Table 2.

Overview of CFD methods and numerical techniques for fluid dynamics simulations.

Category	Method	Description	Typical Applications
Numerical Methods	FVM	Solves equations using discrete control volumes.	Versatile, used in many commercial CFD software.
	FEM	Uses mesh of elements, effective for complex geometries.	Structural analysis, fluid dynamics.
	BEM	Focuses on boundaries, reduces 3D problems to 2D.	Potential and external flow problems.
Turbulence Models	RANS	Averages Navier–Stokes over time for steady and turbulent flows.	Industrial applications, steady-state flows.
	URANS	Extends RANS to unsteady flows.	Vortex shedding, transient flows.
	DES	Hybrid of RANS and LES for flows with separated regions.	Aerospace, automotive industries, and underwater vehicles.
	LES	Resolves large-scale turbulent structures, models smaller scales.	Detailed turbulence research, complex flows.
	DNS	Simulates all turbulent flow scales without modeling.	Fundamental turbulence research.
Mesh-free Methods	SPH	Particle-based method for simulating free-surface flows.	Astrophysics, engineering, and environmental modeling.
Statistical Methods	LBM	Simulates fluid flow using particle distribution functions.	Complex, multiphase flows.
Vortical Flow Methods	Vortex	Focuses on capturing vortical structures in incompressible flows.	Aerodynamics, turbulent flow simulations.