Characteristics method with cubic-spline interpolation for open channel flow computation

2004 ◽  
Vol 46 (6) ◽  
pp. 663-683 ◽  
Author(s):  
Tung-Lin Tsai ◽  
Shih-Wei Chiang ◽  
Jinn-Chuang Yang
Keyword(s):  
Channel Flow ◽  
Open Channel ◽  
Spline Interpolation ◽  
Open Channel Flow ◽  
Cubic Spline ◽  
Cubic Spline Interpolation ◽  
Flow Computation ◽  
Characteristics Method

On the Use of Temporal Reachout Technique for Characteristics Method with Time-Line Cubic Spline Interpolation

2011 ◽  
Vol 27 (2) ◽  
pp. N5-N11 ◽  
Author(s):  
T.-L. Tsai ◽  
J.-Y. Chen
Keyword(s):  
Spline Interpolation ◽  
Cubic Spline ◽  
Higher Order ◽  
Difference Approximation ◽  
Central Difference ◽  
Time Line ◽  
Cubic Spline Interpolation ◽  
First Derivative ◽  
Characteristics Method ◽  
Simulation Results

ABSTRACTThe study had indicated that the computational performances of the characteristics method with the time-line cubic spline interpolation are related to the endpoint constraint, especially for large Courant number in which the foot of the characteristic trajectory is located near the endpoint. The first derivative endpoint constraint with higher-order central difference approximation provides better simulation results among various endpoint constraints, but it still induces some degree of numerical error. In this study, by locating the foot of the characteristic trajectory away from the endpoint, the temporal reachout technique is proposed to avoid the effect of endpoint constraint on the time-line cubic spline interpolation. Modeling the transport of a Gaussian concentration distribution in a uniform flow with constant diffusion coefficient and the viscous Burgers equation is used to examine the temporal reachout technique. The outcomes show that the temporal reachout technique yields much better simulation results than the first derivative endpoint constraint with higher-order central difference approximation. The effect of endpoint constraint on the time-line cubic spline interpolation can be greatly diminished by the use of the temporal reachout technique.

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.

Sign in / Sign up

Export Citation Format

Share Document