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Fully-coupled pressure-based algorithm for compressible flows: Linearisation and iterative solution strategies

COMPUTERS & FLUIDS 2018年 175卷 53-65页

作者： Denner, Fabian Imperial Coll London Dept Mech Engn Exhibit Rd London SW7 2AZ England

The impact of different linearisation and iterative solution strategies for fully-coupled pressure-based algorithms for compressible flows at all speeds is studied, with the aim of elucidating their impact on the performance of the numerical algorithm. A fixed-coefficient linearisation and a Newton linearisation of the transient and advection terms of the governing nonlinear equations are compared, focusing on test cases that feature acoustic, shock and expansion waves. The linearisation and iterative solution strategy applied to discretise and solve the nonlinear governing equations is found to have a significant influence on the performance and stability of the numerical algorithm. The Newton linearisation of the transient terms of the momentum and energy equations is shown to yield a significantly improved convergence of the iterative solution algorithm compared to a fixed-coefficient linearisation, while the linearisation of the advection terms leads to substantial differences in performance and stability at large Mach numbers and large Courant numbers. It is further shown that the consistent Newton linearisation of all transient and advection terms of the governing equations allows, in the context of coupled pressure-based algorithms, to eliminate all forms of underrelaxation and provides a clear performance benefit for flows in all Mach number regimes. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Compressible flows pressure-based algorithm Linearisation schemes Iterative methods Inexact Newton methods Momentum-weighted interpolation

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A fully coupled pressure-based method for compressible flows at all Mach numbers

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APPLIED THERMAL ENGINEERING 2024年 255卷

作者： Ou, Guo-Hui Li, Zhao-Ren Ji, Wen-Tao Tao, Wen-Quan Xian Jiaotong Tong Univ MOE Key Lab Thermo Fluid Sci & Engn Xian 710049 Shaanxi Peoples R China

When extending the fully coupled pressure-based method to resolve compressible flows, the effective treatment of the boundary conditions is crucial due to the inherent characteristics of compressible flows. Failure to properly account for this can result in numerical instability and divergence. In this article, a detailed treatment of boundary conditions for compressible flows has been formulated in terms of the boundary face's contribution to the discretization equation of the boundary element. These boundary conditions involve subsonic inlet, supersonic inlet, subsonic outlet, and supersonic outlet boundary conditions. The analysis has been focused on test cases of flow through a bumped arc channel and a converging-diverging nozzle including quasi-incompressible, subsonic, transonic, supersonic and hypersonic speed regimes, where the Mach number ranges from 0.1 to 10. The results indicate the robust performance of the fully coupled method in resolving compressible flows. The computational results obtained from the fully coupled algorithm exhibit a high degree of consistency with available literature cases and analytical solutions, with a maximum error of less than 5%. Moreover, the findings also suggest that the coupled solver presents promising potential in handling hypersonic flows.

关键词： pressure-based algorithm Finite volume method Compressible flows Boundary conditions All-speeds flows

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Improved implicit potential method for incompressible flows on a fully collocated mesh

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2022年第10期94卷 1706-1723页

作者： Vafakos, Georgios P. Kafkas, Angelos Papadopoulos, Polycarpos K. Univ Patras Dept Mech Engn & Aeronaut Rion 26504 Greece

In the present work, we present a new version of the pressure-based implicit potential (IPOT) method for incompressible flows, which can be applied on a fully collocated mesh. The new version combines the IPOT algorithm with the Rhie and Chow (RC) technique, to produce solutions on collocated grids that are free of spurious pressure modes. The IPOT-RC method retains all the benefits of the original algorithm, i.e. explicit velocity-pressure coupling, easy implementation and reduced iteration time, without requiring a special grid topology. The presentation of the IPOT-RC method is accompanied by an extensive discussion on the cause of the spurious oscillations in zero-div problems in general, and a possible cure that is linked to the RC technique. The IPOT-RC method is validated through several benchmark problems including the lid-driven cavity flow, flow over a backward facing step and direct numerical simulation of turbulent channel flow.

关键词： incompressible flow IPOT numerical methods pressure-based algorithm Rhie-Chow spurious pressure oscillations

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Computations of partial and super cavitating flows using implicit pressure-based algorithm (IPA)

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COMPUTERS & FLUIDS 2013年 73卷 1-9页

作者： Zhang, L. X. Khoo, B. C. Natl Univ Singapore Dept Mech Engn Singapore 119260 Singapore

