A Multigrid Method for Viscoelastic Fluid Flow

Lee, Hyesuk

doi:10.1137/s0036142902415924

Cited by 19 publications

(14 citation statements)

References 11 publications

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“…The method has been implemented using [11] [6,9,15], the right-hand side functions in Equation (1) were appropriately given so that the true solution was…”

Section: Numerical Resultsmentioning

confidence: 99%

Defect correction method for time-dependent viscoelastic fluid flow

Zhang

Hou

2011

International Journal of Computer Mathematics

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A defect correction method for solving the time-dependent viscoelastic fluid flow, aiming at high Weissenberg numbers, is presented. In the defect step, the constitutive equation is computed with the artificially reduced Weissenberg parameter for stability, and the residual is considered in the correction step. We show the convergence of the method and derive an error estimate. Numerical experiments support the theoretical results and demonstrate the effectiveness of the method.

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“…The method has been implemented using [11] [6,9,15], the right-hand side functions in Equation (1) were appropriately given so that the true solution was…”

Section: Numerical Resultsmentioning

confidence: 99%

Defect correction method for time-dependent viscoelastic fluid flow

Zhang

Hou

2011

International Journal of Computer Mathematics

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“…The computations indicate that the numerical solution algorithms are more sensitive to the g a term in the constitutive equation than the convective derivative. The defect-correction method, Algorithm 7.1, could be more efficiently implemented when combined with a multilevel method [19]. A multilevel method could be effectively used in both the defect and correction steps.…”

Section: Discussionmentioning

confidence: 99%

Defect correction method for viscoelastic fluid flows at high Weissenberg number

Ervin

Lee

2005

Numerical Methods Partial

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We study a defect correction method for the approximation of viscoelastic fluid flow. In the defect step, the constitutive equation is computed with an artificially reduced Weissenberg parameter for stability, and the resulting residual is corrected in the correction step. We prove the convergence of the defect correction method and derive an error estimate for the Oseen-viscoelastic model problem. The derived theoretical results are supported by numerical tests for both the Oseen-viscoelastic problem and the Johnson-Segalman model problem.

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“…To test the numerical stability of the new stabilized method, we considered the lowest equal-order FE triples p1 -p1 -p1 dg for velocity, pressure, and stress. Different authors used this experimental pattern for the Stokes and Navier-Stokes equations [11,44,51].…”

Section: Analytical Solution Testmentioning

confidence: 99%

“…Currently, the literature on the FE method is burgeoning to approximate the viscoelastic fluid flow model equations by using a variety of alternative stabilization formulations. The most common among them are streamline-upwind Petrov-Galerkin (SUPG) methods [8], discontinuous Galerkin (DG) methods [9], decoupled FE methods [10], multigrid methods [11], variational multiscale methods [12], and so on.…”

Section: Introductionmentioning

confidence: 99%

Stabilized lowest equal-order mixed finite element method for the Oseen viscoelastic fluid flow

et al. 2018

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In this paper, we present a stabilized lowest equal-order mixed finite element (FE) method for the Oseen viscoelastic fluid flow obeying an Oldroyd-B type constitutive law. To approximate the velocity, pressure, and stress tensor, we choose lowest equal-order FE triples p1-p1-p1 dg respectively. It is well known that these elements don't satisfy the inf-sup (or LBB) condition. Owing to the violation of the essential stability condition, the system became unstable. To overcome this difficulty, a standard pressure stabilization term is added to the discrete variational formulation, which ensures the well-posedness of the FE scheme. The existences and uniqueness of the FE scheme are derived. The desired optimal error bound is obtained. Three numerical experiments are executed to illustrate the validity and efficiency of the numerical method. The stabilized method provides attractive computational advantages, such as simpler data structures, parameter-free, no calculations of higher-order derivatives, and fast solver in simulations.

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A Multigrid Method for Viscoelastic Fluid Flow

Cited by 19 publications

References 11 publications

Defect correction method for time-dependent viscoelastic fluid flow

Defect correction method for time-dependent viscoelastic fluid flow

Defect correction method for viscoelastic fluid flows at high Weissenberg number

Stabilized lowest equal-order mixed finite element method for the Oseen viscoelastic fluid flow

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