Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping. Bonito, A., Guermond, J., & Numerical Mathematics and Advanced Applications - ENUMATH 2013: Proceedings of ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013, Springer International Publishing, 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
@article{BonGueLee2015,
author="Bonito, Andrea
and Guermond, Jean-Luc
and Lee, Sanghyun",
editor="Abdulle, Assyr
and Deparis, Simone
and Kressner, Daniel
and Nobile, Fabio
and Picasso, Marco",
title="Modified Pressure-Correction Projection Methods: Open Boundary and Variable Time Stepping",
journal="Numerical Mathematics and Advanced  Applications - ENUMATH 2013: Proceedings of ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013",
year="2015",
publisher="Springer International Publishing",
pages="623-631",
isbn="978-3-319-10705-9",
doi="10.1007/978-3-319-10705-9_61",
url="http://dx.doi.org/10.1007/978-3-319-10705-9_61",
keywords={Projection method, Variable time stepping, Navier-Stokes},
abstract={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}
}