scholarly journals An accurate and efficient scheme involving unsteady friction for transient pipe flow

2021 ◽  
Author(s):  
Ling Zhou ◽  
Yunjie Li ◽  
Yan Zhao ◽  
Chuanqi Ou ◽  
Yue Zhao
Keyword(s):  
Computation Time ◽  
Second Order ◽  
Courant Number ◽  
Hydraulic Transients ◽  
Friction Factors ◽  
Efficient Scheme ◽  
Friction Models ◽  
Transient Pipe Flow ◽  
Volume Method ◽  
Robust Prediction

Abstract A robust prediction system should monitor all possible hydraulic transients, which is significant for appropriate and safe operations of pipe systems. A second-order finite volume method (FVM) Godunov-type scheme (GTS) considering unsteady friction factors is introduced to simulate hydraulic transients, which was rarely involved in previous work. One explicit-solution source item approach developed in this work is crucial for the proposed GTS to easily incorporate various forms of the existing unsteady friction models, including original convolution-based models (Zielke model and Vardy–Brown model), simplified convolution-based model (Trikha–Vardy–Brown (TVB) model), and Brunone instantaneous acceleration-based model. Results achieved by the proposed models are compared with experimental data as well as predictions by the classic Method of Characteristics (MOC). Results show that the MOC scheme may produce severe numerical attenuation in the case of a low Courant number. The proposed second-order GTS unsteady friction models are accurate, efficient, and stable even for Courant numbers less than one and sparse grid, and only need much less grid number and computation time to reach the same numerical accuracy. The TVB convolution-based model and Brunone model in the second-order GTS are suggested for further applications in hydraulic transients due to their high accuracy and efficiency.

Simplified Second Order Reynolds Equation for Simulating Ultra-Thin Gas Film Lubrication in the Head/Disk Interface

2014 ◽  
Author(s):  
Bao-Jun Shi ◽  
Jia-Dong Ji ◽  
Ting-Yi Yang ◽  
Longqui Li ◽  
Chuanwei Zhang
Keyword(s):  
Mathematical Formulation ◽  
Computation Time ◽  
Rotating Disk ◽  
Mean Free Path ◽  
Second Order ◽  
Disk Drives ◽  
Order Model ◽  
Disk Interface ◽  
Volume Method ◽  
Film Lubrication

To increase the recording density of magnetic disk drives, the spacing between the flying slider and the rotating disk should be as small as possible. If the spacing between the flying head and the rotating disk approximates the molecular mean-free path, rarefaction effects must be taken into account. Starting from a Poiseuille flow rate database, a simplified precise second order (PSO) model is proposed to simulate ultra-thin gas film lubrication. The new model is evaluated using the finite volume method. The numerical results are compared with other models, including the widely used FK (Fukui and Kaneko) model. The new PSO model has three key advantages compared to other models. First, compared with the 1st-order model, the 2nd-order model and the 1.5th-order model, the PSO model has better accuracy in simulating the air bearing film. Second, the PSO model has a simpler mathematical formulation than the FK model. Third, the PSO model has higher accuracy and requires less computation time than other models including the FK model.

A HYBRID RECONSTRUCTION STRATEGY FOR FULLY ADAPTIVE MULTI-RESOLUTION SCHEME

2009 ◽  
Vol 23 (03) ◽  
pp. 333-336
Author(s):  
FENG DENG ◽  
YI-ZHAO WU
Keyword(s):  
Hyperbolic Conservation Laws ◽  
Grid Method ◽  
Second Order ◽  
Hyperbolic Conservation ◽  
Multi Resolution Analysis ◽  
Fully Adaptive ◽  
Resolution Analysis ◽  
Resolution Scheme ◽  
Reconstruction Strategy ◽  
Volume Method

In this paper we propose a second order hybrid reconstruction strategy for the fully adaptive multi-resolution scheme based on the second order finite volume method. The fully adaptive multi-resolution scheme is an adaptive grid method for solving the hyperbolic conservation laws. To improve its robustness, the third order central reconstruction is replaced by the second order hybrid reconstruction, i.e. the anti-ENO (essentially non-oscillatory) reconstruction and the ENO reconstruction have been adopted for the multi-resolution analysis and the inverse multi-resolution analysis, respectively. Several numerical examples indicate that this new hybrid reconstruction strategy is much less sensitive to the tolerance than the central reconstruction.

scholarly journals An Efficient Implementation of the Finite-volume Method For the Solution of Radiation Transport in Circuit Breakers

2017 ◽  
Vol 4 (2) ◽  
pp. 177-181
Author(s):  
A. Mazaheri ◽  
J. Y. Trépanier ◽  
R. Camarero ◽  
P. Robin-Jouan
Keyword(s):  
Finite Volume ◽  
Radiation Transport ◽  
Computation Time ◽  
Discrete Ordinate Method ◽  
Discrete Ordinate ◽  
Circuit Breakers ◽  
Explicit Approach ◽  
Order Of Magnitude ◽  
Implicit Approach ◽  
Volume Method

In this paper, we propose to revisit the method to solve the radiation transport equation in circuit breakers to reduce the computation time. It is based on an explicit approach using a space marching algorithm. The method can further be accelerated using a Cartesian grid and using the axisymmetric assumption. Comparisons performed in terms of accuracy and efficiency between the P1 model, the implicit finite-volume discrete ordinate method and the space-marching finite-volume discrete ordinate method show that the explicit approach is more that an order of magnitude faster than the implicit approach, for the same accuracy.

scholarly journals A second-order face-centred finite volume method for elliptic problems

2020 ◽  
Vol 358 ◽  
pp. 112655 ◽  
Author(s):  
Luan M. Vieira ◽  
Matteo Giacomini ◽  
Ruben Sevilla ◽  
Antonio Huerta
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Problems ◽  
Second Order ◽  
Volume Method

scholarly journals A Finite Volume Method for Modeling Shallow Flows with Wet-Dry Fronts on Adaptive Cartesian Grids

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Sheng Bi ◽  
Jianzhong Zhou ◽  
Yi Liu ◽  
Lixiang Song
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Second Order ◽  
Topographic Features ◽  
Shallow Flows ◽  
Local Complex ◽  
Proposed Model ◽  
Volume Method

A second-order accurate, Godunov-type upwind finite volume method on dynamic refinement grids is developed in this paper for solving shallow-water equations. The advantage of this grid system is that no data structure is needed to store the neighbor information, since neighbors are directly specified by simple algebraic relationships. The key ingredient of the scheme is the use of the prebalanced shallow-water equations together with a simple but effective method to track the wet/dry fronts. In addition, a second-order spatial accuracy in space and time is achieved using a two-step unsplit MUSCL-Hancock method and a weighted surface-depth gradient method (WSDM) which considers the local Froude number is proposed for water depths reconstruction. The friction terms are solved by a semi-implicit scheme that can effectively prevent computational instability from small depths and does not invert the direction of velocity components. Several benchmark tests and a dam-break flooding simulation over real topography cases are used for model testing and validation. Results show that the proposed model is accurate and robust and has advantages when it is applied to simulate flow with local complex topographic features or flow conditions and thus has bright prospects of field-scale application.

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