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First, second and third order fractional step methods for the three-field viscoelastic flow problem.

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Title: First, second and third order fractional step methods for the three-field viscoelastic flow problem.
Authors: Castillo, E.1 ecastillo@cimne.upc.edu, Codina, R.1 ramon.codina@upc.edu
Source: Journal of Computational Physics. Sep2015, Vol. 296, p113-137. 25p.
Subjects: Viscoelasticity, Navier-Stokes equations, Fluid flow, Mathematical variables, Strains & stresses (Mechanics), Newtonian fluids, Incompressible flow
Abstract: In this paper, three different fractional step methods are designed for the three-field viscoelastic flow problem, whose variables are velocity, pressure and elastic stress. The starting point of our methods is the same as for classical pressure segregation algorithms used in the Newtonian incompressible Navier–Stokes problem. These methods can be understood as an inexact LU block factorization of the original system matrix of the fully discrete problem and are designed at the pure algebraic level. The final schemes allow one to solve the problem in a fully decoupled form, where each equation (for velocity, pressure and elastic stress) is solved separately. The first order scheme is obtained from a straightforward segregation of pressure and elastic stress in the momentum equation, whereas the key point for the second order scheme is a first order extrapolation of these variables. The third order fractional step method relies on Yosida's scheme. Referring to the spatial discretization, either the Galerkin method or a stabilized finite element formulation can be used. We describe the fractional step methods first assuming the former, and then we explain the modifications introduced by the stabilized formulation we employ and that has been proposed in a previous work. This discretization in space shows very good stability, permitting in particular the use of equal interpolation for all variables. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: First, second and third order fractional step methods for the three-field viscoelastic flow problem.
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  Data: <searchLink fieldCode="AR" term="%22Castillo%2C+E%2E%22">Castillo, E.</searchLink><relatesTo>1</relatesTo><i> ecastillo@cimne.upc.edu</i><br /><searchLink fieldCode="AR" term="%22Codina%2C+R%2E%22">Codina, R.</searchLink><relatesTo>1</relatesTo><i> ramon.codina@upc.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Physics%22">Journal of Computational Physics</searchLink>. Sep2015, Vol. 296, p113-137. 25p.
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  Data: <searchLink fieldCode="DE" term="%22Viscoelasticity%22">Viscoelasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Navier-Stokes+equations%22">Navier-Stokes equations</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+flow%22">Fluid flow</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+variables%22">Mathematical variables</searchLink><br /><searchLink fieldCode="DE" term="%22Strains+%26+stresses+%28Mechanics%29%22">Strains & stresses (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Newtonian+fluids%22">Newtonian fluids</searchLink><br /><searchLink fieldCode="DE" term="%22Incompressible+flow%22">Incompressible flow</searchLink>
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  Label: Abstract
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  Data: In this paper, three different fractional step methods are designed for the three-field viscoelastic flow problem, whose variables are velocity, pressure and elastic stress. The starting point of our methods is the same as for classical pressure segregation algorithms used in the Newtonian incompressible Navier–Stokes problem. These methods can be understood as an inexact LU block factorization of the original system matrix of the fully discrete problem and are designed at the pure algebraic level. The final schemes allow one to solve the problem in a fully decoupled form, where each equation (for velocity, pressure and elastic stress) is solved separately. The first order scheme is obtained from a straightforward segregation of pressure and elastic stress in the momentum equation, whereas the key point for the second order scheme is a first order extrapolation of these variables. The third order fractional step method relies on Yosida's scheme. Referring to the spatial discretization, either the Galerkin method or a stabilized finite element formulation can be used. We describe the fractional step methods first assuming the former, and then we explain the modifications introduced by the stabilized formulation we employ and that has been proposed in a previous work. This discretization in space shows very good stability, permitting in particular the use of equal interpolation for all variables. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.jcp.2015.04.027
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      – Code: eng
        Text: English
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        PageCount: 25
        StartPage: 113
    Subjects:
      – SubjectFull: Viscoelasticity
        Type: general
      – SubjectFull: Navier-Stokes equations
        Type: general
      – SubjectFull: Fluid flow
        Type: general
      – SubjectFull: Mathematical variables
        Type: general
      – SubjectFull: Strains & stresses (Mechanics)
        Type: general
      – SubjectFull: Newtonian fluids
        Type: general
      – SubjectFull: Incompressible flow
        Type: general
    Titles:
      – TitleFull: First, second and third order fractional step methods for the three-field viscoelastic flow problem.
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            NameFull: Castillo, E.
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            NameFull: Codina, R.
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            – D: 01
              M: 09
              Text: Sep2015
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              Y: 2015
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              Value: 296
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