L. Battaglia - Academia.edu (original) (raw)

Papers by L. Battaglia

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 2014

In this work, a hierarchical variant of a boundary element method and its use in Stokes flow arou... more In this work, a hierarchical variant of a boundary element method and its use in Stokes flow around three-dimensional rigid bodies in steady regime is presented. The proposal is based on the descending hierarchical low-order and self-adaptive algorithm of Barnes-Hut, and it is used in conjunction with an indirect boundary integral formulation of second class, whose source term is a function of the undisturbed velocity. The solution field is the double layer surface density, which is modified in order to complete the eigenvalue spectrum of the integral operator. In this way, the rigid modes are eliminated and both a non-zero force and a non-null torque on the body could be calculated. The elements are low order flat triangles, and an iterative solution by generalized minimal residual (GMRES) is used. Numerical examples include cases with analytical solutions, bodies with edges and vertices, or with intricate shapes. The main advantage of the presented technique is the possibility of considering a greater number of degrees of freedom regarding traditional collocation methods, due to the decreased demand of main memory and the reduction in the computation times.

International Journal for Numerical Methods in Biomedical Engineering, 2011

When a Galerkin discretization of a boundary integral equation with a weakly singular kernel is p... more When a Galerkin discretization of a boundary integral equation with a weakly singular kernel is performed over triangles, a double surface integral must be evaluated for each pair of them. If these pairs are not contiguous or not coincident, the kernel is regular and a Gauss-Legendre quadrature can be employed. When the pairs have a common edge or a common vertex, then edge and vertex weak singularities appear. If the pairs have both facets coincident, the whole integration domain is weakly singular. Taylor (IEEE Trans. Antenn. Propag. 2003; 51(7):1630-1637) proposed a systematic evaluation based on a reordering and partitioning of the integration domain, together with a use of the Duffy transformations in order to remove the singularities, in such a way that a Gauss-Legendre quadrature was performed on three coordinates with an analytic integration in the fourth coordinate. Since this scheme is a bit restrictive because it was designed for electromagnetic kernels, a full numerical quadrature is proposed in order to handle kernels with a weak singularity with a general framework. Numerical tests based on modifications of the one proposed by Wang and Atalla (Commun.

Journal of Fluids Engineering, 2014

An interface-capturing finite element method based on the level set approach is proposed for solv... more An interface-capturing finite element method based on the level set approach is proposed for solving free surface incompressible fluid flows, especially those that are hard to model through an interface-tracking technique, like the one presented in previous works (Battaglia et al., "Stabilized Free Surface Flows", in Mecánica Computacional, Vol. XXVI, 2007). The methodology is developed in the PETSc-FEM code (http://www.cimec.org.ar/petscfem) in order to solve the Navier-Stokes equations for the fluid state and the advection of the level set function which gives the free surface position. Some examples solved by this method are presented, including the collapse of a liquid column problem.

International Journal of Computational Fluid Dynamics, 2010

Transient free surface flows are numerically simulated by a finite element interface capturing me... more Transient free surface flows are numerically simulated by a finite element interface capturing method based on a level set approach. The methodology consists of the solution of two-fluid viscous incompressible flows for a single domain, where the liquid phase is identified by positive values of the level set function, the gaseous phase by negative ones, and the free surface by the zero level set. The numerical solution at each time step is performed in three stages: (i) a two-fluid Navier-Stokes stage, (ii) an advection stage for the transport of the level set function, and (iii) a bounded reinitialization with continuous penalization stage for keeping smoothness of the level set function. The proposed procedure, and particularly the renormalization stage, are evaluated in three typical two and three-dimensional problems.

International Journal for Numerical Methods in Engineering, 2010

In this work, a reinitialization procedure oriented to regularize the Level Set (LS) function fie... more In this work, a reinitialization procedure oriented to regularize the Level Set (LS) function field is presented. In LS approximations for two-fluid flow simulations, a scalar function indicates the presence of one or another phase and the interface between them. In general, the advection of such function produces a degradation of some properties of the LS function, such as the smoothness of the transition between phases and the correct position of the interface. The methodology introduced here, denominated bounded renormalization with continuous penalization, consists of solving by the finite element method a partial differential equation with certain distinguishing properties with the aim of keeping the desirable properties of the LS function. The performance of the strategy is evaluated for several typical cases in one, two and three-dimensional domains, for both the advection and the renormalization stages.

Abstract An indirect boundary integral equation for steady Stokes flow around a rigid body in the ... more Abstract An indirect boundary integral equation for steady Stokes flow around a rigid body in the three-dimensional space is proposed, and is numerically solved by using collocation and Galerkin weight-ing procedures. The resulting double surface integrals of the Galerkin ...

