In this paper we present a new version of the Particle Finite Element Method (PFEM) applied to fr... more In this paper we present a new version of the Particle Finite Element Method (PFEM) applied to free surface and multi-fluid flows problems. In the previous works, the PFEM was applied to this kind of problems taking advantage of the fact that Lagrangian methods are specially well suited for tracking free surfaces and interfaces[1]. Note that in the Lagrangian approaches the problem becomes separated into a geometrical part(tracking the motion of the nodes) and a physical part(calculating how the flow variables evolve in time at each node). The numerical schemes used in the previous versions of PFEM, were able to deal with free-surface and multi-fluid flows. However its main disadvantage consisted in the need of remeshing at every time step due the mesh distortion. This increased the computational cost of the method particularly due to the fact that the time step size had to be small enough in order to avoid the element inversion (which is equivalent to the non-negativity of the Jaco...
Conducting a numerical simulation of a domain where there exist strong or weak discontinuities in... more Conducting a numerical simulation of a domain where there exist strong or weak discontinuities in the unknown field is still a challenge in computational mechanics. There are many cases in real world where the solution procedure using numerical methods require a way of dealing with this sort of situation, such as: simulation of multiple materials with changing physical properties. Moreover, simulation of two materials where one material being very viscous and the other one having small viscosity could be considered as plasticity. There are various solution methodologies for these sorts of cases, where all have their advantages and disadvantages. The work that will be presented here is a solution procedure for the cases mentioned above by enriching the FE space and statically condensing the occurring additional degrees of freedom in the elemental level. A more detailed information could be obtained in [1]. Implementing this procedure, a Stokes Flow solver that uses the ASGS [2] stabi...
Many polymer-made objects show a trend of melting and dripping in fire, a behavior that may be mo... more Many polymer-made objects show a trend of melting and dripping in fire, a behavior that may be modified by adding flame retardants (FRs). These affect materials properties, e.g., heat absorption and viscosity. In this paper, the effect of a flame retardant on the fire behavior of polymers in the UL 94 scenario is studied. This goal is achieved essentially by applying a new computational strategy that combines the particle finite element method for the polymer with an Eulerian formulation for air. The sample selected is a polypropylene (PP) with magnesium hydroxide at 30 wt.%. For modelling, values of density, conductivity, specific heat, viscosity, and Arrhenius coefficients are obtained from different literature sources, and experimental characterization is performed. However, to alleviate the missing viscosity at a high temperature, three viscosity curves are introduced on the basis of the viscosity curve provided by NIST and the images of the test. In the experiment, we burn the ...
Computer Methods in Applied Mechanics and Engineering, 2020
Abstract Particle finite element method (PFEM) is a computational tool suitable for simulating fl... more Abstract Particle finite element method (PFEM) is a computational tool suitable for simulating fluid dynamics problems characterized by presence of moving boundaries. In this paper a new version of the method for incompressible flow problems is proposed aiming at accuracy improvement. This goal is achieved essentially by applying Strang operator splitting to Navier–Stokes equations and selecting adequate integration schemes for the resulting advective and Stokes sub-problems. For achieving efficient implementation, the pressure and the velocity in the Stokes part are decoupled via the fractional step technique as in the classical PFEM. However, at the first fractional step an explicit pressure prediction procedure for alleviating mass losses is introduced. Three test cases are solved, validating the methodology and estimating its accuracy. The numerical evidence proves that the proposed scheme improves the accuracy of the PFEM.
