scholarly journals A Proposed Implicit Friction Source Term Treatment for Simulating Overland Flow

10.29007/fsp8 ◽  
2018 ◽  
Author(s):  
Tian Wang ◽  
Jingming Hou ◽  
Peng Li ◽  
Jiaheng Zhao ◽  
Ilhan Özgen ◽  
...  
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Overland Flow ◽  
Source Term ◽  
Specific Treatment ◽  
Term Treatment ◽  
Finite Volume Scheme ◽  
Flow Problems ◽  
Friction Term ◽  
Water Depths

The fully 2D dynamic shallow water equations have been widely applied for numerical simulation of overland flow in the recent years. However, most of the existing friction term discretisation schemes do not recover the correct asymptotic flow behaviour as water depths becomes small. In this model, the shallow water equations were discretized by the framework of the Godunov-type finite volume scheme. The hydrostatic reconstruction is applied to reconstruct non-negative water depths at wet- dry interfaces. Numerical fluxes are computed with a HLLC solver. The novel aspects of the model include the slope source term treatment. Specific treatment of friction source terms has been proposed to discretize the friction terms to recover the correct asymptotic behaviour of SWEs when the water depth becomes small. The accuracy and robustness of the proposed model are verified by comparing with analytical solutions. The results demonstrate that the proposed method treating friction source term is a relatively more accurate, efficient, straightforward and universal one for evaluating overland flow problems.

An implicit friction source term treatment for overland flow simulation using shallow water flow model

2018 ◽  
Vol 564 ◽  
pp. 357-366 ◽  
Author(s):  
Jingming Hou ◽  
Tian Wang ◽  
Peng Li ◽  
Zhanbin Li ◽  
Xia Zhang ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Flow ◽  
Flow Model ◽  
Overland Flow ◽  
Source Term ◽  
Flow Simulation ◽  
Term Treatment ◽  
Shallow Water Flow

scholarly journals Flood wave propagation in steep mountain rivers

2012 ◽  
Vol 15 (1) ◽  
pp. 120-137 ◽  
Author(s):  
Gabriella Petaccia ◽  
Luigi Natale ◽  
Fabrizio Savi ◽  
Mirjana Velickovic ◽  
Yves Zech ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Source Term ◽  
Term Treatment ◽  
Flood Wave ◽  
Numerical Schemes ◽  
Steady State Condition ◽  
One Dimensional ◽  
The One

Most of the recent developments concerning efficient numerical schemes to solve the shallow-water equations in view of real world flood modelling purposes concern the two-dimensional form of the equations or the one-dimensional form written for rectangular, unit-width channels. Extension of these efficient schemes to the one-dimensional cross-sectional averaged shallow-water equations is not straightforward, especially when complex natural topographies are considered. This paper presents different formulations of numerical schemes based on the HLL (Harten–Lax–van Leer) solver, and the adaptation of the topographical source term treatment when cross-sections of arbitrary shape are considered. Coupled and uncoupled formulations of the equations are considered, in combination with centred and lateralised source term treatment. These schemes are compared to a numerical solver of Lax Friedrichs type based on a staggered grid. The proposed schemes are first tested against two theoretical benchmark tests and then applied to the Brembo River, an Italian alpine river, firstly simulating a steady-state condition and secondly reproducing the 2002 flood wave propagation.

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.

scholarly journals A Well-balanced Finite Volume Scheme for Shallow Water Equations with Porosity: Application to Modelling Flow through Rigid Vegetation

2018 ◽  
Vol 40 ◽  
pp. 05032
Author(s):  
Minh H. Le ◽  
Virgile Dubos ◽  
Marina Oukacine ◽  
Nicole Goutal
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Simple Wave ◽  
Water Model ◽  
Strong Interactions ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Rigid Vegetation ◽  
Vertical Cylinders

Strong interactions exist between flow dynamics and vegetation in open-channel. Depth-averaged shallow water equations can be used for such a study. However, explicit representation of vegetation can lead to very high resolution of the mesh since the vegetation is often modelled as vertical cylinders. Our work aims to study the ability of a single porosity-based shallow water model for these applications. More attention on flux and source terms discretizations are required in order to archive the well-balancing and shock capturing properties. We present a new Godunov-type finite volume scheme based on a simple-wave approximation and compare it with some other methods in the literature. A first application with experimental data was performed.

On the necessity of non-hydrostatic pressure models for free surface flow over complex topography

2020 ◽  
Author(s):  
Isabel Echeverribar ◽  
Pilar Brufau ◽  
Pilar García-Navarro
Keyword(s):  
Free Surface ◽  
Hydrostatic Pressure ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Finite Volume Scheme ◽  
Complex Topography ◽  
Source Terms ◽  
Pressure Correction ◽  
Wide Range

<p><span><strong>There is a wide range of geophysical flows, such as flow in open channels and rivers, tsunami and flood modeling, that can be mathematically represented by the non-linear shallow water 1D equations involving hydrostatic pressure assumptions as an approximation of the Navier Stokes equations. In this context, special attention must be paid to bottom source terms integration and numerical corrections when dealing with wet/dry fronts or strong slopes in order to obtain physically-based solutions (Murillo and García-Navarro, 2010) in complex and realistic cases with irregular topography. However, although these numerical corrections have been developed in recent years achieving not only more robust models but also more accurate results, they still might find a limit when dealing with specific scenarios where vertical information or disspersive effects become crucial. This work presents a 1D shallow water model that introduces vertical information by means of a non-hydrostatic pressure correction when necessary. In particular, the pressure correction method (Hirsch, 2007) is applied to a 1D finite volume scheme for a rectification of the velocity field in free surface scenarios. It is solved by means of an implicit scheme, whereas the depth-integrated shallow water equations are solved using an explicit scheme. It is worth highlighting that it preserves all the advantages and numerical fixes aforementioned for the pure shallow water system. Computations with and without non-hydrostatic corrections are compared for the same cases to test the validity of the conventional hydrostatic pressure assumption at some scenarios involving complex topography.</strong></span></p><p><span>[1] J. Murillo and P. Garcia-Navarro, Weak solutions for partial differential equations with source terms: application to the shallow water equations, Journal of Computational Physics, vol. 229, iss. 11, pp. 4327-4368, 2010.</span></p><p><span>[2] C. Hirsch, Numerical Computation of Internal and External flows: The fundamentals of Computational Fluid Dynamics, Butterworth-Heinemann, 2007.</span></p>

Sign in / Sign up

Export Citation Format

Share Document