Keywords: three dimensional creeping flow, weak singularity, boundary integral equation, variatio... more Keywords: three dimensional creeping flow, weak singularity, boundary integral equation, variational boundary element method, Galerkin boundary element method, double surface integral, Taylor scheme.

In this work, steady creeping three dimensional flow of a viscous and incompressible fluid around... more In this work, steady creeping three dimensional flow of a viscous and incompressible fluid around closed rigid bodies with sharp corners and edges is numerically solved using a Galerkin scheme applied to a modified Power-Miranda boundary integral equation. The related double surface integrals that account the pairwise interaction among all boundary elements are quadruple and they are computed on flat simplex triangles using the scheme proposed by Taylor (D. J. Taylor, IEEE Trans. on Antennas and Propagation, 51 : 1630-1637 (2003)). As a numerical example, the creeping steady flow around the unit cube considering different orientations with respect to the unperturbed fluid velocity, covering issues on the surface traction exponents close to the edges and vertices and compared against semi-analytical computations.

The Partitioned Global Address Space (PGAS) is a parallel programming model that has been develop... more The Partitioned Global Address Space (PGAS) is a parallel programming model that has been developed for distributed memory computers. Furthermore, it can be used in High Performance Computing (HPC) on Beowulf clusters oriented to scientific and engineering applications through computational mechanics. As it is known, the PGAS model is the basis for, among others, some multi-paradigm programming languages such as the UPC (Unified Parallel C) and the Coarray Fortran (CAF or Fortran 2008), as well as the library Global Arrays (GA). All these resources are extensions to provide one-side communication. This work summarizes some of the activities carried out in one of the clusters available in CIMEC, as well as some ideas for a Message Passing Interface (MPI) implementation of coarrays on a fortran compiler.

In this paper we present a summary of numerical methods for solving free surface and two fluid fl... more In this paper we present a summary of numerical methods for solving free surface and two fluid flow problems. We will focus the attention on level set formulations extensively used in the context of the finite element method. In particular, numerical developments to achieve accurate solutions are described. Specific topics of the algorithms, like mass preservation and interface redefinition, are evaluated. To illustrate these aspects, numerical strategies previously developed are applied to the solution of a sloshing and a water column collapse problems. To assess the capabilities of these techniques, the numerical results are compared against each other and with experimental data. Considering these aspects, the present work is aimed to outline some well reported aspects of level set-like formulations.

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 2014

In this work, a hierarchical variant of a boundary element method and its use in Stokes flow arou... more In this work, a hierarchical variant of a boundary element method and its use in Stokes flow around three-dimensional rigid bodies in steady regime is presented. The proposal is based on the descending hierarchical low-order and self-adaptive algorithm of Barnes-Hut, and it is used in conjunction with an indirect boundary integral formulation of second class, whose source term is a function of the undisturbed velocity. The solution field is the double layer surface density, which is modified in order to complete the eigenvalue spectrum of the integral operator. In this way, the rigid modes are eliminated and both a non-zero force and a non-null torque on the body could be calculated. The elements are low order flat triangles, and an iterative solution by generalized minimal residual (GMRES) is used. Numerical examples include cases with analytical solutions, bodies with edges and vertices, or with intricate shapes. The main advantage of the presented technique is the possibility of considering a greater number of degrees of freedom regarding traditional collocation methods, due to the decreased demand of main memory and the reduction in the computation times.

International Journal for Numerical Methods in Biomedical Engineering, 2011

When a Galerkin discretization of a boundary integral equation with a weakly singular kernel is p... more When a Galerkin discretization of a boundary integral equation with a weakly singular kernel is performed over triangles, a double surface integral must be evaluated for each pair of them. If these pairs are not contiguous or not coincident, the kernel is regular and a Gauss-Legendre quadrature can be employed. When the pairs have a common edge or a common vertex, then edge and vertex weak singularities appear. If the pairs have both facets coincident, the whole integration domain is weakly singular. Taylor (IEEE Trans. Antenn. Propag. 2003; 51(7):1630-1637) proposed a systematic evaluation based on a reordering and partitioning of the integration domain, together with a use of the Duffy transformations in order to remove the singularities, in such a way that a Gauss-Legendre quadrature was performed on three coordinates with an analytic integration in the fourth coordinate. Since this scheme is a bit restrictive because it was designed for electromagnetic kernels, a full numerical quadrature is proposed in order to handle kernels with a weak singularity with a general framework. Numerical tests based on modifications of the one proposed by Wang and Atalla (Commun.

