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A segregated spectral finite element method for the 2D transient incompressible Navier-Stokes equations

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2020年第2期79卷 521-537页

作者： He, Wenqiang Qin, Guoliang Lin, Jingxiang Jia, Cheng Xi An Jiao Tong Univ Sch Energy & Power Engn Xian 710049 Peoples R China

In this paper, the spectral element approximation and the velocity-pressure decoupling method implementing the SIMPLE (semi-implicit method for pressure linked equations) algorithm are first combined to form a high-order segregated scheme for the solution of the two-dimensional transient incompressible Navier-Stokes equations. In contrast to previous segregated finite element methods based on the SIMPLE algorithm, the pressure equation is derived from the continuity equation using the element matrices to ensure convergence. High-order element basis functions are adopted, which greatly reduces the number of nodal points used in the calculation. The validation test that has an analytical solution demonstrates the high accuracy and convergence rate of the method. The flow in a lid-driven cavity with different inclination angles and the flow over a backward-facing step are investigated to further illustrate the performance of the scheme. The computed results are in excellent agreement with the benchmark solutions. The almost periodic solution for the flow of Re=10000 in a lid-driven square cavity is also captured by the present scheme. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： segregated algorithm SIMPLE Spectral element method High accuracy Transient incompressible flow

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Projection Based Semi-Implicit Partitioned Reduced Basis Method for Fluid-Structure Interaction Problems

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JOURNAL OF SCIENTIFIC COMPUTING 2023年第1期94卷 4-4页

作者： Nonino, Monica Ballarin, Francesco Rozza, Gianluigi Maday, Yvon Univ Vienna Dept Math Oskar Morgenstern Pl A-1090 Vienna Austria Univ Cattolica Sacro Cuore Dipartimento Matemat & Fis Via Garzetta I-25133 Brescia Italy Scuola Int Super Studi Avanzati MathLab Via Bonomea I-34136 Trieste Italy Univ Paris 06 Lab Jacques Louis Lions Pl Jussieu F-75005 Paris France

In this manuscript a POD-Galerkin based Reduced Order Model for unsteady Fluid-Structure Interaction problems is presented. The model is based on a partitioned algorithm, with semi-implicit treatment of the coupling conditions. A Chorin-Temam projection scheme is applied to the incompressible Navier-Stokes problem, and a Robin coupling condition is used for the coupling between the fluid and the solid. The coupled problem is based on an Arbitrary Lagrangian Eulerian formulation, and the Proper Orthogonal Decomposition procedure is used for the generation of the reduced basis. We extend existing works on a segregated Reduced Order Model for Fluid-Structure Interaction to unsteady problems that couple an incompressible, Newtonian fluid with a linear elastic solid, in two spatial dimensions. We consider three test cases to assess the overall capabilities of the method: an unsteady, non-parametrized problem, a problem that presents a geometrical parametrization of the solid domain, and finally, a problem where a parametrization of the solid's shear modulus is taken into account.

关键词： Fluid-structure interaction Reduced basis method segregated algorithm Proper orthogonal decomposition Incompressible fluid Elastic solid

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Performance analysis and comparison of IDEAL and SIMPLERR algorithms for incompressible fluid flow and heat transfer problems

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2023年第1期205卷

作者： Sun, Dong-Liang Tao, Wen-Quan Beijing Inst Petrochem Technol Sch Mech Engn Beijing 102617 Peoples R China Xi An Jiao Tong Univ Sch Power & Energy Engn Xian 710049 Shaanxi Peoples R China

In this paper, the numerical performances of the algorithm IDEAL proposed by the present authors in 2008, and the recently proposed (2017) SIMPLERR are systematically analyzed and compared via six incompressible fluid flow and heat transfer problems. It is found that the two algorithms are almost identical when the second inner iteration number of IDEAL is fixed at 2. In general, the robustness and convergence of IDEAL are much better than SIMPLERR. The reason why the performance of SIMPLERR deteriorates with the increase of the first inner iteration number is analyzed and detailed comparisons in the robustness and computing time are presented.(c) 2023 Elsevier Ltd. All rights reserved.

关键词： segregated algorithm IDEAL SIMPLERR Convergence Robustness

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A segregated spectral element method for the 2D transient incompressible Navier-Stokes equations

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COMPUTERS & FLUIDS 2021年 216卷 104643-104643页

作者： He, Wenqiang Qin, Guoliang Wang, Yazhou Bao, Zhenzhong Xi An Jiao Tong Univ Sch Energy & Power Engn Xianning West Rd Xian Shaanxi Peoples R China

In this paper, a spectral element method for the solution of the two-dimensional transient incompressible Navier-Stokes equations is introduced, which combines the segregated velocity-pressure equal-order formulation originated from the SIMPLE (semi-implicit method for pressure linked equations) algorithm. In contrast to previous segregated finite element method based on the SIMPLE algorithm, the pressure equation is derived from the momentum and continuity equations using the element matrices to ensure the convergence of the pressure. High-order element basis functions are adopted to construct the discrete form that presents arbitrary order or accuracy. The validation test with analytical solution verifies the high accuracy of the method. The flow in a lid-driven cavity with different inclination angles and the flow over a backward-facing step are investigated to further illustrate the property of the scheme. The computed results are in excellent agreement with the benchmark solutions, even if fewer grid points are used. The almost periodic solution for the flow of Re= 100 00 in a lid-driven square cavity is also captured by the present scheme. The numerical results indicate that the proposed high-order method can significantly reduce the number of grid points used in the calculation. (c) 2020 Published by Elsevier Ltd.

