scholarly journals Hydraulic Transient Analysis of Sewer Pipe Systems Using a Non-Oscillatory Two-Component Pressure Approach

Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2896
Author(s):  
David Khani ◽  
Yeo Howe Lim ◽  
Ahmad Malekpour
Keyword(s):  
Numerical Scheme ◽  
Transient Flow ◽  
Numerical Results ◽  
Test Cases ◽  
Computational Cell ◽  
Transient Flows ◽  
Numerical Viscosity ◽  
Proposed Model ◽  
Two Component ◽  
Numerical Oscillations

On the basis of the two-component pressure approach, we developed a numerical model to capture mixed transient flows in close conduit systems. To achieve this goal, an innovative Godunov finite-volume numerical scheme is proposed to suppress the spurious numerical oscillations occurring during rapid pipe pressurization. To dissipate the spurious numerical oscillations, we admit artificial numerical viscosity to the numerical scheme through applying a proposed Harten, Lax, and van Leer (HLL) Riemann solver for calculating the numerical fluxes at the computational cell interfaces. The proposed solver controls the magnitude of the numerical viscosity through adjusting the left and right wave velocities. A wave velocity calculator is proposed to optimally distribute the numerical viscosity over several computational cells around the computational cell in which the pressurization front is located. The proposed solver admits significant artificial numerical viscosity when the pipe pressurization is imminent and automatically reduces it in other places; in this way the numerical diffusion and data smearing is minimized. The validity of the proposed model is justified by the aid of several test cases in which the numerical results are compared with both experimental data and the results obtained from analytical methods. The results reveal that the proposed model succeeds in completely removing the spurious numerical oscillations, even when the pipe acoustic speed is over 1000 m/s. The numerical results also show that the model can successfully capture occurrence of negative pressures during the course of transient flow.

Development and Validation of a Highly Nonlinear Model for Wave Propagation Over a Variable Bathymetry

2015 ◽  
Author(s):  
Maïté Gouin ◽  
Guillaume Ducrozet ◽  
Pierre Ferrant
Keyword(s):  
Wave Propagation ◽  
Nonlinear Model ◽  
Numerical Scheme ◽  
High Order ◽  
Numerical Results ◽  
Test Case ◽  
Test Cases ◽  
Highly Nonlinear ◽  
Propagating Waves ◽  
Development And Validation

Liu and Yue [1] developed a numerical scheme for propagating waves over a variable bathymetry with a High-Order Spectral (HOS) Method. The development of this nonlinear model is detailed and validated on three different test cases. They intend to demonstrate that such a model may be applied to small bottom variations as considered in [1] but also on cases where the bottom variation may be important. In this concern, the very well documented test case of a 2D underwater bar is studied in details. Comparisons are provided with both experimental and numerical results.

Influence of velocity head on filling transients in a branched pipeline

2018 ◽  
Vol 35 (7) ◽  
pp. 2502-2513 ◽  
Author(s):  
Ling Wang ◽  
Fujun Wang ◽  
Bryan William Karney ◽  
Ahmad Malekpour ◽  
Zhengwei Wang
Keyword(s):  
Method Of Characteristics ◽  
Energy Equation ◽  
Transient Flow ◽  
Numerical Results ◽  
Velocity Head ◽  
Piezometric Head ◽  
Content Type ◽  
High Point ◽  
Hydraulic Transient ◽  
Column Separation

Purpose The velocity head is usually neglected in the energy equation for a pipeline junction when one-dimensional (1D) hydraulic transient flow is solved by method of characteristics. The purpose of this paper is to investigate the effect of velocity head on filling transients in a branched pipeline by an energy equation considering velocity head. Design/methodology/approach An interface tracking method is used to locate the air–water interface during pipeline filling. The pressured pipe flow is solved by a method of characteristics. A discrete gas cavity model is included to permit the occurrence of column separation. A universal energy equation is built by considering the velocity head. The numerical method is provisionally verified in a series pipeline and the numerical results and experimental data accord well with each other. Findings The numerical results show that some differences in filling velocity and piezometric head occur in the branched pipeline. These differences arise because the velocity head in the energy equation can become an important contributor to the hydraulic response of the system. It is also confirmed that a local high point in the profile is apt to experience column separation during rapid filling. Significantly, the magnitude of overpressure and cavity volume induced by filling transients at the local high point is predicted to increase with the velocity in the pipes. Originality/value The velocity head in the energy equation for a pipeline junction could play an important role in the prediction of filling velocity, piezometric head and column separation phenomenon, which should be given more attention in 1D hydraulic transient analysis.

scholarly journals Splitting-particle methods for structured population models: Convergence and applications

2014 ◽  
Vol 24 (11) ◽  
pp. 2171-2197 ◽  
Author(s):  
J. A. Carrillo ◽  
P. Gwiazda ◽  
A. Ulikowska
Keyword(s):  
Numerical Scheme ◽  
Order Of Convergence ◽  
Operator Splitting ◽  
Population Models ◽  
Particle Simulation ◽  
Particle Methods ◽  
Test Cases ◽  
Structured Population Models ◽  
Convergence Error ◽  
Structured Population

