solutions for simplified problems, and numerical simulation. Computational fluid dynamics (CFD) solves discretized forms of the governing equations using finite volume, finite element, or finite difference methods. Turbulence modeling (RANS, LES, DNS) and multiphase or heat-transfer extensions broaden applicability to real-world problems.

Historically, fluid dynamics developed from the work of Euler and d'Alembert and was advanced by Navier and Stokes, who formulated the Navier–Stokes equations. Applications span aerospace and automotive design, civil and environmental engineering, energy systems, meteorology, oceanography, and biomechanics.