关键词： segregated algorithm SIMPLE Spectral element method High accuracy Transient incompressible flow

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Numerical analysis of conservative unstructured discretisations for low Mach flows

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2017年第6期84卷 309-334页

作者： Ventosa-Molina, J. Chiva, J. Lehmkuhl, O. Muela, J. Perez-Segarra, C. D. Oliva, A. Univ Politecn Cataluna CTTC BarcelonaTech ESEIAAT Colom 11 Barcelona 08222 Spain Termo Fluids SL Av Jacquard 97 1-E Barcelona 08222 Spain

Unstructured meshes allow easily representing complex geometries and to refine in regions of interest without adding control volumes in unnecessary regions. However, numerical schemes used on unstructured grids have to be properly defined in order to minimise numerical errors. An assessment of a low Mach algorithm for laminar and turbulent flows on unstructured meshes using collocated and staggered formulations is presented. For staggered formulations using cell-centred velocity reconstructions, the standard first-order method is shown to be inaccurate in low Mach flows on unstructured grids. A recently proposed least squares procedure for incompressible flows is extended to the low Mach regime and shown to significantly improve the behaviour of the algorithm. Regarding collocated discretisations, the odd-even pressure decoupling is handled through a kinetic energy conserving flux interpolation scheme. This approach is shown to efficiently handle variable-density flows. Besides, different face interpolations schemes for unstructured meshes are analysed. A kinetic energy-preserving scheme is applied to the momentum equations, namely, the symmetry-preserving scheme. Furthermore, a new approach to define the far-neighbouring nodes of the quadratic upstream interpolation for convective kinematics scheme is presented and analysed. The method is suitable for both structured and unstructured grids, either uniform or not. The proposed algorithm and the spatial schemes are assessed against a function reconstruction, a differentially heated cavity and a turbulent self-igniting diffusion flame. It is shown that the proposed algorithm accurately represents unsteady variable-density flows. Furthermore, the quadratic upstream interpolation for convective kinematics scheme shows close to second-order behaviour on unstructured meshes, and the symmetry-preserving is reliably used in all computations. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： low Mach segregated algorithm unstructured collocated staggered reacting flows

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A comparative study of high-order variable-property segregated algorithms for unsteady low Mach number flows

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2011年第4期66卷 403-427页

作者： Knikker, R. Univ Lyon CNRS UMR5008 CETHILINSA Lyon F-69621 Villeurbanne France

In this paper, five different algorithms are presented for the simulation of low Mach flows with large temperature variations, based on second-order central-difference or fourth-order compact spatial discretization and a pressure projection-type method. A semi-implicit three-step Runge-Kutta/Crank-Nicolson or second-order iterative scheme is used for time integration. The different algorithms solve the coupled set of governing scalar equations in a decoupled segregate manner. In the first algorithm, a temperature equation is solved and density is calculated from the equation of state, while the second algorithm advances the density using the differential form of the equation of state. The third algorithm solves the continuity equation and the fourth algorithm solves both the continuity and enthalpy equation in conservative form. An iterative decoupled algorithm is also proposed, which allows the computation of the fully coupled solution. All five algorithms solve the momentum equation in conservative form and use a constantor variable-coefficient Poisson equation for the pressure. The efficiency of the fourth-order compact scheme and the performances of the decoupling algorithms are demonstrated in three flow problems with large temperature variations: non-Boussinesq natural convection, channel flow instability, flame-vortex interaction. Copyright (C) 2010 John Wiley & Sons, Ltd.

关键词： low Mach number variable density flows large temperature variations high-order compact schemes segregated algorithm projection methods

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Comparison of different solution algorithms for collocated method of MCIM to calculate steady and unsteady incompressible flows on unstructured grids

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COMPUTERS & FLUIDS 2011年第1期46卷 94-100页

作者： Alisadeghi, H. Karimian, S. M. H. Amir Kabir Univ Technol Dept Aerosp Engn Tehran Iran

