Particle Methods: a possibility to solve in Real-Time the incompressible Navier-Stokes equations with free and/or internal moving boundaries

SERGIO R. IDELSOHN; EUGENIO OÑATE; NORBERTO M. NIGRO; JULIO MARTI; PABLO BECKER; JUAN M. GIMENEZ

Congreso; Congreso USNCCM, Mini simposio de Moving Boundaries and Internal Interfaces; 2013; 2013

One of the main drawbacks of all the time integration algorithms using an Eulerian formulations isthe restricted time-step to be used to have acceptable results.For the case of the Navier-Stoke equations with free-surfaces or moving internal interfaces, it is wellknown that in the explicit integrations, the time-step to be used in the solution is stable only for time-step smaller than two critical values: the Courant-Friedrichs-Lewy (CFL) number and the Fouriernumber. The first one is concerning with the convective terms and the second one with the diffusiveones. Both numbers must be less than one to have stable algorithms. For convection dominantproblems like medium and high Reynolds number flows, the condition CFL