An implicit pressure-based algorithm (IPA) has been developed for the computations of the two-phase cavitating flows. A pressure correction equation is derived to meet the mass conservation law and the pressure-velocity coupled method is used to solve for the governing equations of the flows. Both partial and super cavitating flows are simulated in this work to validate the IPA approach and to investigate the unsteady features of the cavitating flows. It is found that strong re-entrant jets are present for all the simulations of the cavitating flows over the flat-nose cylindrical objects. For partial cavitating flows, the re-entrant jets appear periodically and become the main reason of cavitation shedding. For super cavitating flows, the re-entrant jets mainly interact with the wake flows of the object. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Cavitation pressure-based algorithm Simulation Cylindrical object

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Computational analysis in underexpanded jets simulations

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FLUID DYNAMICS RESEARCH 2022年第6期54卷 065502-065502页

作者： Martins, J. R. Barbosa, J., V Santos, F. P. Silva, L. F. L. R. Univ Fed Rio de Janeiro UFRJ Escola Quim BR-21941909 Rio De Janeiro RJ Brazil

Flammable gases leaks at high pressures are hazardous, especially the free underexpanded jets. Therefore, understanding their behavior is fundamental to guarantee a safe environment. Due to the difficulty to obtain experimental data from free under expanded jets, related to the great speeds and gradients, computational fluid dynamics (CFD) has become an essential tool. Simulations for free underexpanded jets to identify algorithms that better represent this problem were performed in this work. The analysis involved different algorithms for fluid flow solution and a local time stepping approach using both OpenFOAM and ANSYS Fluent CFD packages. Our study concluded that all algorithms and software studied had a satisfactory result compared to experimental data. However, we observed that Fluent had a considerable advantage because the simulation was faster compared with other solvers in OpenFOAM, for instance.

关键词： underexpanded jets pressure-based algorithm density-based algorithm OpenFOAM Fluent

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An implicit algorithm of solving Navier-Stokes equations to simulate flows in anisotropic porous media

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COMPUTERS & FLUIDS 2018年 160卷 164-174页

作者： Kozelkov, A. S. Lashkin, S. V. Efremov, V. R. Volkov, K. N. Tsibereva, Yu. A. Tarasova, N. V. Russian Fed Nucl Ctr Sarov Russia Nizhnii Novgorod State Tech Univ Nizhnii Novgorod Russia JSC KBP Tula Russia Kingston Univ London England

A coupled computational algorithm for modified Navier-Stokes equations to simulate flows in anisotropic porous media is proposed and described. The difference from the classic SIMPLE algorithm is in the completely implicit relationship between velocity and pressure owing to the implicit terms of the pressure and mass flow gradients in the continuity equation and momentum equation. One of the attractive features of this algorithm is the possibility of completely implicit discretization of off-diagonal components of the porous medium resistance tensor in the right-hand side of the momentum equation. Implicit discretization allows reducing the number of linear iterations as compared to the SIMPLE algorithm with explicit discretization of off-diagonal components. The specific features of discretization of modified equations including the discretization of boundary conditions and components of the porous medium resistance tensor are considered. The proposed algorithm is verified in comparison with the SIMPLE algorithm on a series of benchmark problems, such as the problem of a flow through a porous insert, a flow in a divided channel, and a flow through a cylindrical porous filter. The total problem runtimes and the number of iterations required for complete convergence are given to compare the two algorithms. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Navier-Stokes equations Porous media Darcy law Brinkman equations Multigrid method pressure-based algorithm Implicit discretization

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Unified formulation of the momentum-weighted interpolation for collocated variable arrangements

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JOURNAL OF COMPUTATIONAL PHYSICS 2018年 375卷 177-208页

作者： Bartholomew, Paul Denner, Fabian Abdol-Azis, Mohd Hazmil Marquis, Andrew van Wachem, Berend G. M. Imperial Coll London Dept Mech Engn Exhibit Rd London SW7 2AZ England Univ Teknol Malaysia Fac Mech Engn Dept Thermofluids Johor Baharu 81310 Malaysia Otto von Guericke Univ Chair Mech Proc Engn Univ Pl 2 D-39106 Magdeburg Germany

Momentum-weighted interpolation (MWI) is a widely used discretisation method to prevent pressure-velocity decoupling in simulations of incompressible and low Mach number flows on meshes with a collocated variable arrangement. Despite its popularity, a unified and consistent formulation of the MWI is not available at present. In this work, a discretisation procedure is devised following an in-depth analysis of the individual terms of the MWI, derived from physically consistent arguments, based on which a unified formulation of the MWI for flows on structured and unstructured meshes is proposed, including extensions for discontinuous source terms in the momentum equations as well as discontinuous changes of density. As shown by the presented analysis and numerical results, the MWI enforces a low-pass filter on the pressure field, which suppresses oscillatory solutions. Furthermore, the numerical dissipation of kinetic energy introduced by the MWI is shown to converge with third order in space and is independent of the time-step, if the MWI is derived consistently from the momentum equations. In the presence of source terms, the low-pass filter on the pressure field can be shaped by a careful choice of the interpolation coefficients to ensure the filter only acts on the driving pressure gradient that is associated with the fluid motion, which is shown to be vitally important for the accuracy of the numerical solution. To this end, a force-balanced discretisation of the source terms is proposed, that precisely matches the discretisation of the pressure gradients and preserves the force applied to the flow. Using representative test cases of incompressible and low Mach number flows, including flows with discontinuous source terms and two-phase flows with large density ratios, the newly proposed formulation of the MWI is favourably compared against existing formulations and is shown to significantly reduce, or even eliminate, solution errors, with an increased stability f

