Hydraulic and Hydrologic Analysis of Unsteady Flow in Prismatic Open Channel

2018 ◽  
Author(s):  
Eugene Retsinis ◽  
Erna Daskalaki ◽  
Panos Papanicolaou
Keyword(s):  
Unsteady Flow ◽  
Open Channels ◽  
Finite Difference Schemes ◽  
Flow Conditions ◽  
Commercial Software ◽  
One Dimensional ◽  
Hydrologic Analysis ◽  
Dependent Variables ◽  
Implicit Finite Difference ◽  
Implicit Code

Comparison between hydraulic and hydrologic computational methods is conducted in this study, regarding prismatic open channels under unsteady subcritical flow conditions. One-dimensional unsteady flow continuity and momentum equations are solved using explicit and implicit finite difference schemes for a symmetrical trapezoidal cross section, where the flow discharge and depth are the dependent variables. The results have been compared to those derived from Muskingum-Cunge hydraulic/hydrologic method as well as the commercial software HEC-RAS. The results from explicit and implicit code compare well to those from commercial software and hydraulic/hydrologic methods for long prismatic channels, thus directing the hydraulic engineer to quick preliminary design of prismatic open channels for unsteady flow with satisfactory accuracy.

scholarly journals Hydraulic and Hydrologic Analysis of Unsteady Flow in Prismatic Open Channel

Proceedings ◽  
2018 ◽  
Vol 2 (11) ◽  
pp. 571 ◽  
Author(s):  
Eugene Retsinis ◽  
Erna Daskalaki ◽  
Panos Papanicolaou
Keyword(s):  
Unsteady Flow ◽  
Open Channels ◽  
Finite Difference Schemes ◽  
Flow Conditions ◽  
Commercial Software ◽  
One Dimensional ◽  
Hydrologic Analysis ◽  
Dependent Variables ◽  
Implicit Finite Difference ◽  
Implicit Code

Comparison between hydraulic and hydrologic computational methods is conducted in this study, regarding prismatic open channels under unsteady subcritical flow conditions. One-dimensional unsteady flow continuity and momentum equations are solved using explicit and implicit finite difference schemes for a symmetrical trapezoidal cross section, where the flow discharge and depth are the dependent variables. The results have been compared to those derived from Muskingum-Cunge hydraulic/hydrologic method as well as the commercial software HEC-RAS. The results from explicit and implicit code compare well to those from commercial software and hydraulic/hydrologic methods for long prismatic channels, thus directing the hydraulic engineer to quick preliminary design of prismatic open channels for unsteady flow with satisfactory accuracy.

ONE-DIMENSIONAL HYDRODYNAMIC MODEL SIMULATING WATER STAGE IN OPEN CHANNELS (WS-1)

2010 ◽  
Vol 01 (02) ◽  
pp. 303-316
Author(s):  
M. A. NASSAR
Keyword(s):  
Unsteady Flow ◽  
Hydrodynamic Model ◽  
Water Levels ◽  
Open Channels ◽  
Nile River ◽  
Improvement Project ◽  
One Dimensional ◽  
Water Stage ◽  
The Impact ◽  
Good Agreement

One-dimensional (1D) numerical model was developed to simulate water stage in open channels in order to suggest solutions for practical problems in the Nile River and its branches. The continuity and momentum equations describe the unsteady flow were solved using the finite difference technique. The developed model is verified using two types of data. The first type, simulating steady flow, is a field data collected at Elbogdady reach. It is a reach located 712.80 km upstream of Roda's staff gauge on the Nile River. The second type, simulating unsteady flow, is a result of the 1D SOBEK model. It is simulating the flow field at El-Mahrousa canal. It is one of El-Kanobia canal branches at 11.47 km left side, which is fed from El-Mahmoudia canal. Simplifications were made to simulate the flow patterns around the hydraulic structures using the developed hydrodynamic model. Actually, the water levels in many branch canals under continuous flow after implementation of Irrigation Improvement Project (IIP) need to be checked. The model could be applied to estimate the water stage under different abstraction values where some reaches of the Nile River and its branch suffering. In addition, it can be used to assess the impact of water allocation. Good agreement was observed between the model results and the field observations.

Transient Flow in Natural Gas Pipelines Using Implicit Finite Difference Schemes

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Jan Fredrik Helgaker ◽  
Bernhard Müller ◽  
Tor Ytrehus
Keyword(s):  
High Pressure ◽  
Natural Gas ◽  
Finite Difference ◽  
Difference Approximation ◽  
Finite Difference Schemes ◽  
Solution Strategy ◽  
One Dimensional ◽  
First Order ◽  
Backward Euler ◽  
Implicit Finite Difference

Transmission of natural gas through high pressure pipelines has been modeled by numerically solving the governing equations for one-dimensional compressible flow using implicit finite difference methods. In the first case the backward Euler method is considered using both standard first-order upwind and second-order centered differences for the spatial derivatives. The first-order upwind approximation, which is a one-sided approximation, is found to be unstable for CFL numbers less than 1, while the centered difference approximation is stable for any CFL number. In the second case a cell centered method is considered where flow values are calculated at the midpoint between grid points. This method is also stable for any CFL number. However, for a discontinuous change in inlet temperature, the method is observed to introduce unphysical oscillations in the temperature profile along the pipeline. A solution strategy where the hydraulic and thermal models are solved separately using different discretization techniques is suggested. Such a solution strategy does not introduce unphysical oscillations for discontinuous changes in inlet boundary conditions and is found to be stable for any CFL number. The one-dimensional flow model is validated using operational data from a high pressure natural gas pipeline.

scholarly journals One-dimensional finite difference schemes for splitting method realization in axisymmetric equations of the dynamics of elastic medium

2021 ◽  
pp. 47-66
Author(s):  
В.М. Садовский ◽  
О.В. Садовская ◽  
Е.А. Ефимов
Keyword(s):  
Energy Dissipation ◽  
Finite Difference ◽  
Splitting Method ◽  
Finite Difference Schemes ◽  
Computing Systems ◽  
One Dimensional ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Comparison Of The Results ◽  
Predictor Corrector

Строятся экономичные разностные схемы сквозного счета для решения прямых задач сейсмики в осесимметричной постановке. При распараллеливании алгоритмов, реализующих схемы на многопроцессорных вычислительных системах, применяется метод двуциклического расщепления по пространственным переменным. Одномерные системы уравнений на этапах расщепления решаются на основе явных сеточно-характеристических схем и неявной разностной схемы типа "предиктор-корректор" с контролируемой искусственной диссипацией энергии. Верификация алгоритмов и программ выполнена на точных решениях одномерных задач типа бегущих монохроматических волн. Сравнение результатов показало неоспоримые преимущества схемы с контролируемой диссипацией энергии по точности расчета гладких решений и целесообразность применения явных монотонных схем при расчете разрывов. We construct efficient finite difference shock-capturing schemes for the solution of direct seismic problems in axisymmetric formulation. When parallelizing the algorithms implementing the schemes on multiprocessor computing systems, the two-cyclic splitting method with respect to the spatial variables is used. One-dimensional systems of equations are solved at the stages of splitting on the basis of explicit gridcharacteristic schemes and an implicit finite difference scheme of the “predictor–corrector” type with controllable artificial energy dissipation. The verification of algorithms and programs is fulfilled on the exact solutions of one-dimensional problems describing traveling monochromatic waves. The comparison of the results showed the advantages of the scheme with controllable energy dissipation in terms of the accuracy of computing smooth solutions and the advisability of application of explicit monotone schemes when calculating discontinuities.

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

Sign in / Sign up

Export Citation Format

Share Document