قارن الطرق

	نموذج التدفق المروري (نموذج LWR)	منهج هاردي كروس	نمذجة تدفق المياه الجوفية MODFLOW
المجال	الهندسة المدنية	الهندسة المدنية	الهندسة المدنية
العائلة	Process / pipeline	Process / pipeline	Process / pipeline
سنة النشأة	1955	1936	1984 (original release); continuously updated through MODFLOW-6 (2017)
صاحب الطريقة	M. J. Lighthill and G. B. Whitham	Hardy Cross	Michael G. McDonald and Arlen W. Harbaugh (U.S. Geological Survey)
النوع	Macroscopic traffic flow modeling using conservation laws	Iterative method for pipe network flow distribution	Numerical groundwater flow simulation
المصدر التأسيسي	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.	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.
الأسماء البديلة	LWR model, Traffic wave, Kinematic wave theory	Cross method, Moment distribution method, Iterative balancing	MODFLOW-2005, MODFLOW-6, modular groundwater flow model, USGS groundwater model
ذات صلة	3	3	0
الملخص	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.	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.