On the analysis of heterogeneous fluids with jumps in the viscosity using a discontinuous pressure field

Numerical Methods in Fluids

Oñate

2010

In this work, we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking interfaces.\ud We develop a numerical scheme able to deal with large jumps in the physical properties, included surface tension, and able to accurately represent all types of discontinuities in the flow variables. The scheme is based on decoupling the velocity and pressure variables through a pressure segregation method that takes into account the interface conditions. The interface is defined to be aligned with the moving mesh, so that it remains sharp along time, and pressure degrees of freedom are duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity. Furthermore, the mesh is refined in the vicinity of the interface to improve the accuracy and the efficiency of the\ud computations. We apply the resulting scheme to the benchmark problem of a two-dimensional bubble rising in a liquid column presented in Hysing et al. (International Journal for Numerical Methods in Fluids 2009; 60: 1259–1288), and propose two breakup and coalescence problems to assess the ability of a multi-fluid code to model topology changes.Peer ReviewedPostprint (author’s final draft

“…Both differences in viscosity and the presence of surface tension cause a C −1 discontinuity in the pressure field (Figures 2(b) and (c)), as shown in [2]:…”

Section: Interface Discontinuitiesmentioning

confidence: 93%

“…In particular, the pressure field has been made double-valued at the interface, i.e. pressure degrees of freedom have been duplicated ( p + , p − ) in the interface nodes [2]. The pressure discontinuity is thus optimally approximated.…”

Section: Particle Finite Element Methodsmentioning

confidence: 99%

Advances in the simulation of multi‐fluid flows with the particle finite element method. Application to bubble dynamics

Mier-Torrecilla

Numerical Methods in Fluids

Oñate

2010

“…This also provides the closure equations for computing the p variables. PGP and OSS stabilization methods are useful for homogeneous flows lacking free surfaces but encounter difficulties to satisfy incompressibility for fluids with heterogeneous (and discontinuous) physical properties [29][30][31] and, in some cases, for free-surface flows when pressure segregation techniques are used for solving the Navier-Stokes equations. Furthermore, PGP and OSS methods increase the number of problem variables (u, p and p) as well as the connectivity (bandwidth) of the stabilization matrices to be solved.…”

Section: Introductionmentioning

confidence: 99%

“…The split of Equation (55) ensures that the term (1/ i ) i is discontinuous between adjacent elements after discretization. This is essential for accurately capturing high discontinuous pressure gradient jumps typical of fluids with heterogeneous physical properties (either the viscosity or the pressure) [29][30][31]. In this manner the term (1/ i ) i can match the discrete pressure gradient term * p/*x i which is naturally discontinuous between elements for a linear approximation of the pressure.…”

mentioning

confidence: 99%

A family of residual‐based stabilized finite element methods for Stokes flows

Oñate

Nadukandi

Numerical Methods in Fluids

et al. 2010

Self Cite

SUMMARYWe present a collection of stabilized finite element (FE) methods derived via first-and second-order finite calculus (FIC) procedures. It is shown that several well known existing stabilized FE methods such as the penalty technique, the Galerkin Least Square (GLS) method, the Pressure Gradient Projection (PGP) method and the orthogonal sub-scales (OSS) method are recovered from the general residual-based FIC stabilized form. A new family of stabilized Pressure Laplacian Stabilization (PLS) FE methods with consistent nonlinear forms of the stabilization parameters are derived. The distinct feature of the family of PLS methods is that they are residual-based, i.e. the stabilization terms depend on the discrete residuals of the momentum and/or the incompressibility equations. The advantages and disadvantages of the different stabilization techniques are discussed and several examples of application are presented.

“…Up to now, the method has been successfully applied to naval and coastal engineering [4,20,23,28,29], fluid-structure interaction [14-16, 21, 35], melting of polymers in fire [30], excavation problems [3], forming processes [8,27] and multifluid flows [17,18].…”

Section: Particle Finite Element Methodsmentioning

confidence: 99%

The Particle Finite Element Method for Multi-Fluid Flows

Mier-Torrecilla

Marti

et al. 2011

Particle-Based Methods

This paper presents the Particle Finite Element Method (PFEM) and its application to multi-fluid flows. Key features of the method are the use of a Lagrangian description to model the motion of the fluid particles (nodes) and that all the information is associated to the particles. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral form, are solved as in the standard FEM. We have extended the method to problems involving several different fluids with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking any kind of interfaces.