In this paper, the collocated method of MCIM (Mass Corrected Interpolation Method) is employed for solving two-dimensional incompressible flows on unstructured grid systems. A control-volume-based finite element (CVFEM) approach has been taken in which conservation equations are formed for each control volume throughout the solution domain. In this study, three different algorithms are proposed and investigated. In the first algorithm a fully coupled formulation is used, however in the second algorithm a segregated approach without pressure correction is employed. In the third solution algorithm, the scheme of MCIM is implemented to SIMPLE-like segregated algorithm. The linear system of equations obtained in these algorithms is solved using a direct sparse solver. The accuracy and performance of the proposed algorithms are demonstrated by solving different steady and unsteady benchmark problems. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Incompressible flow Collocated unstructured grid Fully coupled segregated algorithm SIMPLE-like algorithm

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Performance analysis of IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problems

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2009年第10期61卷 1132-1160页

作者： Sun, Dong-Liang Qu, Zhi-Guo He, Ya-Ling Tao, Wen-Quan Xi An Jiao Tong Univ Sch Energy & Power Engn Xian 710049 Shaanxi Peoples R China

Recently, an efficient segregated algorithm for incompressible fluid flow and heat transfer problems, called inner doubly iterative efficient algorithm for linked equations (IDEAL), has been proposed by the present authors. In the algorithm there exist inner doubly iterative processes for pressure equation at each iteration level, which almost completely overcome two approximations in SIMPLE algorithm. Thus, the Coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of solution process. However, validations have only been conducted for two-dimensional cases. In the present paper the performance of the IDEAL algorithm for three-dimensional incompressible fluid flow and heat transfer problems is analyzed and a systemic comparison is made between the algorithm and three other most widely used algorithms (SIMPLER, SIMPLEC and PISO). By the comparison of five application examples, it is found that the IDEAL algorithm is the most robust and the most efficient one among the four algorithms compared. For the five three-dimensional cases studied, when each algorithm works at its own optimal under-relaxation factor, the IDEAL algorithm can reduce the computation time by 12.9-52.7% over SIMPLER algorithm, by 45.3-73.4% over SIMPLEC algorithm and by 10.7-53.1% over PISO algorithm. Copyright (C) 2009 John Wiley & Sons, Ltd. C,

关键词： segregated algorithm IDEAL algorithm SIMPLER algorithm SIMPLEC algorithm PISO algorithm three-dimensional cases

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A Mach-uniform algorithm: Coupled versus segregated approach

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JOURNAL OF COMPUTATIONAL PHYSICS 2007年第1期224卷 314-331页

作者： Nerinckx, Krista Vierendeels, Jan Dick, Erik Univ Ghent Dept Flow Heat & Combust Mech B-9000 Ghent Belgium

A Mach-uniform algorithm is an algorithm with a good convergence rate for any level of the Mach number. In this paper, the severe time step restriction for low speed flows is removed by treating the acoustic and diffusive terms implicitly. After identification of these terms in the conservative set, we end up with a semi-implicit system. The way to solve this system can be chosen. Three different solution techniques are presented: a fully coupled algorithm, the coupled pressure and temperature correction algorithm [K. Nerinckx, J. Vierendeels, E. Dick, Mach-uniformity through the coupled pressure and temperature correction algorithm, Journal of Computational Physics 206 (2005) 597-623], and a fully segregated pressure-correction algorithm. We analyse the convergence behavior of the considered algorithms for some typical flow problems. Moreover, a Fourier stability analysis is done. For inviscid flow, the fully segregated and the fully coupled algorithm need about as much time steps to reach steady state. Therefore, the more segregation is introduced, the faster the calculation can be done. In case of heat transfer, the fully segregated pressure-correction algorithm suffers from a diffusive time step limit. This is not the case for the semi-segregated coupled pressure and temperature correction algorithm. Finally, when the gravity terms play an important role, only the fully coupled algorithm can avoid an additional time step restriction. (c) 2007 Elsevier Inc. All rights reserved.

关键词： Mach-uniform segregated algorithm coupled algorithm pressure-correction Fourier analysis inviscid flow heat transfer gravity

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Mach-uniformity through the coupled pressure and temperature correction algorithm

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JOURNAL OF COMPUTATIONAL PHYSICS 2005年第2期206卷 597-623页

作者： Nerinckx, K Vierendeels, J Dick, E State Univ Ghent Dept Flow Heat & Combust Mech B-9000 Ghent Belgium

We present a new type of algorithm: the coupled pressure and temperature correction algorithm. It is situated in between the fully coupled and the fully segregated approach, and is constructed such that Mach-uniform accuracy and efficiency are obtained. The essential idea is the separation of the convective and the acoustic/thermodynamic phenomena: a convective predictor is followed by an acoustic/thermodynamic corrector. For a general case, the corrector consists of a coupled solution of the energy and the continuity equations for both pressure and temperature corrections. For the special case of an adiabatic perfect gas flow, the algorithm reduces to a fully segregated method, with a pressure-correction equation based on the energy equation. Various test cases are considered, which confirm that Mach-uniformity is obtained. (c) 2005 Elsevier Inc. All rights reserved.

关键词： mach-uniform segregated algorithm coupled algorithm pressure-correction general fluids perfect gas adiabatic non-adiabatic

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