Journal of Fluids Engineering, 2014

An interface-capturing finite element method based on the level set approach is proposed for solv... more An interface-capturing finite element method based on the level set approach is proposed for solving free surface incompressible fluid flows, especially those that are hard to model through an interface-tracking technique, like the one presented in previous works (Battaglia et al., "Stabilized Free Surface Flows", in Mecánica Computacional, Vol. XXVI, 2007). The methodology is developed in the PETSc-FEM code (http://www.cimec.org.ar/petscfem) in order to solve the Navier-Stokes equations for the fluid state and the advection of the level set function which gives the free surface position. Some examples solved by this method are presented, including the collapse of a liquid column problem.

International Journal of Computational Fluid Dynamics, 2010

Transient free surface flows are numerically simulated by a finite element interface capturing me... more Transient free surface flows are numerically simulated by a finite element interface capturing method based on a level set approach. The methodology consists of the solution of two-fluid viscous incompressible flows for a single domain, where the liquid phase is identified by positive values of the level set function, the gaseous phase by negative ones, and the free surface by the zero level set. The numerical solution at each time step is performed in three stages: (i) a two-fluid Navier-Stokes stage, (ii) an advection stage for the transport of the level set function, and (iii) a bounded reinitialization with continuous penalization stage for keeping smoothness of the level set function. The proposed procedure, and particularly the renormalization stage, are evaluated in three typical two and three-dimensional problems.

International Journal for Numerical Methods in Engineering, 2010

In this work, a reinitialization procedure oriented to regularize the Level Set (LS) function fie... more In this work, a reinitialization procedure oriented to regularize the Level Set (LS) function field is presented. In LS approximations for two-fluid flow simulations, a scalar function indicates the presence of one or another phase and the interface between them. In general, the advection of such function produces a degradation of some properties of the LS function, such as the smoothness of the transition between phases and the correct position of the interface. The methodology introduced here, denominated bounded renormalization with continuous penalization, consists of solving by the finite element method a partial differential equation with certain distinguishing properties with the aim of keeping the desirable properties of the LS function. The performance of the strategy is evaluated for several typical cases in one, two and three-dimensional domains, for both the advection and the renormalization stages.

Abstract An indirect boundary integral equation for steady Stokes flow around a rigid body in the ... more Abstract An indirect boundary integral equation for steady Stokes flow around a rigid body in the three-dimensional space is proposed, and is numerically solved by using collocation and Galerkin weight-ing procedures. The resulting double surface integrals of the Galerkin ...

Keywords: three dimensional creeping flow, weak singularity, boundary integral equation, variatio... more Keywords: three dimensional creeping flow, weak singularity, boundary integral equation, variational boundary element method, Galerkin boundary element method, double surface integral, Taylor scheme.

In this work, steady creeping three dimensional flow of a viscous and incompressible fluid around... more In this work, steady creeping three dimensional flow of a viscous and incompressible fluid around closed rigid bodies with sharp corners and edges is numerically solved using a Galerkin scheme applied to a modified Power-Miranda boundary integral equation. The related double surface integrals that account the pairwise interaction among all boundary elements are quadruple and they are computed on flat simplex triangles using the scheme proposed by Taylor (D. J. Taylor, IEEE Trans. on Antennas and Propagation, 51 : 1630-1637 (2003)). As a numerical example, the creeping steady flow around the unit cube considering different orientations with respect to the unperturbed fluid velocity, covering issues on the surface traction exponents close to the edges and vertices and compared against semi-analytical computations.

The Partitioned Global Address Space (PGAS) is a parallel programming model that has been develop... more The Partitioned Global Address Space (PGAS) is a parallel programming model that has been developed for distributed memory computers. Furthermore, it can be used in High Performance Computing (HPC) on Beowulf clusters oriented to scientific and engineering applications through computational mechanics. As it is known, the PGAS model is the basis for, among others, some multi-paradigm programming languages such as the UPC (Unified Parallel C) and the Coarray Fortran (CAF or Fortran 2008), as well as the library Global Arrays (GA). All these resources are extensions to provide one-side communication. This work summarizes some of the activities carried out in one of the clusters available in CIMEC, as well as some ideas for a Message Passing Interface (MPI) implementation of coarrays on a fortran compiler.

In this paper we present a summary of numerical methods for solving free surface and two fluid fl... more In this paper we present a summary of numerical methods for solving free surface and two fluid flow problems. We will focus the attention on level set formulations extensively used in the context of the finite element method. In particular, numerical developments to achieve accurate solutions are described. Specific topics of the algorithms, like mass preservation and interface redefinition, are evaluated. To illustrate these aspects, numerical strategies previously developed are applied to the solution of a sloshing and a water column collapse problems. To assess the capabilities of these techniques, the numerical results are compared against each other and with experimental data. Considering these aspects, the present work is aimed to outline some well reported aspects of level set-like formulations.