قارن الطرق

	معادلات نافييه-ستوكس المُمَثّلة برينولدز (RANS)	المحاكاة العددية المباشرة
المجال	ديناميكا الموائع	ديناميكا الموائع
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1895	1971
صاحب الطريقة	Osborne Reynolds	Steven Orszag
النوع	Computational turbulence modeling approach	Full-scale turbulence resolution method
المصدر التأسيسي	Reynolds, O. (1895). On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philosophical Transactions of the Royal Society A, 186, 123-164.	Orszag, S. A. (1971). Numerical simulation of incompressible flows within simple boundaries: accuracy. Journal of Fluid Mechanics, 49(1), 75-112.
الأسماء البديلة	RANS, Reynolds-averaged flow simulation	DNS, resolved turbulence simulation
ذات صلة	5	5
الملخص	The Reynolds-Averaged Navier-Stokes (RANS) equations represent a time-averaged form of the Navier-Stokes equations developed by Osborne Reynolds in 1895. This approach decomposes turbulent flow into mean and fluctuating components, enabling practical simulation of turbulent flows by modeling turbulent stresses rather than resolving all scales. RANS remains the most widely used computational fluid dynamics method in engineering applications due to its computational efficiency.	Direct Numerical Simulation (DNS) is a computational approach that solves the Navier-Stokes equations without turbulence models, resolving all scales of motion from the largest energy-containing eddies down to the smallest dissipative scales (Kolmogorov microscales). Pioneered by Steven Orszag in 1971, DNS provides complete information about turbulent flow fields and serves as a reference solution for validating turbulence models. However, extreme computational demands limit DNS to relatively simple geometries and low to moderate Reynolds numbers.