Particle Methods: the best solution for Computational Fluid Dynamic problems

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

Congreso; COMPDYN 2013, 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering and 3rd South-East European Conference on Computational Mechanics; 2013

One of the main drawbacks of all the time integration algorithms using an Eulerian formulations is the 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 well known that in the explicit integrations, the time-step to be used in the solution is stable only for timestep smaller than two critical values: the Courant-Friedrichs-Lewy (CFL) number and the Fourier number. The first one is concerning with the convective terms and the second one with the diffusive ones. Both numbers must be less than one to have stable algorithms. For convection dominant problems like medium and high Reynolds number flows, the condition CFL