A Particle Method with Second Order Approximation in Space-Time

JUAN M. GIMENEZ; HORACIO J. AGUERRE; SERGIO R. IDELSOHN; NORBERTO M. NIGRO

New York

Congreso; 13th World Congress on Computational Mechanics. 2nd Pan American Congress on Computational Mechanics; 2018

International Associaction for Computational Mechanics

Lagrangian-based methods using particles are established methodologies which rely on the goodness of particlesfor solving the convective term of transport equations. Despite having shown impressive results for some particularapplications and presenting promissory potential for parallel architectures, the efficiency of particle-based methodssolving the incompressible Navier-Stokes equations currently does not justify its massive use in replace of classicalEulerian methodologies. Strategies such as PFEM-2 [1] have decreased the huge computational cost of particlemethods, but mainly because of the low order schemes employed. This work presents the first proposal of asecond order accurate particle method in both time and space for solving incompressible flows equations within aLagrangian formulation. This methodology consists on reinterpreting the convective term of any transport equationas a source term estimated with particles. An updated version of the eXplicit Integration Following the Accelerationand Streamlines (X-IVAS) method [2] is used and a second order projection scheme is employed to transfer datafrom the particles to the mesh. In the case of incompressible flows, the modified momentum equation is used asvelocity predictor without modifying the original rate of convergence of the Eulerian solution but improving thenumerical approximation of the convective term. With the aim of presenting the methodology and particle-meshinteraction, firstly the solution of scalar transport equations is shown. Then, incompressible flow problems aresolved where the rate of convergence of the method is assessed experimentally and the need of iterating theX-IVAS during velocity-pressure coupling is revealed. The implementation on the open source platform OpenFOAMallows employing general polyhedral meshes and obtaining reliable computing times comparisons. Results revealsthat, for the analyzed cases, the current method is able to obtain the same or lower level of error than a fastEulerian alternative, but saving considerably total computing time. [1] ?Lagrangian versus Eulerian integrationerrors?; Sergio Idelsohn, Eugenio Oñate, Norberto Nigro, Pablo Becker, Juan Gimenez; Comput. Methods Appl.Mech. Engrg. 293, 15,191?206. [2] ?Analysis of multi-fluid flows with large time steps using the Particle FiniteElement Method?; Sergio Idelsohn, Julio Marti, Pablo Becker, Eugenio Oñate. Int. Journal for Num. Methods inFluids, 75, 621-644.