In this article, a detailed study on the effects of different modelings of cell-face velocities on pressure-velocity coupling, accuracy and convergence rate of the solution has been conducted. Discussions are focused ...
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In this article, a detailed study on the effects of different modelings of cell-face velocities on pressure-velocity coupling, accuracy and convergence rate of the solution has been conducted. Discussions are focused on the collocated scheme of Schneider and Karimian (Computational Mechanics 1994;14: 1-16) in the context of a control-volume finite-element Method. In this scheme, variables at the control volume surface are evaluated based on the physics of their governing equations, and the fully coupled system obtained is solved using a direct sparse solver. A special test problem has been defined to check the pressure-velocity coupling for all of the formulations. Other test cases, including Taylor problem, inviscid converging-diverging nozzle and the lid-driven cavity, have been conducted for different Reynolds numbers, mesh sizes and time steps to investigate the accuracy and the performance of the formulations. Finally, a reliable and efficient scheme for the evaluation of cell-face velocities is proposed, which can be easily extended to three dimensions. Copyright (C) 2010 John Wiley & Sons, Ltd.
Two difficulties are always encountered in the simulation of variable density low Mach number flows by the primitive variable methods: (1) the decoupling of pressure and velocity caused by the extremely small velocity...
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Two difficulties are always encountered in the simulation of variable density low Mach number flows by the primitive variable methods: (1) the decoupling of pressure and velocity caused by the extremely small velocity;(2) the spurious oscillations, nonsmooth solutions and sharp resolution caused by discontinuities, making that the flow cannot be successfully simulated by low-ordered schemes. In this paper, a pressure-based compressible flow solver with a scheme of high-resolution is developed to overcome these difficulties. In the present work, we adopt pressure correction algorithm to overcome the decoupling and the MUSCL scheme to predict the discontinuities at low Mach number. We applied the proposed compressible flow solver to simulate the compressible flows in a planar nozzle, are bumps and the lid-driven cavity and found that the numerical results are in good agreement with those reported in the previous works, indicating that the numerical algorithm developed in this work is a reliable and accurate tool for studying thermal variable density low Mach number flows. (C) 2006 Published by Elsevier Ltd.
The finite-volume methods normally utilize either simple or complicated mathematical expressions to interpolate the fluxes at the cell faces of their unstructured volumes. Alternatively, we benefit from the advantages...
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The finite-volume methods normally utilize either simple or complicated mathematical expressions to interpolate the fluxes at the cell faces of their unstructured volumes. Alternatively, we benefit from the advantages of both finite-volume and finite-element methods and estimate the advection terms on the cell faces, Using an inclusive pressure-weighted upwinding scheme extended on unstructured grids. The present pressure-based method treats the steady and unsteady flows on a collocated grid arrangement. However, to avoid a non-physical Spurious pressure field pattern, two mass flux per volume expressions are derived at the cell interfaces. The dual advantages of using an unstructured-based discretization and a pressure-weighted upwinding scheme result in obtaining high accurate Solutions with noticeable progress in the performance of the primitive method extended on the structured grids. The accuracy and performance of the extended formulations are demonstrated by solving different standard and benchmark problems. The results show that there are excellent agreements with both benchmark and analytical solutions as well as experimental data. Copyright (C) 2007 John Wiley & Sons, Ltd.
This paper reports on the implementation and testing, within a full non-linear multi-grid environment, of a new pressure-based algorithm for the prediction of multi-fluid flow at all speeds. The algorithm is part of t...
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This paper reports on the implementation and testing, within a full non-linear multi-grid environment, of a new pressure-based algorithm for the prediction of multi-fluid flow at all speeds. The algorithm is part of the mass conservation-basedalgorithms (MCBA) group in which the pressure correction equation is derived from overall mass conservation. The performance of the new method is assessed by solving a series of two-dimensional two-fluid flow test problems varying from turbulent low Mach number to supersonic flows, and from very low to high fluid density ratios. Solutions are generated for several grid sizes using the single grid (SG), the prolongation grid (PG), and the full non-linear multi-grid (FMG) methods. The main outcomes of this study are: (i) a clear demonstration of the ability of the FMG method to tackle the added non-linearity of multi-fluid flows, which is manifested through the performance jump observed when using the non-linear multi-grid approach as compared to the SG and PG methods;(ii) the extension of the FMG method to predict turbulent multi-fluid flows at all speeds. The convergence history plots and CPU-times presented indicate that the FMG method is far more efficient than the PG method and accelerates the convergence rate over the SG method, for the problems solved and the grids used, by a factor reaching a value as high as 15. Copyright (C) 2003 John Wiley Sons, Ltd.
A new finite volume-based numerical algorithm for predicting incompressible and compressible multi-phase flow phenomena is presented. The technique is equally applicable in the subsonic, transonic, and supersonic regi...
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A new finite volume-based numerical algorithm for predicting incompressible and compressible multi-phase flow phenomena is presented. The technique is equally applicable in the subsonic, transonic, and supersonic regimes. The method is formulated on a non-orthogonal coordinate system in collocated primitive variables. pressure is selected as a dependent variable in preference to density because changes in pressure are significant at all speeds as opposed to variations in density, which become very small at low Mach numbers. The pressure equation is derived from overall mass conservation. The performance of the new method is assessed by solving the following two-dimensional two-phase flow problems: (i) incompressible turbulent bubbly flow in a pipe, (ii) incompressible turbulent air-particle flow in a pipe, (iii) compressible dilute gas-solid flow over a flat plate, and (iv) compressible dusty flow in a converging diverging nozzle. Predictions are shown to be in excellent agreement with published numerical and/or experimental data. (C) 2003 Elsevier Science B.V. All rights reserved.
A new collocated finite-volume-based solution procedure for predicting viscous compressible and incompressible Rows is presented. The technique is equally applicable in the subsonic, transonic, and supersonic regimes....
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A new collocated finite-volume-based solution procedure for predicting viscous compressible and incompressible Rows is presented. The technique is equally applicable in the subsonic, transonic, and supersonic regimes. pressure is selected as a dependent variable in preference to density because changes in pressure are significant at all speeds as opposed to variations in density, which become very small at low Mach numbers. The newly developed algorithm has two new features: (i) the use of the normalized variable and space formulation (NVSF) methodology to bound the convective fluxes and (ii) the use of a high-resolution scheme in calculating interface density values to enhance the shock-capturing property of the algorithm. The virtues of the newly developed method are demonstrated by solving a wide range of flows spanning the subsonic, transonic. and supersonic spectrum. Results obtained indicate higher accuracy when calculating interface density values using a high-resolution scheme. (C) 2001 Academic Press.
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