A second-order in time and space particle-based method to solve flow problems on arbitrary meshes

A pseudo-DNS method for the simulation of incompressible fluid flows with instabilities at different scales

“…A structured mesh of 80 × 80 × 80 cells was employed with a controlled time-step fulfilling the Courant-Friedrichs-Lewy limit C <= 1, where C is the Courant number. A standard unsteady FVM solver with second-order space and time discretization was employed in an ad-hoc code developed by the authors [29], based on solver pimpleFoam (OpenFOAM R suite).…”

“…As mentioned above, adopting a Lagrangian formulation allows for accurately and naturally convecting and spreading the instabilities, even with a coarse mesh. Good resolution may be obtained by using either the first [30,31] or the second generation of the Particle Finite Element Method (PFEM-2) [32][33][34][35] or its finite volume version, called Particle Finite Volume Method (PFVM) [36]. The readers are referred to these references for further details on these technologies.…”

“…Two particles per cell are initially seeded, and a requirement is imposed for having at least one and at most ten particles per cell during the simulation. The implementation of the second-order in time and space methodology for particle-based methods, presented in [36], is used. Simulations are run up to a final time T f = 50s and the mean fields are obtained by an averaging of the last 20 simulated seconds, a window large enough for obtaining reliable statistics.…”

A second-order semi-Lagrangian particle finite element method for fluid flows

“…However, Lagrangian and semi-Lagrangian methods are usually based on first order in time integration schemes, which limits its rate of convergence. As an exception, a recent work [4] within the semi-Lagrangian Particle Finite Element Method (SL-PFEM) framework, has proposed a second order scheme. It is based on Strang´s symmetric operator splitting, a third order projector to transfer data from the particle to the mesh, and on estimating the particle´s trajectories using a linear approximation to the instantaneous streamline determined by the velocity field.…”

“…Until [4], the SL-PFEM framework has been developed based on explicit integrators that compute streamlines to approximate the particle´s trajectories. This approach has been successfully applied to many different problems [1,2,3,4]. In fact, the more convection dominates the flow, the better the streamlines approximate the pathlines and the larger the time step that can be used.…”