Abstract

Particle methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied on it. In this paper the Particle Finite Element Method based on finite element shape functions is used to solve the continuous fluid mechanics equations in the case of heterogeneous density. To evaluate the external applied forces to each particle, the incompressible Navier–Stokes equations are solved at each time step using a Lagrangian formulation. All the information in the fluid is transmitted via the particles. All kinds of density heterogeneous fluids and multiphase flows with internal interfaces including or not free-surfaces, breaking waves and fluid separations may be easily solved with this methodology. 

Abstract

Heterogeneous incompressible fluid flows with jumps in the viscous properties are solved with the particle finite element method using continuous and discontinuous pressure fields. We show the importance of using discontinuous pressure fields to avoid errors in the incompressibility condition near the interface.

Abstract

The latest generation of the particle finite element method (PFEM-2) is a numerical method based on the Lagrangian formulation of the equations, which presents advantages in terms of robustness and efficiency over classical Eulerian methodologies when certain kind of flows are simulated, especially those where convection plays an important role. These situations are often encountered in real engineering problems, where very complex geometries and operating conditions require very large and long computations. The advantages that the parallelism introduced in the computational fluid dynamics making affordable computations with very fine spatial discretizations are well known. However, it is not possible to have the time parallelized, despite the effort that is being dedicated to use space–time formulations. In this sense, PFEM-2 adds a valuable feature in that its strong stability with little loss of accuracy provides an interesting way of satisfying the real-life computation needs. After having already demonstrated in previous publications its ability to achieve academic-based solutions with a good compromise between accuracy and efficiency, in this work, the method is revisited and employed to solve several nonacademic problems of technological interest, which fall into that category. Simulations concerning oil–water separation, waste-water treatment, metallurgical foundries, and safety assessment are presented. These cases are selected due to their particular requirements of long simulation times and or intensive interface treatment. Thus, large time-steps may be employed with PFEM-2 without compromising the accuracy and robustness of the simulation, as occurs with Eulerian alternatives, showing the potentiality of the methodology for solving not only academic tests but also real engineering problems.

Abstract

Multifluids are those fluids in which their physical properties (viscosity or density) vary internally and abruptly forming internal interfaces that introduce a large nonlinearity in the Navier–Stokes equations. For this reason, standard numerical methods require very small time steps in order to solve accurately the internal interface position. In a previous paper, the authors developed a particle‐based method (named particle finite element method (PFEM)) based on a Lagrangian formulation and FEM for solving the fluid mechanics equations for multifluids. PFEM was capable of achieving accurate results, but the limitation of small time steps was still present. In this work, a new strategy concerning the time integration for the analysis of multifluids is developed allowing time steps one order of magnitude larger than the previous method. The advantage of using a Lagrangian solution with PFEM is shown in several examples. All kind of heterogeneous fluids (with different densities or viscosities), multiphase flows with internal interfaces, breaking waves, and fluid separation may be easily solved with this methodology without the need of small time steps.