scholarly journals Diffusive Wave Approximation to the Shallow Water Equations: Computational Approach

2011 ◽  
Vol 4 ◽  
pp. 1828-1833 ◽  
Author(s):  
Nathan Collier ◽  
Hany Radwan ◽  
Lisandro Dalcin ◽  
Victor M. Calo
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Computational Approach ◽  
Wave Approximation

Time adaptivity in the diffusive wave approximation to the shallow water equations

2013 ◽  
Vol 4 (3) ◽  
pp. 152-156 ◽  
Author(s):  
Nathan Collier ◽  
Hany Radwan ◽  
Lisandro Dalcin ◽  
Victor M. Calo
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Wave Approximation

On the diffusive wave approximation of the shallow water equations

2008 ◽  
Vol 19 (5) ◽  
pp. 575-606 ◽  
Author(s):  
R. ALONSO ◽  
M. SANTILLANA ◽  
C. DAWSON
Keyword(s):  
Shallow Water ◽  
Water Flow ◽  
Shallow Water Equations ◽  
Numerical Algorithms ◽  
Approximate Solutions ◽  
Topographic Effects ◽  
Linear Diffusion ◽  
Flow Models ◽  
Wave Approximation ◽  
Non Linear

In this paper, we study basic properties of the diffusive wave approximation of the shallow water equations (DSW). This equation is a doubly non-linear diffusion equation arising in shallow water flow models. It has been used as a model to simulate water flow driven mainly by gravitational forces and dominated by shear stress, that is, under uniform and fully developed turbulent flow conditions. The aim of this work is to present a survey of relevant results coming from the studies of doubly non-linear diffusion equations that can be applied to the DSW equation when topographic effects are ignored. In fact, we present proofs of the most relevant results existing in the literature using constructive techniques that directly lead to the implementation of numerical algorithms to obtain approximate solutions.

scholarly journals An urban pluvial flood simulation model based on diffusive wave approximation of shallow water equations

2017 ◽  
Vol 50 (1) ◽  
pp. 138-154 ◽  
Author(s):  
Boni Su ◽  
Hong Huang ◽  
Wei Zhu
Keyword(s):  
Simulation Model ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Drainage System ◽  
Full Account ◽  
Flood Simulation ◽  
Diffusion Wave ◽  
New Model ◽  
Wave Approximation ◽  
Model Based

Abstract Urban floods caused by sudden heavy rainstorms are becoming more frequent and causing serious problems in many cities. Developing methods to simulate urban rainstorm floods is helpful in disaster prevention and mitigation. In this paper, we establish an urban pluvial flood simulation model based on diffusion wave approximation of shallow-water equations. The model takes full account of the characteristics in urban pluvial floods, and includes many improvements in simulation details. These details include building a consideration method, a rainfall consideration method, and so on. A new calculation method of water surface gradient is established, which is suitable for complex topology in urban pluvial flood simulation and can reduce unnecessary simulation error introduced by calculation methods. The accuracy and stability of the model are verified through simple cases with analytical solution and experiments with measured data. The results show that the new model is more accurate than common diffusion wave approximation models. A new treatment to avoid ‘checkerboard oscillation’ is established. In comparison with existing methods, the new method proved to be the best. A proof of concept shows that the new model can deal with complex situations and is helpful for urban drainage system planning.

MAPPING TIDAL CURRENTS AND RESIDUAL CURRENTS BY USE OF COASTAL ACOUSTIC TOMOGRAPHY

2017 ◽  
Author(s):  
Xiao-Hua Zhu ◽  
Xiao-Hua Zhu ◽  
Ze-Nan Zhu ◽  
Ze-Nan Zhu ◽  
Xinyu Guo ◽  
...  
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Mean Amplitude ◽  
Momentum Equation ◽  
Tidal Currents ◽  
Acoustic Tomography ◽  
Mean Values ◽  
Residual Currents ◽  
Water Depths ◽  
Deep Area

A coastal acoustic tomography (CAT) experiment for mapping the tidal currents in the Zhitouyang Bay was successfully carried out with seven acoustic stations during July 12 to 13, 2009. The horizontal distributions of tidal current in the tomography domain are calculated by the inverse analysis in which the travel time differences for sound traveling reciprocally are used as data. Spatial mean amplitude ratios M2 : M4 : M6 are 1.00 : 0.15 : 0.11. The shallow-water equations are used to analyze the generation mechanisms of M4 and M6. In the deep area, velocity amplitudes of M4 measured by CAT agree well with those of M4 predicted by the advection terms in the shallow water equations, indicating that M4 in the deep area where water depths are larger than 60 m is predominantly generated by the advection terms. M6 measured by CAT and M6 predicted by the nonlinear quadratic bottom friction terms agree well in the area where water depths are less than 20 m, indicating that friction mechanisms are predominant for generating M6 in the shallow area. Dynamic analysis of the residual currents using the tidally averaged momentum equation shows that spatial mean values of the horizontal pressure gradient due to residual sea level and of the advection of residual currents together contribute about 75% of the spatial mean values of the advection by the tidal currents, indicating that residual currents in this bay are induced mainly by the nonlinear effects of tidal currents.

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