Fast solvers for discretized Navier-Stokes problems using vector extrapolation

Duminil, Sébastien; Sadok, H.; Silvester, David J.

doi:10.1007/s11075-013-9726-7

Cited by 13 publications

(5 citation statements)

References 21 publications

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“…u and p are respectively velocity vector and pressure. The first convective term is quadratic non-linear, which can be linearised via so-called Newton correction and Picard's method 15 . By matrix description this velocity-pressure coupling system AW = b is:…”

Section: Methodsmentioning

confidence: 99%

Stabilisation of Discrete Adjoint Solvers for Incompressible Flow

Wang

Akbarzadeh

Müeller

2015

22nd AIAA Computational Fluid Dynamics Conference

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The pressure-correction equation and its coupling to the momentum equation as used in the popular incompressible approaches such as SIMPLE algorithm often exhibit poor stability and only converge to limit-cycle oscillations. Steady-state discrete adjoint solvers inherit the spectral properties of the flow solver from which they are derived and typically diverge if the flow discretisation is not stable. The paper discusses derivation of the discrete adjoint solver 1 using Automatic Differentiation (AD) and demonstrates the lack of stability of the SIMPLE scheme. An alternative strategy for the coupling of the flow equations is proposed that offers improved stability of the flow solver, as well as its adjoint. Numerical experiments comparing the standard SIMPLE scheme to the new stabilisation technique demonstrate the effectiveness and improved convergence of primal and adjoint system.

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Section: Methodsmentioning

confidence: 99%

Stabilisation of Discrete Adjoint Solvers for Incompressible Flow

Wang

Akbarzadeh

Müeller

2015

22nd AIAA Computational Fluid Dynamics Conference

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“…Vector extrapolation methods were used in many applications such as google page rank by Golub et al [14,15] and in other fields such as in statistics [16] or for solving discretized Navier-Stokes problems [17]. In the present paper, we consider tensor sequence transformations and propose new tensor extrapolation methods that generalize the classical vector ones.…”

Section: Introductionmentioning

confidence: 99%

Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products

2020

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In this paper, we present new Tensor extrapolation methods as generalizations of well known vector, matrix and block extrapolation methods such as polynomial extrapolation methods or ϵ-type algorithms. We will define new tensor products that will be used to introduce global tensor extrapolation methods. We discuss the application of these methods to the solution of linear and non linear tensor systems of equations and propose an efficient implementation of these methods via the global-QR decomposition.

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“…NCSC can be studied with the help of successful experience in such equations. For dealing with nonlinear iteration problems, generally speaking, some of the most common iterations for fluid equations are adopted, that is Stokes iteration, Oseen iteration and Newton iteration [18,19], as well as fixed-point iteration [20], extrapolation iteration [21] and C-N scheme [22], and so forth.…”

Section: Introductionmentioning

confidence: 99%

Pressure stabilization method for the 2D/3D time‐dependent natural convection equations with salt concentration

Liang,

Liu

2024

Z Angew Math Mech

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In this paper, the pressure stabilization method for the 2D/3D time‐dependent natural convection equations with salt concentration (NCSC) is considered. The artificial pressure diffusion term is introduced to reduce the constraint of the incompressible condition. The first‐order backward difference formula is adopted to approximate the temporal derivative terms, the diffusion terms in NCSC are treated implicitly, the convective terms in momentum equation are treated semi‐implicitly, the convective terms in energy equation and salt concentration equation are treated implicitly. The error estimates for the semi‐discrete pressure stabilization method are given. Some numerical experiments are presented to verify the theoretical results and show the reliability of the proposed method.

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Fast solvers for discretized Navier-Stokes problems using vector extrapolation

Cited by 13 publications

References 21 publications

Stabilisation of Discrete Adjoint Solvers for Incompressible Flow

Stabilisation of Discrete Adjoint Solvers for Incompressible Flow

Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products

Pressure stabilization method for the 2D/3D time‐dependent natural convection equations with salt concentration

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