We propose a new numerical scheme designed for a wide class of structured population models based on the idea of operator splitting and particle approximations. This scheme is related to the Escalator Boxcar Train (EBT) method commonly used in biology, which is in essence an analogue of particle methods used in physics. Our method exploits the split-up technique, thanks to which the transport step and the nonlocal integral terms in the equation can be separately considered. The order of convergence of the proposed method is obtained in the natural space of finite non-negative Radon measures equipped with the flat metric. This convergence is studied even adding reconstruction and approximation steps in the particle simulation to keep the number of approximation particles under control. We validate our scheme in several test cases showing the theoretical convergence error. Finally, we use the scheme in situations in which the EBT method does not apply showing the flexibility of this new method to cope with the different terms in general structured population models.

scholarly journals Analysis of a Four-Dimensional Hyperchaotic System Described by the Caputo–Liouville Fractional Derivative

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Ndolane Sene
Keyword(s):  
Fractional Derivative ◽  
Financial Market ◽  
Numerical Scheme ◽  
Hyperchaotic System ◽  
Financial Model ◽  
Investment Demand ◽  
Proposed Model ◽  
Liouville Fractional Derivative ◽  
The Interest Rate ◽  
The Stability

A new four-dimensional hyperchaotic financial model is introduced. The novelties come from the fractional-order derivative and the use of the quadric function x 4 in modeling accurately the financial market. The existence and uniqueness of its solutions have been investigated to justify the physical adequacy of the model and the numerical scheme proposed in the resolution. We offer a numerical scheme of the new four-dimensional fractional hyperchaotic financial model. We have used the Caputo–Liouville fractional derivative. The problems addressed in this paper have much importance to approach the interest rate, the investment demand, the price exponent, and the average profit margin. The validation of the chaotic, hyperchaotic, and periodic behaviors of the proposed model, the bifurcation diagrams, the Lyapunov exponents, and the stability analysis has been analyzed in detail. The proposed numerical scheme for the hyperchaotic financial model is destined to help the agents decide in the financial market. The solutions of the 4D fractional hyperchaotic financial model have been analyzed, interpreted theoretically, and represented graphically in different contexts. The present paper is mathematical modeling and is a new tool in economics and finance. We also confirm, as announced in the literature, there exist hyperchaotic systems in the fractional context, which admit one positive Lyapunov exponent.

scholarly journals Numerical assessment of bed-load discharge formulations for transient flow in 1D and 2D situations

2013 ◽  
Vol 15 (4) ◽  
pp. 1234-1257 ◽  
Author(s):  
Carmelo Juez ◽  
Javier Murillo ◽  
Pilar García-Navarro
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Scheme ◽  
Transient Flow ◽  
Morphological Evolution ◽  
Bed Load ◽  
Steady Flows ◽  
Numerical Experimentation ◽  
Load Discharge ◽  
Hydrodynamic Situation

Two-dimensional (2D) transient flow over an erodible bed can be modelled using shallow-water equations and the Exner equation to describe the morphological evolution of the bed. Considering the fact that well-proven capacity formulae are based on one-dimensional (1D) experimental steady flows, the assessment of these empirical relations under unsteady 1D and 2D situations is important. In order to ensure the reliability of the numerical experimentation, the formulation has to be general enough to allow the use of different empirical laws. Moreover, the numerical scheme must handle correctly the coupling between the 2D shallow-water equations and the Exner equation under any condition. In this work, a finite-volume numerical scheme that includes these two main features will be exploited here in 1D and 2D laboratory test cases. The relative performances of Meyer-Peter and Müller, Ashida and Michiue, Engelund and Fredsoe, Fernandez Luque and Van Beek, Parker, Smart, Nielsen, Wong and Camenen and Larson formulations are analysed in terms of the root mean square error. A new discretization of the Smart formula is provided, leading to promising predictions of the erosion/deposition rates. The results arising from this work are useful to justify the use of an empirical sediment bed-load discharge formula among the ones studied, regardless of the hydrodynamic situation.

A New Force-Displacement Model for Continuous Indentation of Bilayer Materials

2001 ◽  
Vol 695 ◽  
Author(s):  
A. Nayebi ◽  
R. El Abdi ◽  
G. Mauvoisin ◽  
O. Bartier
Keyword(s):  
Flow Stress ◽  
Strain Hardening ◽  
Indentation Load ◽  
Numerical Results ◽  
Stress And Strain ◽  
Proposed Model ◽  
Displacement Model ◽  
Force Displacement ◽  
Continuous Indentation

ABSTRACTA new relationship between indentation load and depth in relation to flow stress and strain hardening exponents of film and substrate of bilayers is given. The comparison between the numerical results and those experimentally obtained from known materials, confirms the interest of the proposed model for film characterization of these materials.

scholarly journals A 2D HLL-based weakly coupled model for transient flows on mobile beds

2020 ◽  
Vol 22 (5) ◽  
pp. 1351-1369
Author(s):  
Robin Meurice ◽  
Sandra Soares-Frazão
Keyword(s):  
Numerical Models ◽  
Morphological Evolution ◽  
Coupled Model ◽  
Dam Break ◽  
Water Levels ◽  
Test Cases ◽  
Transient Flows ◽  
Dam Breaks ◽  
Weakly Coupled ◽  
High Interaction

