Lagrangian frames. An efficient and accurate way to solve multi-fluids flows.

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

Stanford

Workshop; Workshop on Computational Methods for Problems with Evolving Domains and Discontinuities; 2013

Stanford University

Many of the previous works for solving the incompressible Navier-Stokes equations have been thought for homogeneous fluids. For multi-fluids flows there are two main differences: the possibility to have evolving discontinuities on the pressure field or to have evolving discontinuities on the pressure gradients. The first case appears when there are surface tensions at the internal interfaces, or there is an internal jump in the viscosity. The second case is typical of problems with internal jumps in the density. The use of evolving discontinuous pressure or pressure gradient fields is fundamental to achieve acceptable results in multi-fluid fluid flows. In this workshop a new generation of the Particle Finite Element Method[1] (PFEM) will be developed and applied for solving the incompressible Navier-Stokes equations for heterogeneous fluid flows. In a previous version of PFEM, the authors showed the ability of Lagrangian frames to deal with problems ranging from simple fluids with a single interface to fluid mixtures with multiple interfaces [2]. Now, we will introduce a new strategy, named ?X-IVAS?, that allows us to solve the same problems in a very efficient way concerning computer time. In fact, in all the cases tested, the computer times were smaller than for similar problems solved with classical Eulerian frames. This new strategy may be seen as a different way of linearizing the N-S equations that allows large time-steps with an excellent convergence rate. This particular linearization of the non-linear N-S equations exists only if the equations are written in a Lagrangian frame. In fact, in all the examples tested, only one iteration of the non-linear N-S equations was enough to achieve an excellent result. This conclusion opens a new perspective for the Lagrangian formulation of the N-S equations. To our knowledge, nowadays PFEM is the fastest algorithm for solving multi-fluid flows with nonstructured meshes.