Volume 3, Issue 2
A New Incompressible Smoothed Particle Hydrodynamics-Immersed Boundary Method

RODRIGUE KÉOU NOUTCHEUWA AND ROBERT G. OWENS

Int. J. Numer. Anal. Mod. B, 3 (2012), pp. 126-167

Published online: 2012-03

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  • Abstract
In this article we develop a new smoothed particle hydrodynamics (SPH) method suitable for solving the incompressible Navier-Stokes equations, even with singular forces. Singular source terms are handled in a manner similar to that in the immersed boundary (IB) method of Peskin (2002). The numerical scheme implements a second-order pressure-free projection method due to Kim and Moin (1985) and completely obviates the difficulties that may be faced in prescribing Neumann pressure boundary conditions. The proposed SPH method is first tested on the planar start-up Poiseuille problem and a detailed error analysis is performed. For this problem, the results are similar whether the SPH particles are free to move or fixed on a regular grid. Our hybrid SPH-IB method is then used to calculate the dynamics of a stretched immersed elastic membrane and the advantages in this case of fixing the SPH particles, rather than allowing them to move with the fluid, are discussed.
  • AMS Subject Headings

74F10 76M28

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COPYRIGHT: © Global Science Press

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@Article{IJNAMB-3-126, author = {RODRIGUE KÉOU NOUTCHEUWA AND ROBERT G. OWENS}, title = { A New Incompressible Smoothed Particle Hydrodynamics-Immersed Boundary Method}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2012}, volume = {3}, number = {2}, pages = {126--167}, abstract = {In this article we develop a new smoothed particle hydrodynamics (SPH) method suitable for solving the incompressible Navier-Stokes equations, even with singular forces. Singular source terms are handled in a manner similar to that in the immersed boundary (IB) method of Peskin (2002). The numerical scheme implements a second-order pressure-free projection method due to Kim and Moin (1985) and completely obviates the difficulties that may be faced in prescribing Neumann pressure boundary conditions. The proposed SPH method is first tested on the planar start-up Poiseuille problem and a detailed error analysis is performed. For this problem, the results are similar whether the SPH particles are free to move or fixed on a regular grid. Our hybrid SPH-IB method is then used to calculate the dynamics of a stretched immersed elastic membrane and the advantages in this case of fixing the SPH particles, rather than allowing them to move with the fluid, are discussed.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/275.html} }
TY - JOUR T1 - A New Incompressible Smoothed Particle Hydrodynamics-Immersed Boundary Method AU - RODRIGUE KÉOU NOUTCHEUWA AND ROBERT G. OWENS JO - International Journal of Numerical Analysis Modeling Series B VL - 2 SP - 126 EP - 167 PY - 2012 DA - 2012/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/275.html KW - Smoothed particle hydrodynamics KW - incompressible flow KW - projection method KW - singular force KW - immersed boundary AB - In this article we develop a new smoothed particle hydrodynamics (SPH) method suitable for solving the incompressible Navier-Stokes equations, even with singular forces. Singular source terms are handled in a manner similar to that in the immersed boundary (IB) method of Peskin (2002). The numerical scheme implements a second-order pressure-free projection method due to Kim and Moin (1985) and completely obviates the difficulties that may be faced in prescribing Neumann pressure boundary conditions. The proposed SPH method is first tested on the planar start-up Poiseuille problem and a detailed error analysis is performed. For this problem, the results are similar whether the SPH particles are free to move or fixed on a regular grid. Our hybrid SPH-IB method is then used to calculate the dynamics of a stretched immersed elastic membrane and the advantages in this case of fixing the SPH particles, rather than allowing them to move with the fluid, are discussed.
RODRIGUE KÉOU NOUTCHEUWA AND ROBERT G. OWENS. (2012). A New Incompressible Smoothed Particle Hydrodynamics-Immersed Boundary Method. International Journal of Numerical Analysis Modeling Series B. 3 (2). 126-167. doi:
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