关键词： Momentum-weighted interpolation Rhie-Chow interpolation pressure-velocity decoupling Collocated variable arrangement Source terms pressure-based algorithm

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A pressure-based algorithm FOR CAVITATING FLOW COMPUTATIONS

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Journal of Hydrodynamics 2011年第1期23卷 42-47页

作者： ZHANG Ling-xin ZHAO Wei-guo SHAO Xue-ming Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang UniversityHangzhou 310027 China

A pressure-based algorithm for the prediction of cavitating flows is *** algorithm employs a set of equations including the Navier-Stokes equations and a cavitation model explaining the phase change between liquid and vapor.A pressure-based method is used to construct the algorithm and the coupling between pressure and velocity is *** pressure correction equation is derived from a new continuity equation which employs a source term related to phase change rate instead of the material derivative of density Dρ/*** pressure-based algorithm allows for the computation of steady or unsteady,2-D or 3-D cavitating *** 2-D cases,flows around a flat-nose cylinder and around a NACA0015 hydrofoil,are simulated respectively,and the periodic cavitation behaviors associated with the re-entrant jets are *** algorithm shows good capability of computating time-dependent cavitating flows.

关键词： cavitating flow pressure-based algorithm cavitation model numerical simulation

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A pressure-based Mach-uniform method for viscous fluid flows

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INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS 2016年第7-10期30卷 516-530页

作者： Ong, Kian C. Chan, Andy Univ Nottingham Dept Civil Engn Malaysia Campus Selangor Darul Ehsan Malaysia

A pressure-based, Mach-uniform method is developed by combining the SLAU2 numerical scheme and the higher temporal order pressure-based algorithm. This hybrid combination compensates the limitation of the SLAU2 numerical scheme in the low-Mach number regime and deficiencies of the pressure-based method in the high-Mach number regime. A momentum interpolation method is proposed to replace the Rhie-Chow interpolation for accurate shock-capturing and to alleviate the carbuncle phenomena. The momentum interpolation method is consistent in addition to preserving pressure-velocity coupling in the incompressible limit. The postulated pressure equation allows the algorithm to compute the subsonic flows without empirical scaling of numerical dissipation at low-Mach number computation. Several test cases involving a broad range of Mach number regimes are presented. The numerical results demonstrate that the present algorithm is remarkable for the calculation of viscous fluid flows at arbitrary Mach number including shock wave/laminar boundary layer interaction and aerodynamics heating problem.

关键词： pressure-based algorithm Mach-uniform method SLAU2 shock wave/laminar boundary layer interaction aerodynamics heating

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Accurate implementation of forcing terms for two-phase flows into SIMPLE algorithm

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INTERNATIONAL JOURNAL OF MULTIPHASE FLOW 2012年 45卷 40-52页

作者： Montazeri, Hanif Bussmann, Markus Mostaghimi, Javad Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada

A consistent numerical method for two-phase flows has been devised, that properly includes generic body forces in the framework of a collocated variable arrangement. We first discuss the accurate implementation of body forces, and then apply this to interfacial forces. Having shown the problems associated with applying forcing terms in a collocated framework, we introduce piezometric pressure into the governing equations for two-phase flow. As a result, the Navier-Stokes equations written for variable property flow, developed by Hong and Walker, are revised to be consistent with the numerical implementation of the level-set function. Consequently, the interfacial forces consist of both surface tension and gravity. We develop appropriate numerical methods to incorporate a generic body force, including the interfacial forces, within the framework of pressure-based algorithms (e.g. SIMPLE algorithm). A suitable pressure-velocity coupling scheme is then proposed for this type of flow solver and compared with other schemes. To validate the formulation, the results of several test cases including the Rayleigh-Taylor instability, a magnetized ferrofluid, and a falling water droplet are presented and compared with the results obtained by a conventional implementation of body forces. The advantages of confining the effect of gravity to the vicinity of an interface are explained, and we demonstrate how this approach enhances numerical solutions. Crown Copyright (c) 2012 Published by Elsevier Ltd. All rights reserved.

关键词： pressure-based algorithm Level-set method Two-phase flow Surface tension Gravity force Ferrofluids Piezometric pressure

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