In this paper the so-called added-mass effect is investigated from a different point of view of p... more In this paper the so-called added-mass effect is investigated from a different point of view of previous publications. The monolithic fluid structure problem is partitioned using a static condensation of the velocity terms. Following this procedure the classical stabilized projection method for incompressible fluid flows is introduced. The procedure allows obtaining a new pressure segregated scheme for fluid-structure interaction problems
ABSTRACT Over the last twenty years, computer simulation of incompressible fluid flow has been ba... more ABSTRACT Over the last twenty years, computer simulation of incompressible fluid flow has been based on the Eulerian formulation of the fluid mechanics equations on continuous domains. However, it is still difficult to analyze problems in which the shape of the free surfaces or internal interfaces changes continuously or in fluid-structure interactions where complicated contact problems are involved. More recently, Particle Methods in which each fluid particle is followed in a Lagrangian manner have been used. The first ideas on this approach were proposed by Monaghan for the treatment of astrophysical hydrodynamic problems with the so called Smooth Particle Hydrodynamics Method (SPH). This method was later generalized to fluid mechanic problems. Kernel approximations are used in the SPH method to interpolate the unknowns. More particle methods have been developed based on similar ideas and applied to multi-phase flows [6-8 and references therein] It must be noted that particle methods may be used with both: mesh or meshless shape functions. The only practical limitation is that the connectivity in meshless methods or the mesh generation in methods with mesh needs to be evaluated at each time step. For these reason the evaluation of the connectivity must not consume much computing time. The Particle Finite Element Method – PFEM- (Idelsohn et al. 2004) combines the particle precept with the finite element shape functions using an auxiliary finite element mesh that is quickly built at each time step. PFEM has been successfully used to solve the Navier-Stokes equations for multi-fluid flows, fluid-structure interactions (Idelsohn et al. 2006), fire spread, combustion with melting and dripping and erosion or sedimentation problems (Oñate et. al. 2008). During this presentation the advantages of PFEM to solve fluid mechanics problems including immiscible heterogeneous flows will be illustrated with several examples. Finally, the way to achieve Real Time Computational Mechanics taking advantage of the possibility to integrate explicitly with large time steps the Lagrangian formulation will be shown.
We present some developments in the formulation of the Particle Finite Element Method (PFEM) for ... more We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems on fluid and solid mechanics in engineering accounting for fluid-structure interaction and coupled thermal effects, material degradation and surface wear. The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations are solved, as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. The procedure for modelling frictional contact conditions at fluid-solid and solid-solid interfaces via mesh generation are described. A simple algorithm to treat soil erosion in fluid beds is presented. An straight forward extension of the PFEM to model excavation processes and wear of rock cutting tools is described. Examples of application of the PFEM to solve a wide number of coupled problems in engineering such as the effect of large waves on breakwaters and bridges, the large motions of floating and submerged bodies, bed erosion in open channel flows, the wear of rock cutting tools during excavation and tunneling and the melting, dripping and burning of polymers in fire situations are presented.Postprint (published version
In this paper we present a new version of the Particle Finite Element Method (PFEM) applied to fr... more In this paper we present a new version of the Particle Finite Element Method (PFEM) applied to free surface and multi-fluid flows problems. In the previous works, the PFEM was applied to this kind of problems taking advantage of the fact that Lagrangian methods are specially well suited for tracking free surfaces and interfaces[1]. Note that in the Lagrangian approaches the problem becomes separated into a geometrical part(tracking the motion of the nodes) and a physical part(calculating how the flow variables evolve in time at each node). The numerical schemes used in the previous versions of PFEM, were able to deal with free-surface and multi-fluid flows. However its main disadvantage consisted in the need of remeshing at every time step due the mesh distortion. This increased the computational cost of the method particularly due to the fact that the time step size had to be small enough in order to avoid the element inversion (which is equivalent to the non-negativity of the Jaco...
Conducting a numerical simulation of a domain where there exist strong or weak discontinuities in... more Conducting a numerical simulation of a domain where there exist strong or weak discontinuities in the unknown field is still a challenge in computational mechanics. There are many cases in real world where the solution procedure using numerical methods require a way of dealing with this sort of situation, such as: simulation of multiple materials with changing physical properties. Moreover, simulation of two materials where one material being very viscous and the other one having small viscosity could be considered as plasticity. There are various solution methodologies for these sorts of cases, where all have their advantages and disadvantages. The work that will be presented here is a solution procedure for the cases mentioned above by enriching the FE space and statically condensing the occurring additional degrees of freedom in the elemental level. A more detailed information could be obtained in [1]. Implementing this procedure, a Stokes Flow solver that uses the ASGS [2] stabi...
Many polymer-made objects show a trend of melting and dripping in fire, a behavior that may be mo... more Many polymer-made objects show a trend of melting and dripping in fire, a behavior that may be modified by adding flame retardants (FRs). These affect materials properties, e.g., heat absorption and viscosity. In this paper, the effect of a flame retardant on the fire behavior of polymers in the UL 94 scenario is studied. This goal is achieved essentially by applying a new computational strategy that combines the particle finite element method for the polymer with an Eulerian formulation for air. The sample selected is a polypropylene (PP) with magnesium hydroxide at 30 wt.%. For modelling, values of density, conductivity, specific heat, viscosity, and Arrhenius coefficients are obtained from different literature sources, and experimental characterization is performed. However, to alleviate the missing viscosity at a high temperature, three viscosity curves are introduced on the basis of the viscosity curve provided by NIST and the images of the test. In the experiment, we burn the ...
