Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

2011 ◽  
Vol 45 (7) ◽  
pp. 1035-1061 ◽  
Author(s):  
R.X. Zhong ◽  
A. Sumalee ◽  
T.L. Friesz ◽  
William H.K. Lam
Keyword(s):  
Numerical Solution ◽  
User Equilibrium ◽  
Solution Algorithm ◽  
Theoretical Development ◽  
Traffic Network ◽  
Dynamic User Equilibrium ◽  
Side Constraints

Numerical solutions to wave interaction with rubblemound breakwaters

1990 ◽  
Vol 17 (2) ◽  
pp. 252-261 ◽  
Author(s):  
Kevin R. Hall
Keyword(s):  
Numerical Modelling ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Scale Effects ◽  
Numerical Models ◽  
Internal Flow ◽  
Wave Interaction ◽  
Theoretical Development ◽  
Porous Media Flow ◽  
Complex Flow

The interaction of a wave with a rubblemound breakwater results in a complex flow field which is both nonlinear and turbulent, particularly within a region close to the surface of the structure. Numerical models describing internal flow in a rubblemound breakwater are becoming increasingly important, particularly as the influence of scale effects on internal flow in physical hydraulic models are becoming understood as important. A number of numerical models to predict the internal breakwater flow kinematics have been produced in the past two decades. This paper provides a review of the state-of-the-art of numerical modelling of wave interaction with rubblemound breakwaters. Details of the theoretical development and the resulting numerical solution techniques are presented. Methods for incorporating secondary effects such as two-phase (air–water) flow, inertia, and unbalanced boundary conditions are discussed. Limitations of the models resulting from the validity of the assumptions made in order to effect a numerical solution are discussed. Key words: breakwaters, internal flow, porous media flow, numerical modelling, rubblemound breakwaters.

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