Abstract We propose a finite-volume model that aims at improving the ability of 2D numerical models to accurately predict the morphological evolution of sandy beds when subjected to transient flows like dam-breaks. This model solves shallow water and Exner equations with a weakly coupled approach while the fluxes at the interfaces of the cells are calculated thanks to a lateralized HLLC flux scheme. Besides describing the model, we ran it for four different test cases: a steady flow on an inclined bed leading to aggradation or degradation, a dam-break leading to high interaction between the flow and the bed, a dam-break with a symmetrical enlargement close to the gate and a dam-break in a channel with a 90° bend. The gathered results are discussed and compared to an existing fully coupled approach based on HLLC fluxes. Although both models equally perform regarding water levels, the weakly coupled model looks to better predict the bed evolution for the four test cases. In particular, its results are not affected by an excessive numerical diffusion encountered by the coupled model. Moreover, it usually better estimates the amplitudes of the maximum deposits and scours. It is also more stable when subject to high bed–flow interaction.

Nonlinear Numerical Simulation on Galloping of Twin Bundle Conductor Considering the Wake Effect

2012 ◽  
Vol 614-615 ◽  
pp. 1390-1393
Author(s):  
Xue Ping Zhan ◽  
Ya Duo Liu ◽  
Bin Liu ◽  
Kuan Jun Zhu
Keyword(s):  
Numerical Results ◽  
Windward Side ◽  
Leeward Side ◽  
Wake Effect ◽  
Aerodynamic Parameter ◽  
Aerodynamic Loads ◽  
Runge Kutta Method ◽  
Proposed Model ◽  
Actual Movement ◽  
Nonlinear Numerical Simulation

In this paper, the models of the multi-bundled conductors are constructed by finite element method. The wake effect of aerodynamic parameter of sub-conductor of the windward side relative to the leeward side is studied. The numerical results are given by using the 4th order Runge-Kutta method. Similarly, the proposed model can be added to the different aerodynamic loads on each individual sub-conductor of a bundle conductor during the simulation of galloping. Thus the numerical results are much closer to the actual movement of galloping and provide a useful reference for anti-galloping.

A new and efficient procedure for dispersive tsunami simulations on spherical coordinates based on a hyperbolic approach

2020 ◽  
Author(s):  
Cipriano Escalante Sanchez ◽  
Manuel J. Castro Díaz ◽  
José Manuel González Vida ◽  
Jorge Macías Sánchez ◽  
Stefano Lorito ◽  
...  
Keyword(s):  
Hydrostatic Pressure ◽  
Water Waves ◽  
Numerical Scheme ◽  
Applied Mathematics ◽  
Computational Effort ◽  
Numerical Results ◽  
Spherical Coordinates ◽  
Tsunami Propagation ◽  
Time Step ◽  
Curvature Effects

<p>When tsunamigenic events are simulated in deep to moderately deep waters, frequency dispersion effects may become mandatory. In the framework of dispersive systems, non-hydrostatic pressure type models have been shown to be able to describe weakly dispersive waves [2,3]. Although promising results begin to glimpse nowadays, dispersive solvers are still far from being robust, efficient and able to compute on a faster than real-time (FTRT) basis. The main difficulty that presents this type of systems is that at each time step a parabolic-elliptic problem has to be numerically solved and a high computational effort is required.</p><p>In [1] a novel weakly non-linear and weakly dispersive system that takes into account dispersive effects is presented. The main advantage is that the system is strictly hyperbolic and that any explicit numerical scheme can be applied to solve numerically the equations.</p><p>We will present new numerical results from an upgrade of the system presented in [1], considering curvature effects through a rewriting of the system in spherical coordinates. The numerical results will cover some standard field validation tests involving tsunami propagation waves. Besides, the explicit numerical scheme has been implemented exploiting the power of modern GPU architectures (CUDA). Then, numerical results along with some computational times will show that this numerical model opens a new line on tsunami simulation scenarios, using a new, efficient and accurate procedure to produce FTRT tsunami propagation including dispersive effects.</p><p>Acknowledgments: This research has been partially supported by the Spanish Government Research project MEGAFLOW (RTI2018-096064-B-C21), Universidad de Málaga, Campus de Excelencia Internacional Andalucía Tech and ChEESE project (EU Horizon 2020, grant agreement Nº 823844), https://cheese-coe.eu</p><p>[1] C. Escalante, M. Dumbser, M. Castro, An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution<br>with high order discontinuous galerkin schemes, Journal of Computational Physics 394 (2019) 385 – 416.</p><p>[2] C. Escalante, T. Morales, M. Castro, Non-hydrostatic pressure shallow flows: Gpu implementation using finite volume and finite difference<br>scheme, Applied Mathematics and Computation (2018) 631–659.</p><p>[3] Y. Yamazaki, Z. Kowalik, K. Cheung, Depth-integrated, non-hydrostatic model for wave breaking and run-up, Numerical Methods in Fluids<br>61 (2008) 473–497.</p>

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