قارن الطرق

	نموذج التدفق المروري (نموذج LWR)	منهج هاردي كروس	نمذجة تدفق المياه الجوفية MODFLOW	طريقة موسكينغم (Muskingum Routing)
المجال	الهندسة المدنية	الهندسة المدنية	الهندسة المدنية	الهندسة المدنية
العائلة	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
سنة النشأة	1955	1936	1984 (original release); continuously updated through MODFLOW-6 (2017)	1938
صاحب الطريقة	M. J. Lighthill and G. B. Whitham	Hardy Cross	Michael G. McDonald and Arlen W. Harbaugh (U.S. Geological Survey)	George McCarthy
النوع	Macroscopic traffic flow modeling using conservation laws	Iterative method for pipe network flow distribution	Numerical groundwater flow simulation	Hydrologic method for flood attenuation in rivers
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.	McCarthy, G. T. (1938). The Unit Hydrograph and Flood Routing. US Army Corps of Engineers Document 608.
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	Flood routing, Stream flow attenuation, Hydrologic routing
ذات صلة	3	3	0	3
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.	The Muskingum method is a hydrologic flood routing technique that predicts how a flood wave attenuates (reduces in peak) and spreads as it travels down a river reach. Developed by McCarthy in 1938 for the US Army Corps of Engineers, the method is simple enough for hand calculations while capturing the essential physics of flood propagation.