scholarly journals Deficiency of finite difference methods for capturing shock waves and wave propagation over uneven bottom seabed

2018 ◽  
Vol 7 (3.28) ◽  
pp. 97
Author(s):  
Mohammad Fadhli Ahmad ◽  
Mohd Sofiyan Suliman ◽  
. .
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Source Term ◽  
Finite Difference Methods ◽  
Dam Break ◽  
Numerical Schemes ◽  
Inaccurate Information ◽  
Uneven Bottom

The implementation of finite difference method is used to solve shallow water equations under the extreme conditions. The cases such as dam break and wave propagation over uneven bottom seabed are selected to test the ordinary schemes of Lax-Friederichs and Lax-Wendroff numerical schemes. The test cases include the source term for wave propagation and exclude the source term for dam break. The main aim of this paper is to revisit the application of Lax-Friederichs and Lax-Wendroff numerical schemes at simulating dam break and wave propagation over uneven bottom seabed. For the case of the dam break, the two steps of Lax-Friederichs scheme produce non-oscillation numerical results, however, suffering from some of dissipation. Moreover, the two steps of Lax-Wendroff scheme suffers a very bad oscillation. It seems that these numerical schemes cannot solve the problem at discontinuities which leads to oscillation and dissipation. For wave propagation case, those numerical schemes produce inaccurate information of free surface and velocity due to the uneven seabed profile. Therefore, finite difference is unable to model shallow water equations under uneven bottom seabed with high accuracy compared to the analytical solution.  

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.

Finite difference methods for 2D shallow water equations with dispersion

2019 ◽  
Vol 34 (2) ◽  
pp. 105-117 ◽  
Author(s):  
Gayaz S. Khakimzyanov ◽  
Zinaida I. Fedotova ◽  
Oleg I. Gusev ◽  
Nina Yu. Shokina
Keyword(s):  
Finite Difference ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Difference Methods ◽  
Original System ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Elliptic Type ◽  
Two Dimensional ◽  
Nonlinear Hyperbolic System

Abstract Basic properties of some finite difference schemes for two-dimensional nonlinear dispersive equations for hydrodynamics of surface waves are considered. It is shown that stability conditions for difference schemes of shallow water equations are qualitatively different in the cases the dispersion is taken into account, or not. The difference in the behavior of phase errors in one- and two-dimensional cases is pointed out. Special attention is paid to the numerical algorithm based on the splitting of the original system of equations into a nonlinear hyperbolic system and a scalar linear equation of elliptic type.

Characteristics of finite difference methods for dispersive shallow water equations

2016 ◽  
Vol 31 (3) ◽  
Author(s):  
Zinaida I. Fedotova ◽  
Gayaz S. Khakimzyanov
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Difference Methods ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Hydrodynamic Equations ◽  
Difference Methods

AbstractThe paper contains a description of the most important properties of numerical methods for solving nonlinear dispersive hydrodynamic equations and their distinctions from similar properties of finite difference schemes approximating classic dispersion-free shallow water equations.

scholarly journals Wave propagation speeds and source term influences in single and integral porosity shallow water equations

2017 ◽  
Vol 10 (4) ◽  
pp. 275-286 ◽  
Author(s):  
Ilhan Özgen ◽  
Jia-heng Zhao ◽  
Dong-fang Liang ◽  
Reinhard Hinkelmann
Keyword(s):  
Wave Propagation ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Source Term
Sign in / Sign up

Export Citation Format

Share Document