Finite Element Solution of Saint-Venant Equations

Cooley, Richard L.; Moin, Syed Afaq

doi:10.1061/jyceaj.0004556

Cited by 53 publications

(9 citation statements)

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“…These parameters are ∅ Figs. (5) and (6) show the effect of different values of ∅ on the results obtained by the simulation model, respectively. The comparison illustrated in these figures between the calculated and observed values indicates that the appropriate value ∅…”

Section: Results and Analysismentioning

confidence: 99%

“…The basic flow equations mathematically describing unsteady river flow are the continuity equation, derived from the principle of conservation of mass, and momentum equation, derived from the principle of conservation of momentum. The derivation details of Saint-Venant equations may be found in standard works of hydraulics [2,5].…”

Section: Theoretical Conceptsmentioning

confidence: 99%

“…For the purpose of keeping the calculations simple, the linear shape function was selected, and the time cost will be minimal. If a function defined as y(x, t) (or y for simplicity) was assumed to be linearly varied in the elements forming the flow field, the following relationship results [2,5]:…”

Section: Numerical Solutionmentioning

confidence: 99%

“…Flow in streams is seldom steady, the mathematical model derived from the continuity and the momentum, the Saint-Venant equations, can simulate the gradually varied unsteady flow in a river reach. These are generally expressed as one-dimensional nonlinear partial differential equations [4,5]. There is no analytical solution for these equations, so numerous finite difference methods have been developed for solving these equations using different schemes and approaches [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Finite Element Modeling Of Saint-Venant Equations For Shatt-Al Hilla

Abed

2020

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Shatt Al-Hilla was considered one of the important branches of Euphrates River that supplies irrigation water to millions of dunams of planted areas. It is important to control the velocity and water level along the river to maintain the required level for easily diverting water to the branches located along the river. So, in this research, a numerical model was developed to simulate the gradually varied unsteady flow in Shatt AL-Hilla. The present study aims to solve the continuity and momentum (Saint-Venant) equations numerically to predict the hydraulic characteristics in the river using Galerkin finite element method. A computer program was designed and built using the programming language FORTRAN-77. Fifty kilometers was considered starting from downstream of Hindiyah Barrage towards Hilla City. The gathered field measurements along different periods were used for the purpose of calibration and verification of the model. The results show that the suitable Manning roughness was 0.023. A comparison with field observations was conducted to identify the validity of the numerical solution of the flow equations. The obtained results indicate the feasibility of the numerical techniques using a weighting factor of 0.667 and a time increment of 6 hr. High accuracy and good agreement were achieved, and minimum Root Mean Square Error (RMSE) of 0.029 was gained for the obtained results compared with the corresponding field observations.

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Section: Results and Analysismentioning

confidence: 99%

Section: Theoretical Conceptsmentioning

confidence: 99%

Section: Numerical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite Element Modeling Of Saint-Venant Equations For Shatt-Al Hilla

Abed

2020

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“…By moving away from this area, the stress decreases, and a stress jump occurs. Based on the principle of the Saint-Venant, by going far away from the heat source region, the effects of stress concentration disappear and start to stabilize throughout the tissue after a particular period [62]. Due to the energy equation, the average Von Mises stress in the contact line between tumor and healthy tissue approaches a steady state at around 100 s, as shown in Fig.…”

Section: ) Von Mises Stress Distributionmentioning

confidence: 99%

Thermomechanical Modeling of Laser Ablation Therapy of Tumors: Sensitivity Analysis and Optimization of Influential Variables

Mohammadi

Bianchi

Korganbayev

et al. 2022

IEEE Trans. Biomed. Eng.

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In cancer treatment, laser ablation is a promising technique used to induce localized thermal damage. Different variables influence the temperature distribution in the tissue and the resulting therapy efficacy; thus, the optimal therapy settings are required for obtaining the desired clinical outcome. In this work, thermomechanical modeling of contactless laser ablation was implemented to analyze the sensitivity of independent variables on the optimal treatment conditions. The Finite Element Method was utilized to solve the governing equations, i.e., the bioheat, mechanical deformation, and the Navier-Stokes equations. Validation of the model was performed by comparing experimental and simulated temperatures, which indicated high accuracy for estimating temperature. In particular, the results showed that the model can estimate temperature with a good correlation factor (R=0.98) and low Mean Absolute Error (3.9 °C). A sensitivity analysis based on laser irradiation time, power, beam distribution, and the blood vessel depth on temperature distribution and fraction of necrotic tissue was performed. An optimization process was performed based on the most significant variables, i.e., laser irradiation time and power. This resulted in an indication of the optimal therapy settings for achieving maximum procedure efficiency i.e., the required fraction of necrotic tissue within the target volume, constituted by tumor and safety margins around it.

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Algorithms for solving the diffusive wave flood routing equation

Moussa

Bocquillon

1996

Hydrol. Process.

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Generally, the diffusive wave equation, obtained by neglecting the acceleration terms in the Saint-Venant equations, is used in flood routing in rivers. Methods based on the finite-difference discretization techniques are often used to calculate discharges at each time step. A modified form of the diffusive wave equation has been developed and new resolution algorithms proposed which are better adapted to flood routing along a complex river network. The two parameters of the equation, celerity and diffusivity, can then be taken as functions of the discharge. The resolution algorithm allows the use of any distribution of lateral inflow in space and time. The accuracy of the new algorithms were compared with a traditional algorithm by numerical experimentation. Special attention was given to the instability caused by the inflow signal which constitutes the upstream boundary condition. For the fully diffusive wave flood routing problem, all three algorithms tested gave good results. The results also indicate that the efficiency of the new algorithms could be significantly improved if the position of the x-axis is modified by rotation. The new algorithms were applied to flood routing simulation over the Gardon d'Anduze catchment (542 km2) in southern France.

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Finite Element Solution of Saint-Venant Equations

Cited by 53 publications

References 0 publications

Finite Element Modeling Of Saint-Venant Equations For Shatt-Al Hilla

Finite Element Modeling Of Saint-Venant Equations For Shatt-Al Hilla

Thermomechanical Modeling of Laser Ablation Therapy of Tumors: Sensitivity Analysis and Optimization of Influential Variables

Algorithms for solving the diffusive wave flood routing equation

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