CIMEC   24726
CENTRO DE INVESTIGACION DE METODOS COMPUTACIONALES
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Particle methods: A possibility of drastically reducing the computing time to solve the incompressible Navier-Stokes equations
Autor/es:
IDELSOHN, SERGIO; NIGRO NORBERTO; GIMENEZ JUAN; OÑATE EUGENIO
Lugar:
San Diego
Reunión:
Congreso; Finite Elements in Flow Problems; 2013
Institución organizadora:
Elsevier, Wiley, World Scientific, Springer, the International Association for Computational Mechanics (IACM), and the US Association for Computational Mechanics (USACM).
Resumen:
<!-- @page { margin: 0.79in } P { margin-bottom: 0.08in } A:link { color: #0000ff } --> 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<1 becomes crucial andlimit the use of explicit method or outdistance it to be efficient.On the other hand, implicit solutions using Eulerian formulations is restricted in the time step sizedue to the lack of convergence of the convective non-linear terms. Both time integrations, explicit orimplicit are, in most cases, limited to CFL no much larger than one.The possibility to perform parallel processing and the recent upcoming of new processors like GPUand GPGPU increase the possibilities of the explicit integration in time due to the facility toparallelize explicit methods having results with speed-up closed to one. Although the incompressiblecondition cannot be solved explicitly, the solution of the momentum conservation equations with anexplicit integration of the convective terms together with a parallel processing reduces considerablythe computing time to solve the whole problem provided that a large time-step may be preservedindependently to the discretization in space.In this lecture we will present a Particle Method to solve the incompressible Navier-Stokes equationsthat use a Lagrangian formulation with an explicit time integrator without the CFL<1 restriction forthe convective terms. This allows large time-steps, independent of the spatial discretization, havingequal or better precision that an implicit integration. Concerning the viscous terms, the integrationmay be implicit, but 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 using the Particle Finite Element Method (PFEM)[1] andcompared as well in accuracy as in computing time with other more standard Eulerian formulations. in http://th70.tafsm.org/frontal/progtodo.asp