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Defect-deferred correction method for the two-domain convection-dominated convection–diffusion problem.

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Title: Defect-deferred correction method for the two-domain convection-dominated convection–diffusion problem.
Authors: Erkmen, Dilek1,2 derkmen@mtu.edu, Labovsky, Alexander E.1 aelabovs@mtu.edu
Source: Journal of Mathematical Analysis & Applications. Jun2017, Vol. 450 Issue 1, p180-196. 17p.
Subjects: Transport equation, Mathematical domains, Diffusion coefficients, Correction factors, Spacetime
Abstract: We present a method for solving a fluid–fluid interaction problem (two convection-dominated convection–diffusion problems adjoined by an interface), which is a simplified version of the atmosphere–ocean coupling problem. The method resolves some of the issues that can be crucial to the fluid–fluid interaction problems: it is a partitioned time stepping method, yet it is of high order accuracy in both space and time (the two-step algorithm considered in this report provides second order accuracy); it allows for the usage of the legacy codes (which is a common requirement when resolving flows in complex geometries), yet it can be applied to the problems with very small viscosity/diffusion coefficients. This is achieved by combining the defect correction technique for increased spatial accuracy (and for resolving the issue of high convection-to-diffusion ratio) with the deferred correction in time (which allows for the usage of the computationally attractive partitioned scheme, yet the time accuracy is increased beyond the usual result of partitioned methods being only first order accurate) into the defect-deferred correction method (DDC). The results are readily extendable to the higher order accuracy cases by adding more correction steps. Both the theoretical results and the numerical tests provided demonstrate that the computed solution is unconditionally stable and the accuracy in both space and time is improved after the correction step. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Mathematical Analysis & Applications 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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DbLabel: Engineering Source
An: 121157586
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  Data: Defect-deferred correction method for the two-domain convection-dominated convection–diffusion problem.
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  Data: <searchLink fieldCode="AR" term="%22Erkmen%2C+Dilek%22">Erkmen, Dilek</searchLink><relatesTo>1,2</relatesTo><i> derkmen@mtu.edu</i><br /><searchLink fieldCode="AR" term="%22Labovsky%2C+Alexander+E%2E%22">Labovsky, Alexander E.</searchLink><relatesTo>1</relatesTo><i> aelabovs@mtu.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Jun2017, Vol. 450 Issue 1, p180-196. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Transport+equation%22">Transport equation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+domains%22">Mathematical domains</searchLink><br /><searchLink fieldCode="DE" term="%22Diffusion+coefficients%22">Diffusion coefficients</searchLink><br /><searchLink fieldCode="DE" term="%22Correction+factors%22">Correction factors</searchLink><br /><searchLink fieldCode="DE" term="%22Spacetime%22">Spacetime</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We present a method for solving a fluid–fluid interaction problem (two convection-dominated convection–diffusion problems adjoined by an interface), which is a simplified version of the atmosphere–ocean coupling problem. The method resolves some of the issues that can be crucial to the fluid–fluid interaction problems: it is a partitioned time stepping method, yet it is of high order accuracy in both space and time (the two-step algorithm considered in this report provides second order accuracy); it allows for the usage of the legacy codes (which is a common requirement when resolving flows in complex geometries), yet it can be applied to the problems with very small viscosity/diffusion coefficients. This is achieved by combining the defect correction technique for increased spatial accuracy (and for resolving the issue of high convection-to-diffusion ratio) with the deferred correction in time (which allows for the usage of the computationally attractive partitioned scheme, yet the time accuracy is increased beyond the usual result of partitioned methods being only first order accurate) into the defect-deferred correction method (DDC). The results are readily extendable to the higher order accuracy cases by adding more correction steps. Both the theoretical results and the numerical tests provided demonstrate that the computed solution is unconditionally stable and the accuracy in both space and time is improved after the correction step. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Mathematical Analysis & Applications 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.jmaa.2017.01.018
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      – Code: eng
        Text: English
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        PageCount: 17
        StartPage: 180
    Subjects:
      – SubjectFull: Transport equation
        Type: general
      – SubjectFull: Mathematical domains
        Type: general
      – SubjectFull: Diffusion coefficients
        Type: general
      – SubjectFull: Correction factors
        Type: general
      – SubjectFull: Spacetime
        Type: general
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      – TitleFull: Defect-deferred correction method for the two-domain convection-dominated convection–diffusion problem.
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              M: 06
              Text: Jun2017
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              Y: 2017
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