The incompressible Navier-Stokes Equations is an example of moving boundary problem for which the spatial domain depends on the solution of the equations. When the fluid domain is strongly deformed, classical meshed methods may fail due to bad mesh conditionning. Another approach was proposed called "meshless" or "particle" methods that relies on interpolation points not dependent on a mesh. One of those methods named the Smoothed Particle Hydrodynamics (SPH) is particularly well suited for solving the Navier-Stokes Equations due to the intrinsinc treatment of the free-surface boundary condition.
The SPH method was then used from an engineering perspective to compute violent, low regularity flows, notably present in Fluid-Structure Interaction problems. This however raises interesting questions notably about the robustness of the method at low regularity data.
The presentation introduces the SPH method and review the few results known. Then, the SPH coupling with a solid solver is investigated, and highlights added-mass instability, for which a stabilization procedure was proposed. Finally, a study about the robustness of the SPH method to low regularity data for the Stokes problem is presented.
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