scholarly journals BORE FRONT MODELING IN TERMS OF BURGERS EQUATION AND ITS NUMERICAL CALCULATION METHOD

1988 ◽  
Vol 1 (21) ◽  
pp. 192
Author(s):  
Takao Yamashita ◽  
Yoshito Ysuchiya ◽  
David R. Basco
Keyword(s):  
Numerical Calculation ◽  
Water Surface ◽  
Open Channel ◽  
Burgers Equation ◽  
Equation System ◽  
Diffusion Term ◽  
One Dimensional ◽  
The One ◽  
Numerical Calculation Method ◽  
Front Dynamics

Bore front hydraulics are investigated in terms of Burgers equation to clarify the dynamics of a moving discontinuity in water flow. Burgers equation has been derived from the one dimensional open channel equation with the horizontal turbulent diffusion term. The derived equation system consists of Burgers with respect to dynamic characteristic and hyperbolic equation with respect to water surface elevation, which satisfys Jeffery-Vedernikov condition FT — 2 through discontinuity. It has been verified from the experiments that the condition FT = 2 is a good approximation of bore front dynamics. The numercal calulation method of Burgers equation employing Cole-Hopf transformation and QUICKEST algorithm was also proposed and confirmed its efficiency.

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

scholarly journals Exact statistical properties of the Burgers equation

2000 ◽  
Vol 417 ◽  
pp. 323-349 ◽  
Author(s):  
L. FRACHEBOURG ◽  
Ph. A. MARTIN
Keyword(s):  
White Noise ◽  
Large Distance ◽  
Burgers Equation ◽  
Higher Order ◽  
Statistical Properties ◽  
Inviscid Limit ◽  
Initial Condition ◽  
Spatial Correlations ◽  
One Dimensional ◽  
The One

The one-dimensional Burgers equation in the inviscid limit with white noise initial condition is revisited. The one- and two-point distributions of the Burgers field as well as the related distributions of shocks are obtained in closed analytical forms. In particular, the large distance behaviour of spatial correlations of the field is determined. Since higher-order distributions factorize in terms of the one- and two- point functions, our analysis provides an explicit and complete statistical description of this problem.

REACTION-FRONT DYNAMICS IN A+B→C WITH INITIALLY-SEPARATED REACTANTS

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 405-415 ◽  
Author(s):  
S. HAVLIN ◽  
M. ARAUJO ◽  
H. LARRALDE ◽  
A. SHEHTER ◽  
H.E. STANLEY
Keyword(s):  
Reaction Front ◽  
Reaction Rate ◽  
Reaction System ◽  
Diffusion Reaction ◽  
Dimensional System ◽  
Scaling Exponent ◽  
One Dimensional ◽  
Recent Developments ◽  
The One ◽  
Front Dynamics

We review recent developments in the study of the diffusion reaction system of the type A+B→C in which the reactants are initially separated. We consider the case where the A and B particles are initially placed uniformly in Euclidean space at x>0 and x<0 respectively. We find that whereas for d≥2 a single scaling exponent characterizes the width of the reaction zone, a multiscaling approach is needed to describe the one-dimensional system. We also present analytical and numerical results for the reaction rate on fractals and percolation systems.

scholarly journals Numerical Analysis of Soil Settlement Prediction and Its Application In Large-Scale Marine Reclamation Artificial Island Project

2017 ◽  
Vol 24 (s3) ◽  
pp. 4-11 ◽  
Author(s):  
Jie Zhao ◽  
Lingyun Bao ◽  
Guixuan Wang
Keyword(s):  
Numerical Calculation ◽  
Numerical Analysis ◽  
Large Scale ◽  
Structural Characteristics ◽  
Silty Clay ◽  
Two Dimensional ◽  
Analysis Method ◽  
One Dimensional ◽  
Soil Settlement ◽  
Numerical Calculation Method

