Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping

Andrea Bonito; Jean-Luc Guermond; Sanghyun Lee

doi:10.1007/978-3-319-10705-9_61

Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping

Andrea Bonito, Jean-Luc Guermond, Sanghyun Lee

Research output: Chapter in Book/Report/Conference proceeding › Chapter

4 Scopus citations

Abstract

© Springer International Publishing Switzerland 2015. In this paper, we design and study two modifications of the first order standard pressure increment projection scheme for the Stokes system. The first scheme improves the existing schemes in the case of open boundary condition by modifying the pressure increment boundary condition, thereby minimizing the pressure boundary layer and recovering the optimal first order decay. The second scheme allows for variable time stepping. It turns out that the straightforward modification to variable time stepping leads to unstable schemes. The proposed scheme is not only stable but also exhibits the optimal first order decay. Numerical computations illustrating the theoretical estimates are provided for both new schemes.

Original language	English (US)
Title of host publication	Numerical Mathematics and Advanced Applications - ENUMATH 2013
Publisher	Springer Nature
Pages	623-631
Number of pages	9
ISBN (Print)	9783319107042
DOIs	https://doi.org/10.1007/978-3-319-10705-9_61
State	Published - Oct 31 2014
Externally published	Yes

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10.1007/978-3-319-10705-9_61

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title = "Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping",

abstract = "{\textcopyright} Springer International Publishing Switzerland 2015. In this paper, we design and study two modifications of the first order standard pressure increment projection scheme for the Stokes system. The first scheme improves the existing schemes in the case of open boundary condition by modifying the pressure increment boundary condition, thereby minimizing the pressure boundary layer and recovering the optimal first order decay. The second scheme allows for variable time stepping. It turns out that the straightforward modification to variable time stepping leads to unstable schemes. The proposed scheme is not only stable but also exhibits the optimal first order decay. Numerical computations illustrating the theoretical estimates are provided for both new schemes.",

author = "Andrea Bonito and Jean-Luc Guermond and Sanghyun Lee",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: Partially supported by NSF grant DMS-1254618 and award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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T1 - Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping

AU - Bonito, Andrea

AU - Guermond, Jean-Luc

AU - Lee, Sanghyun

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: Partially supported by NSF grant DMS-1254618 and award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2014/10/31

Y1 - 2014/10/31

N2 - © Springer International Publishing Switzerland 2015. In this paper, we design and study two modifications of the first order standard pressure increment projection scheme for the Stokes system. The first scheme improves the existing schemes in the case of open boundary condition by modifying the pressure increment boundary condition, thereby minimizing the pressure boundary layer and recovering the optimal first order decay. The second scheme allows for variable time stepping. It turns out that the straightforward modification to variable time stepping leads to unstable schemes. The proposed scheme is not only stable but also exhibits the optimal first order decay. Numerical computations illustrating the theoretical estimates are provided for both new schemes.

AB - © Springer International Publishing Switzerland 2015. In this paper, we design and study two modifications of the first order standard pressure increment projection scheme for the Stokes system. The first scheme improves the existing schemes in the case of open boundary condition by modifying the pressure increment boundary condition, thereby minimizing the pressure boundary layer and recovering the optimal first order decay. The second scheme allows for variable time stepping. It turns out that the straightforward modification to variable time stepping leads to unstable schemes. The proposed scheme is not only stable but also exhibits the optimal first order decay. Numerical computations illustrating the theoretical estimates are provided for both new schemes.

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BT - Numerical Mathematics and Advanced Applications - ENUMATH 2013

PB - Springer Nature

ER -

Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping

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