INVESTIGADORES
NIGRO Norberto Marcelo
congresos y reuniones científicas
Título:
Particle Methods: a possibility to solve in Real-Time the incompressible Navier-Stokes equations with free and/or internal moving boundaries
Autor/es:
IDELSOHN, SERGIO; OÑATE EUGENIO; NIGRO NORBERTO; MARTI JULIO; BECKER PABLO; GIMENEZ JUAN
Lugar:
Rayleigh
Reunión:
Congreso; Congreso USNCCM, Mini simposio de Moving Boundaries and Internal Interfaces; 2013
Institución organizadora:
USCM
Resumen:
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<1 becomes crucial andlimit the use of explicit methods or outdistance its to be efficient. On the other hand, implicitintegrations using Eulerian formulations are restricted in the time-step size due to the lack ofconvergence of the convective non-linear terms. Both time integrations, explicit or implicit are, inmost cases, limited to CFL no much larger than one.In this lecture we will present a Particle Method to solve the incompressible Navier-Stokes equationswith free-surfaces or moving internal interfaces that use a Lagrangian formulation with explicit orimplicit time integration without the CFL<1 restriction. This allows large time-steps, independent ofthe spatial discretization, having equal or better precision that an Eulerian integration. Concerning theviscous terms, thanks to the Lagrangian formulation, the non-linear terms are not present in thetangent matrix and then, it can be triangularized only once, reducing drastically the computing timeto solve the whole problem.The proposal will be tested numerically for free-surface and/or multi-fluids flows using the ParticleFinite Element Method (PFEM)[1]. The results are then compared as well in accuracy as incomputing time with other more standard Eulerian formulations.