Abstract In an artificial island construction project based on the large-scale marine reclamation land, the soil settlement is a key to affect the late safe operation of the whole field. To analyze the factors of the soil settlement in a marine reclamation project, the SEM method in the soil micro-structural analysis method is used to test and study six soil samples such as the representative silt, mucky silty clay, silty clay and clay in the area. The structural characteristics that affect the soil settlement are obtained by observing the SEM charts at different depths. By combining numerical calculation method of Terzaghi’s one-dimensional and Biot’s two-dimensional consolidation theory, the one-dimensional and two-dimensional creep models are established and the numerical calculation results of two consolidation theories are compared in order to predict the maximum settlement of the soils 100 years after completion. The analysis results indicate that the micro-structural characteristics are the essential factor to affect the settlement in this area. Based on numerical analysis of one-dimensional and two-dimensional settlement, the settlement law and trend obtained by two numerical analysis method is similar. The analysis of this paper can provide reference and guidance to the project related to the marine reclamation land.

scholarly journals Observation of broad-band water waveguiding in shallow water: a revival

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Fabián Sepúlveda-Soto ◽  
Diego Guzmán-Silva ◽  
Edgardo Rosas ◽  
Rodrigo A. Vicencio ◽  
Claudio Falcón
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Open Channel ◽  
Fluid Layer ◽  
Broad Band ◽  
Shallow Water Waves ◽  
One Dimensional ◽  
The One ◽  
Complex Phenomena

Abstract We report on the observation and characterization of broad-band waveguiding of surface gravity waves in an open channel, in the shallow water limit. The waveguide is constructed by changing locally the depth of the fluid layer, which creates conditions for surface waves to propagate along the generated guide. We present experimental and numerical results of this shallow water waveguiding, which can be straightforwardly matched to the one-dimensional water wave equation of shallow water waves. Our work revitalizes water waveguiding research as a relevant and controllable experimental setup to study complex phenomena using waveguide geometries.

Comparison of two numerical methods for the integration of the Takagi–Taupin equations

1981 ◽  
Vol 14 (6) ◽  
pp. 432-436 ◽  
Author(s):  
C. Nourtier ◽  
D. Taupin
Keyword(s):  
Numerical Calculation ◽  
Numerical Methods ◽  
Two Dimensions ◽  
Integration Step ◽  
Order Method ◽  
Third Order ◽  
Acta Cryst ◽  
One Dimensional ◽  
Numerical Resolution ◽  
The One

Two methods for the numerical resolution of the Takagi-Taupin equations are compared. It is shown that for a small integration step Taupin's [Acta Cryst. (1967), 23, 25–35] extension to two dimensions of the one-dimensional Runge–Kutta third-order method is more accurate than the algorithm of Authier, Malgrange & Tournarie [Acta Cryst. (1968), A24, 126–136] but, for a given precision, Authier, Malgrange & Tournarie's method is faster than Taupin's so the former will usually be preferred for numerical calculation.

An Improved Water Surface Images Segmentation Algorithm Based on the Otsu Method

2020 ◽  
Vol 29 (15) ◽  
pp. 2050251
Author(s):  
Ning Li ◽  
Xin Lv ◽  
Shoukun Xu ◽  
Bo Li ◽  
Yuwan Gu
Keyword(s):  
Water Surface ◽  
Evaluation Method ◽  
Threshold Method ◽  
Threshold Segmentation ◽  
One Dimensional ◽  
Otsu Method ◽  
Segmentation Accuracy ◽  
Surface Image ◽  
Performance Evaluation Method ◽  
The One

The one-dimensional Otsu method is an adaptive threshold method. It obtains the optimal threshold for image segmentation by the maximum between-class variance, without considering the minimum within-class variance. As the background of water surface image is mostly uniform, using this feature, the threshold selection tactics adopt the combination of the one-dimensional Otsu method and the uniformity measurement, proposes the threshold segmentation method based on uniformity measurement, and adopts the performance evaluation method based on GT image to compare the segmentation result. Experimental results demonstrate that effectiveness of the improved Otsu method is generally better than the traditional Otsu method, and the other four commonly used threshold segmentation methods for the water surface image, which improves the segmentation accuracy of such images and reduces the segmentation error rate. At the same time, as the water surface image is usually affected by light intensity, water ripple and other factors, this paper also adopts the relevant correction algorithm to further improve the segmentation accuracy.

Sign in / Sign up

Export Citation Format

Share Document