Particle methods: A possibility of drastically reducing the computing time to solve the incompressible Navier-Stokes equations

SERGIO R. IDELSOHN; NORBERTO M. NIGRO; JUAN M. GIMENEZ; EUGENIO OÑATE

San Diego

Congreso; Advances in Computational Mechanics and 17th International Conference on Finite Elements in Flow Problems; 2013

One of the main drawbacks of the explicit integration using Eulerian formulations is the restrictedstability of the solution with the time steps and with the spatial discretization. For the case of theNavier-Stoke equations, it is well known that the time step to be used in the solution is stable only fortime step smaller than two critical values: the Courant-Friedrichs-Lewy (CFL) number and theFourier number. The first one is concerning with the convective terms and the second one with thediffusive ones. Both numbers must be less than one to have stable algorithms. For convectiondominant problems like high Reynolds number flows, the condition CFL