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.

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.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

scholarly journals Urban Flood Modeling Using 2D Shallow-Water Equations in Ouagadougou, Burkina Faso

Water ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 2120
Author(s):  
Gnenakantanhan Coulibaly ◽  
Babacar Leye ◽  
Fowe Tazen ◽  
Lawani Adjadi Mounirou ◽  
Harouna Karambiri
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Urban Areas ◽  
Flood Hazard ◽  
Scientific Information ◽  
Roughness Coefficient ◽  
Flood Events ◽  
African Countries ◽  
Numerical Tool ◽  
2D Shallow Water Equations

Appropriate methods and tools accessibility for bi-dimensional flow simulation leads to their weak use for floods assessment and forecasting in West African countries, particularly in urban areas where huge losses of life and property are recorded. To mitigate flood risks or to elaborate flood adaptation strategies, there is a need for scientific information on flood events. This paper focuses on a numerical tool developed for urban inundation extent simulation due to extreme tropical rainfall in Ouagadougou city. Two-dimensional (2D) shallow-water equations are solved using a finite volume method with a Harten, Lax, Van Leer (HLL) numerical fluxes approach. The Digital Elevation Model provided by NASA’s Shuttle Radar Topography Mission (SRTM) was used as the main input of the model. The results have shown the capability of the numerical tool developed to simulate flow depths in natural watercourses. The sensitivity of the model to rainfall intensity and soil roughness coefficient was highlighted through flood spatial extent and water depth at the outlet of the watershed. The performance of the model was assessed through the simulation of two flood events, with satisfactory values of the Nash–Sutcliffe criterion of 0.61 and 0.69. The study is expected to be useful for flood managers and decision makers in assessing flood hazard and vulnerability.

scholarly journals A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids

2014 ◽  
Vol 7 (3) ◽  
pp. 909-929 ◽  
Author(s):  
J. Thuburn ◽  
C. J. Cotter ◽  
T. Dubos
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Model Comparison ◽  
Mass Conservation ◽  
Time Discretization ◽  
Water Model ◽  
Tracer Transport ◽  
Exact Mass ◽  
Large Wave ◽  
Cubed Sphere

Abstract. A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

Development of a Novel Mixing Plane Interface Using a Fully Implicit Averaging for Stage Analysis

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Lucian Hanimann ◽  
Luca Mangani ◽  
Ernesto Casartelli ◽  
Thomas Mokulys ◽  
Sebastiano Mauri
Keyword(s):  
Mass Conservation ◽  
Solution Procedure ◽  
Algebraic Multigrid ◽  
Radial Compressor ◽  
Fully Implicit ◽  
Multigrid Solvers ◽  
Algorithm Stability ◽  
Speed Up ◽  
Stage Analysis ◽  
Development And Validation

This paper describes the development and validation steps of a characteristics-based explicit along with a novel fully implicit mixing plane implementation for turbomachinery applications. The framework is an unstructured 3D RANS in-house modified solver, based on open-source libraries. Particular attention was paid to mass-conservation, accurate variables interpolation, and algorithm stability in order to improve robustness and convergence. By introducing a specific interface, allowing the use of algebraic multigrid solvers together with multiprocessor computation, a speed up of the numerical solution procedure was achieved. The validation of both mixing plane algorithms is carried out on an industrial radial compressor and a cold air 1.5 stages axial turbine.

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 The Numerical Simulation of Shallow Water: Estimation of the Roughness Coefficient on the Flood Stage

2013 ◽  
Vol 5 ◽  
pp. 787016 ◽  
Author(s):  
Sergey S. Khrapov ◽  
Andrey V. Pisarev ◽  
Ivan A. Kobelev ◽  
Artur G. Zhumaliev ◽  
Ekaterina O. Agafonnikova ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Shallow Water ◽  
Roughness Coefficient
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