Transient solutions for three‐dimensional lid‐driven cavity flows by a least‐squares finite element method

Tang, Li Qiang; Cheng, Tiwu; Tsang, Tate T. H.

doi:10.1002/fld.1650210505

Cited by 41 publications

(21 citation statements)

References 23 publications

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“…As shown in this figure, the results calculated by the IDEAL algorithm are in excellent agreement with those reported by Tang et al [28]. This comparison gives some support to the reliability of Figure 4(a) show that in the two ranges of E the two inner iterative times are 1 and 1 and 1 and 2, respectively.…”

Section: Problems Of Closed System Problem 1: Lid-driven Cavity Flowsupporting

confidence: 93%

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

Sun

et al. 2009

Numerical Methods in Fluids

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SUMMARYRecently, 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.

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Section: Problems Of Closed System Problem 1: Lid-driven Cavity Flowsupporting

confidence: 93%

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

Sun

et al. 2009

Numerical Methods in Fluids

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“…In the graphics corresponding to the plane x = 0.5, we can see the corner eddies caused by the presence of the walls in the planes y = 0 and y = 1; moreover, we observe, in the plane y = 0.5, the existence of the main circulation cell and the downstream secondary eddy formed in the bottom left corner, whereas we can see the Taylor-Göter-like vortices in the plane z = 0.5 . These results are in perfect agreement with those reported in Hachem et al [16] and Tang et al [28].…”

Section: Lid-driven Cavity Flowsupporting

confidence: 94%

“…Plane x = 0.5 Plane y = 0.5 Plane z = 0.5 The pressure contours on the three middle planes are displayed in Figure 4, they are similar to those obtained by Tang et al [28].…”

Section: Lid-driven Cavity Flowsupporting

confidence: 84%

Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review

Bermejo

Saavedra

2016

Communications in Applied and Industrial Mathematics

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We review in this paper the development of Lagrange-Galerkin (LG) methods to integrate the incompressible Navier-Stokes equations (NSEs) for engineering applications. These methods were introduced in the computational fluid dynamics community in the early eighties of the past century, and at that time they were considered good methods for both their theoretical stability properties and the way of dealing with the nonlinear terms of the equations; however, the numerical experience gained with the application of LG methods to different problems has identified drawbacks of them, such as the calculation of specific integrals that arise in their formulation and the calculation of the flow trajectories, which somehow have hampered the applicability of LG methods. In this paper, we focus on these issues and summarize the convergence results of LG methods; furthermore, we shall briefly introduce a new stabilized LG method suitable for high Reynolds numbers.

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“…The limited space did not allow us to consider many other important areas, such as hyperbolic problems, time dependent problems, and time-space leastsquares. For further details on such applications, we refer interested readers to [4], [9], [39], [40], [41], [62], [63], [88], [89], and [110]- [113], among others.…”

Section: Restricted Least-squares Methodsmentioning

confidence: 99%

Finite Element Methods of Least-Squares Type

Bochev¹,

Gunzburger²

1998

SIAM Rev.

284

237

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Abstract. We consider the application of least-squares variational principles to the numerical solution of partial differential equations. Our main focus is on the development of least-squares finite element methods for elliptic boundary value problems arising in fields such as fluid flows, linear elasticity, and convection-diffusion. For many of these problems, least-squares principles offer numerous theoretical and computational advantages in the algorithmic design and implementation of corresponding finite element methods, that are not present in standard Galerkin discretizations. Most notably, the use of least-squares principles leads to symmetric and positive definite algebraic problems and allows one to circumvent stability conditions such as the inf-sup condition arising in mixed methods for the Stokes and Navier-Stokes equations. As a result, application of least-squares principles has led to the development of robust and efficient finite element methods for a large class of problems of practical importance.

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Transient solutions for three‐dimensional lid‐driven cavity flows by a least‐squares finite element method

Cited by 41 publications

References 23 publications

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

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

Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review

Finite Element Methods of Least-Squares Type

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