مقایسهٔ روش‌ها

	متد هاردی کراس	MODFLOW Groundwater Modeling	تئوری تحکیم تراژاگی (Terzaghi Consolidation)	مدل جریان ترافیک (مدل LWR)
حوزه	مهندسی عمران	مهندسی عمران	مهندسی عمران	مهندسی عمران
خانواده	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
سال پیدایش	1936	1984 (original release); continuously updated through MODFLOW-6 (2017)	1943	1955
پدیدآور	Hardy Cross	Michael G. McDonald and Arlen W. Harbaugh (U.S. Geological Survey)	Karl Terzaghi	M. J. Lighthill and G. B. Whitham
نوع	Iterative method for pipe network flow distribution	Numerical groundwater flow simulation	Diffusion equation for pore pressure dissipation and soil settlement	Macroscopic traffic flow modeling using conservation laws
منبع بنیادین	Cross, H. (1936). Analysis of flow in networks of conduits or conductors. University of Illinois Bulletin, 34(17), 3-29.	Harbaugh, A. W. (2005). MODFLOW-2005, the U.S. Geological Survey modular ground-water model — the Ground-Water Flow Process. U.S. Geological Survey Techniques and Methods 6-A16.	Terzaghi, K. (1943). Theoretical Soil Mechanics. John Wiley & Sons. ISBN: 0-471-85305-1	Lighthill, M. J., & Whitham, G. B. (1955). On kinematic waves I. Flow movement in long rivers. Proceedings of the Royal Society A, 229(1178), 281-316.
نام‌های دیگر	Cross method, Moment distribution method, Iterative balancing	MODFLOW-2005, MODFLOW-6, modular groundwater flow model, USGS groundwater model	Primary consolidation, Soil settlement, Effective stress	LWR model, Traffic wave, Kinematic wave theory
مرتبط	3	0	3	3
خلاصه	The Hardy Cross method is an iterative technique for solving steady-state flow distribution in pipe networks, originally developed for water distribution systems. Introduced by Hardy Cross in 1936, this method balances flow continuity and pressure head constraints through successive iterations, making it ideal for hand calculations and gaining physical insight into network behavior.	MODFLOW is the U.S. Geological Survey's open-source, modular finite-difference model for simulating three-dimensional groundwater flow through porous media. First released in 1984 and continuously updated — most recently as MODFLOW-6 — it is the global standard for quantitative hydrogeological analysis, widely used in civil engineering, environmental consulting, water-resource management, and groundwater contamination studies.	Terzaghi consolidation theory describes how water-saturated clay soils compress over time as excess pore water pressure dissipates and effective stress increases. Formulated by Karl Terzaghi in 1943, this foundational theory enables prediction of settlement rates for foundations on compressible soils, a critical design concern in geotechnical engineering.	The Lighthill-Whitham-Richards (LWR) model is a macroscopic traffic flow model that treats traffic as a compressible fluid, applying conservation of vehicles and a flow-density relationship. Introduced independently by Lighthill and Whitham (1955) and Richards (1956), the model predicts traffic wave propagation, congestion formation, and bottleneck behavior on highways.