Computer Methods in Applied Mechanics and Engineering, 2020
Abstract Particle finite element method (PFEM) is a computational tool suitable for simulating fl... more Abstract Particle finite element method (PFEM) is a computational tool suitable for simulating fluid dynamics problems characterized by presence of moving boundaries. In this paper a new version of the method for incompressible flow problems is proposed aiming at accuracy improvement. This goal is achieved essentially by applying Strang operator splitting to Navier–Stokes equations and selecting adequate integration schemes for the resulting advective and Stokes sub-problems. For achieving efficient implementation, the pressure and the velocity in the Stokes part are decoupled via the fractional step technique as in the classical PFEM. However, at the first fractional step an explicit pressure prediction procedure for alleviating mass losses is introduced. Three test cases are solved, validating the methodology and estimating its accuracy. The numerical evidence proves that the proposed scheme improves the accuracy of the PFEM.
In this paper the so-called added-mass effect is investigated from a different point of view of p... more In this paper the so-called added-mass effect is investigated from a different point of view of previous publications. The monolithic fluid structure problem is partitioned using a static condensation of the velocity terms. Following this procedure the classical stabilized projection method for incompressible fluid flows is introduced. The procedure allows obtaining a new pressure segregated scheme for fluid-structure interaction problems
ABSTRACT Over the last twenty years, computer simulation of incompressible fluid flow has been ba... more ABSTRACT Over the last twenty years, computer simulation of incompressible fluid flow has been based on the Eulerian formulation of the fluid mechanics equations on continuous domains. However, it is still difficult to analyze problems in which the shape of the free surfaces or internal interfaces changes continuously or in fluid-structure interactions where complicated contact problems are involved. More recently, Particle Methods in which each fluid particle is followed in a Lagrangian manner have been used. The first ideas on this approach were proposed by Monaghan for the treatment of astrophysical hydrodynamic problems with the so called Smooth Particle Hydrodynamics Method (SPH). This method was later generalized to fluid mechanic problems. Kernel approximations are used in the SPH method to interpolate the unknowns. More particle methods have been developed based on similar ideas and applied to multi-phase flows [6-8 and references therein] It must be noted that particle methods may be used with both: mesh or meshless shape functions. The only practical limitation is that the connectivity in meshless methods or the mesh generation in methods with mesh needs to be evaluated at each time step. For these reason the evaluation of the connectivity must not consume much computing time. The Particle Finite Element Method – PFEM- (Idelsohn et al. 2004) combines the particle precept with the finite element shape functions using an auxiliary finite element mesh that is quickly built at each time step. PFEM has been successfully used to solve the Navier-Stokes equations for multi-fluid flows, fluid-structure interactions (Idelsohn et al. 2006), fire spread, combustion with melting and dripping and erosion or sedimentation problems (Oñate et. al. 2008). During this presentation the advantages of PFEM to solve fluid mechanics problems including immiscible heterogeneous flows will be illustrated with several examples. Finally, the way to achieve Real Time Computational Mechanics taking advantage of the possibility to integrate explicitly with large time steps the Lagrangian formulation will be shown.
We present some developments in the formulation of the Particle Finite Element Method (PFEM) for ... more We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems on fluid and solid mechanics in engineering accounting for fluid-structure interaction and coupled thermal effects, material degradation and surface wear. The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations are solved, as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. The procedure for modelling frictional contact conditions at fluid-solid and solid-solid interfaces via mesh generation are described. A simple algorithm to treat soil erosion in fluid beds is presented. An straight forward extension of the PFEM to model excavation processes and wear of rock cutting tools is described. Examples of application of the PFEM to solve a wide number of coupled problems in engineering such as the effect of large waves on breakwaters and bridges, the large motions of floating and submerged bodies, bed erosion in open channel flows, the wear of rock cutting tools during excavation and tunneling and the melting, dripping and burning of polymers in fire situations are presented.Postprint (published version
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Papers by Julio Marcelo Marti