Hybrid finite analytic solutions of shallow water circulation

2003 ◽  
Vol 24 (9) ◽  
pp. 1081-1088 ◽  
Author(s):  
Huai Wen-xin ◽  
Y. Peter Sheng ◽  
T. Komatsu
Keyword(s):  
Shallow Water ◽  
Analytic Solutions ◽  
Water Circulation

Shallow-water circulation on the northern coast of Rio Grande do Sul, Brazil: A wave-dominated system

2021 ◽  
pp. 101973
Author(s):  
Mauro Michelena Andrade ◽  
Elírio E. Toldo ◽  
Pedro Veras Guimarães ◽  
Nicolas de Assis Bose
Keyword(s):  
Shallow Water ◽  
Rio Grande ◽  
Water Circulation ◽  
Northern Coast ◽  
Rio Grande Do Sul

scholarly journals A Weighted-Least-Squares Meshless Model for Non-Hydrostatic Shallow Water Waves

Water ◽  
2021 ◽  
Vol 13 (22) ◽  
pp. 3195
Author(s):  
Nan-Jing Wu ◽  
Yin-Ming Su ◽  
Shih-Chun Hsiao ◽  
Shin-Jye Liang ◽  
Tai-Wen Hsu
Keyword(s):  
Least Squares ◽  
Shallow Water ◽  
Water Waves ◽  
Dynamic Pressure ◽  
Weighted Least Squares ◽  
Shallow Water Equation ◽  
Analytic Solutions ◽  
Numerical Results ◽  
Benchmark Problems ◽  
Time Marching

In this paper, an explicit time marching procedure for solving the non-hydrostatic shallow water equation (SWE) problems is developed. The procedure includes a process of prediction and several iterations of correction. In these processes, it is essential to accurately calculate the spatial derives of the physical quantities such as the temporal water depth, the average velocities in the horizontal and vertical directions, and the dynamic pressure at the bottom. The weighted-least-squares (WLS) meshless method is employed to calculate these spatial derivatives. Though the non-hydrostatic shallow water equations are two dimensional, on the focus of presenting this new time marching approach, we just use one dimensional benchmark problems to validate and demonstrate the stability and accuracy of the present model. Good agreements are found in the comparing the present numerical results with analytic solutions, experiment data, or other numerical results.

Models of non-Boussinesq lock-exchange flow

2011 ◽  
Vol 675 ◽  
pp. 1-26 ◽  
Author(s):  
R. ROTUNNO ◽  
J. B. KLEMP ◽  
G. H. BRYAN ◽  
D. J. MURAKI
Keyword(s):  
Free Boundary ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Water System ◽  
Analytic Solutions ◽  
Analytical Models ◽  
Navier Stokes ◽  
Exchange Flow

Nearly all analytical models of lock-exchange flow are based on the shallow-water approximation. Since the latter approximation fails at the leading edges of the mutually intruding fluids of lock-exchange flow, solutions to the shallow-water equations can be obtained only through the specification of front conditions. In the present paper, analytic solutions to the shallow-water equations for non-Boussinesq lock-exchange flow are given for front conditions deriving from free-boundary arguments. Analytic solutions are also derived for other proposed front conditions – conditions which appear to the shallow-water system as forced boundary conditions. Both solutions to the shallow-water equations are compared with the numerical solutions of the Navier–Stokes equations and a mixture of successes and failures is recorded. The apparent success of some aspects of the forced solutions of the shallow-water equations, together with the fact that in a real fluid the density interface is a free boundary, shows the need for an improved theory of lock-exchange flow taking into account non-hydrostatic effects for density interfaces intersecting rigid boundaries.

A combined computational algorithm for solving the problem of long surface waves runup on the shore

2016 ◽  
Vol 31 (4) ◽  
Author(s):  
Yurii I. Shokin ◽  
Alexander D. Rychkov ◽  
Gayaz S. Khakimzyanov ◽  
Leonid B. Chubarov
Keyword(s):  
Numerical Simulation ◽  
Shallow Water ◽  
Nonlinear Waves ◽  
Laboratory Experiments ◽  
Computational Algorithm ◽  
Analytic Solutions ◽  
Shallow Water Theory ◽  
Sph Method ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear

AbstractIn the present paper we study features and abilities of the combined TVD+SPH method relative to problems of numerical simulation of long waves runup on a shore within the shallow water theory. The results obtained by this method are compared to analytic solutions and to the data of laboratory experiments. Examples of successful application of the TVD+SPH method are presented for the case of study of runup processes for weakly nonlinear and strongly nonlinear waves, and also for

scholarly journals Validation of Depth-Averaged Flow Model Using Flat-Bottomed Benchmark Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Il Won Seo ◽  
Young Do Kim ◽  
Chang Geun Song
Keyword(s):  
Shallow Water ◽  
Mass Conservation ◽  
Analytic Solutions ◽  
Benchmark Problems ◽  
Roughness Coefficient ◽  
Spanwise Direction ◽  
Clear Trend ◽  
Recirculating Flow ◽  
Fully Implicit ◽  
Algorithmic Approaches

In this study, a shallow water flow code was developed and tested against four benchmark problems of practical relevance. The results demonstrated that as the eddy viscosity increased, the velocity slope along the spanwise direction decreased, and the larger roughness coefficient induced a higher flow depth over the channel width. The mass conservation rate was determined to be 99.2%. This value was measured by the variation of the total volume of the fluid after a cylinder break. As the Re increased to 10,000 in the internal recirculating flow problem, the intensity of the primary vortex had a clear trend toward the theoretically infinite Re value of −1.886. The computed values of the supercritical flow evolved by the oblique hydraulic jump agreed well with the analytic solutions within an error bound of 0.2%. The present model adopts the nonconservative form of shallow water equations. These equations are weighted by the SU/PG scheme and integrated by a fully implicit method, which can reproduce physical problems with various properties. The model provides excellent results under various flow conditions, and the solutions of benchmark tests can present criteria for the evaluation of various algorithmic approaches.

Streaming of fluid under a near-bottom membrane

1983 ◽  
Vol 137 ◽  
pp. 385-392 ◽  
Author(s):  
H. Allison
Keyword(s):  
Shallow Water ◽  
Theoretical Basis ◽  
Pressure Head ◽  
Water Circulation ◽  
Closed Circuit ◽  
Total Flow ◽  
Flexible Membrane ◽  
Steady Streaming ◽  
Wave Basin ◽  
Low Efficiency

Experiments are described which show the steady streaming of fluid under a flexible membrane, located near the bottom of a wave basin in shallow water. Circulation of fluid in a closed circuit was thus obtained, and measurements were made of the pressure head and total flow. The phenomenon might be used to extract power from waves at very low efficiency, but the theoretical basis is not yet understood.

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