A NEW INCOMPRESSIBLE SMOOTHED PARTICLE HYDRODYNAMICS-IMMERSED BOUNDARY METHOD

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.

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