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

Type
Book Chapter

Authors
Bonito, Andrea
Guermond, Jean-Luc
Lee, Sanghyun

KAUST Grant Number
KUS-C1-016-04

Online Publication Date
2014-10-31

Print Publication Date
2015

Date
2014-10-31

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.

Citation
Bonito A, Guermond J-L, Lee S (2014) Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping. Numerical Mathematics and Advanced Applications - ENUMATH 2013: 623–631. Available: http://dx.doi.org/10.1007/978-3-319-10705-9_61.

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).

Publisher
Springer Nature

Journal
Numerical Mathematics and Advanced Applications - ENUMATH 2013

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

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