scholarly journals Transient Numerical Solutions of an Extended Korteweg-De Vries Equation Describing Solitary Waves in Open-Channel Flow

2017 ◽  
Vol 61 (1) ◽  
pp. 55-59 ◽  
Author(s):  
Richard Jurisits ◽  
Keyword(s):  
Channel Flow ◽  
Solitary Waves ◽  
Open Channel ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Open Channel Flow ◽  
De Vries

scholarly journals Computational and Numerical Solutions for 2+1-Dimensional Integrable Schwarz–Korteweg–de Vries Equation with Miura Transform

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Raghda A. M. Attia ◽  
S. H. Alfalqi ◽  
J. F. Alzaidi ◽  
Mostafa M. A. Khater ◽  
Dianchen Lu
Keyword(s):  
Solitary Waves ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Adomian Decomposition Method ◽  
Simplest Equation Method ◽  
Adomian Decomposition ◽  
Tanh Method ◽  
De Vries ◽  
Parameter Values

This paper investigates the analytical, semianalytical, and numerical solutions of the 2+1–dimensional integrable Schwarz–Korteweg–de Vries (SKdV) equation. The extended simplest equation method, the sech-tanh method, the Adomian decomposition method, and cubic spline scheme are employed to obtain distinct formulas of solitary waves that are employed to calculate the initial and boundary conditions. Consequently, the numerical solutions of this model can be investigated. Moreover, their stability properties are also analyzed. The solutions obtained by means of these techniques are compared to unravel relations between them and their characteristics illustrated under the suitable choice of the parameter values.

MODELING THE ORGANIC REMOVAL AND OXYGEN CONSUMPTION BY BIOFILMS IN AN OPEN-CHANNEL FLOW

1994 ◽  
Vol 30 (2) ◽  
pp. 53-61 ◽  
Author(s):  
Shiyu Li ◽  
Guang Hao Chen
Keyword(s):  
Water Quality ◽  
Oxygen Consumption ◽  
River Water ◽  
Channel Flow ◽  
Diffusion Layer ◽  
Open Channel ◽  
Open Channel Flow ◽  
River Water Quality ◽  
Monod Kinetics ◽  
Organic Removal

A mathematical model is proposed to predict the removal of dissolved organic substances and the consumption of dissolved oxygen by attached biofilms in an open-channel flow. The model combines the biofilm equations with the conventional Streeter–Phelps type equations of river water quality by considering the mass transfer of organics and oxygen in the river water through the diffusion layer into the biofilm. It is assumed that the diffusion and reaction within the biofilm are of steady-state, and follow Monod kinetics. The model is solved numerically with a trial-and-error method. The simulation results of the model for an ideal case of river flow and biofilm show that the organic removal rate and oxygen consumption rate caused by the biofilm are greater than that by suspended biomass. The effects of diffusion layer thickness, flow velocity, and biofilm thickness on the change of river water quality are discussed.

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