Adaptive least-squares finite element approximations to Stokes equations

Lee, Hsueh-Chen; Chen, Tsu-Fen

doi:10.1016/j.cam.2014.11.041

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…Therefore, difficulties in solving non-Newtonian flow problems include computational limitations and singularities caused by the high number of unknowns and geometric discontinuities, respectively. To resolve these problems, adaptive LS methods have been extensively used as powerful tools for obtaining more efficient and accurate results [6]- [8]. In [7], an adaptive refined LS approach (ALS) generated using a velocity magnitude is developed to refine the mesh adaptively for the Carreau generalized Newtonian fluid flows.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulations of Viscoelastic Fluid Flows Using a Least-Squares Finite Element Method Based on Von Mises Stress Criteria

Lee¹

2017

IJAPM

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Abstract:The work concerns least-squares (LS) finite element solutions of the Oldroyd-B viscoelastic fluid flows using adaptive grids. To capture the viscoelastic flow region, adaptive grids are automatically generated on the basis of the von Mises stress from stress component transfer functions, and these generated refined grids agree with the physical flow attributes. Model problems considered are the flow past a slot channel problems. Numerical solutions of the flow pass through a slot channel indicate that the viscoelastic polymer solution flow characteristics are described by the refinement results of the von Mises stress. In additions, adaptive grids using the von Mises stress outperform those using functions of velocity, and satisfactory results are obtained using a lower total numbers of elements. The developed method is effective for analyzing viscoelastic fluid flows. Furthermore, the effects of low Weissenberg numbers are also investigated.

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Section: Introductionmentioning

confidence: 99%

Numerical Simulations of Viscoelastic Fluid Flows Using a Least-Squares Finite Element Method Based on Von Mises Stress Criteria

Lee¹

2017

IJAPM

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“…In recent years, there has been an increased interest in the least-squares finite element method for the approximation of partial differential equations, see e.g. [1]- [6]. This technique is attractive because the linear systems generated by the discretization are symmetric and positive definite, thus the algebraic system can be solved by fast direct or iterative algorithms.…”

Section: Introductionmentioning

confidence: 99%

Least-Squares Finite Element Method for the Steady Upper-Convected Maxwell Fluid

Zhou¹,

Hou²

2015

APM

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In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a leastsquares method to the linearized version of the viscoelastic UCM model. The L 2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.

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Efficient stress–velocity least-squares finite element formulations for the incompressible Navier–Stokes equations

Nisters

Schwarz

2018

Computer Methods in Applied Mechanics and Engineering

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Adaptive least-squares finite element approximations to Stokes equations

Cited by 5 publications

References 12 publications

Numerical Simulations of Viscoelastic Fluid Flows Using a Least-Squares Finite Element Method Based on Von Mises Stress Criteria

Numerical Simulations of Viscoelastic Fluid Flows Using a Least-Squares Finite Element Method Based on Von Mises Stress Criteria

Least-Squares Finite Element Method for the Steady Upper-Convected Maxwell Fluid

Efficient stress–velocity least-squares finite element formulations for the incompressible Navier–Stokes equations

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