M. Tomé | Universidade de São Paulo (original) (raw)

Papers by M. Tomé

Research paper thumbnail of A numerical method for solving the Oldroyd-B model for 3D free surface flows

This work presents a numerical method for solving three-dimensional viscoelastic free surface flo... more This work presents a numerical method for solving three-dimensional viscoelastic free surface flows governed by the Oldroyd-B constitutive equation. It is an extension to three dimensions of the technique introduced by Tomé et al. 1 The governing equations are solved by a finite difference method on a 3D-staggered grid. Marker particles are employed to describe the fluid providing the visualization and the location of the fluid free surface. As currently implemented, the numerical method presented in this work can simulate three-dimensional free surface flows of an Oldroyd-B fluid. The numerical technique presented in this paper is validated by using an exact solution of the flow of an Oldroyd-B fluid inside a pipe. Numerical simulation of the extrudated swell is given.

Research paper thumbnail of A finite difference technique for solving the Oldroyd-B model for 3D-unsteady free surface flows

Journal of Non-Newtonian Fluid Mechanics, 2008

This work presents a numerical method for solving three-dimensional (3D) viscoelastic unsteady fr... more This work presents a numerical method for solving three-dimensional (3D) viscoelastic unsteady free surface flows governed by the Oldroyd-B constitutive equation. It is an extension of the two-dimensional (2D) technique introduced by Tomé et al. [M.F. Tomé, N. Mangiavacchi, J.A. Cuminato, A. Castelo, S. McKee, A numerical technique for solving unsteady viscoelastic free surface flows, J. Non-Newt. Fluid Mech. 106 (2002) 61-106]. The governing equations are solved by a finite difference method on a 3D-staggered grid. Marker particles are employed to describe the fluid providing both visualization and the location of the free surface. The numerical technique is validated by using an exact solution of the flow of an Oldroyd-B fluid inside a 3D-pipe. Numerical results include the simulation of the transient extrudate swell and jet buckling.

Research paper thumbnail of The MAC method

Research paper thumbnail of Two studies in process modelling: injection moulding and resin film infusion

Research paper thumbnail of Numerical simulations of 3D free-surface flows with surface tension

… 5th International Meeting …, 2002

Research paper thumbnail of A Study of Numerical Schemes for Incompressible Fluid Flows

TEMA - Tendências em Matemática Aplicada e Computacional, 2005

The present work is concerned with a study of numerical schemes for solving two-dimensional time-... more The present work is concerned with a study of numerical schemes for solving two-dimensional time-dependent incompressible free-surface fluid flow problems. The primitive variable flow equations are discretized by the finite difference method. A projection method is employed to uncouple the velocity components and pressure, thus allowing the solution of each variable separately (a segregated approach). The diffusive terms are discretized by Implicit Backward and Crank-Nicolson schemes, and the non-linear advection terms are approximated by the high order upwind VONOS (Variable-Order Non-oscillatory Scheme) technique. In order to improved numerical stability of the schemes, the boundary conditions for the pressure field at the free surface are treated implicitly, and for the velocity field explicitly. The numerical schemes are then applied to the simulation of the Hagen-Poiseuille flow, and container filling problems. The results show that the semi-implicit techniques eliminate the stability restriction in the original explicit GENSMAC method.

Research paper thumbnail of A Numerical Technique for Solving the Maxwell Model for Free Surface Flows

TEMA - Tendências em Matemática Aplicada e Computacional, 2004

ABSTRACT This work is concerned with the development of a numerical technique for solving free su... more ABSTRACT This work is concerned with the development of a numerical technique for solving free surface flows of a Maxwell fluid. The governing equations for the flow of a Maxwell type fluid together with appropriate boundary conditions are given. The free surface stress conditions are treated in details. A novel formulation for calculating the extra stress components on rigid boundaries is given. The numerical technique presented in this work employs the finite difference method on a staggered grid and employs the ideas of the MAC (Marker-and-Cell) method. Numerical results demonstrating that this numerical technique can solve viscoelastic flows governed by the Maxwell model are presented. Moreover, validation results are presented.

Research paper thumbnail of UM MÉTODO SEMI-IMPLÍCITO PARA RESOLVER ESCOAMENTOS IN-COMPRESSÍVEIS COM SUPERFÍCIE LIVRE

Research paper thumbnail of A NEW APPROACH FOR SOLVING THE OLDROYD-B MODEL FOR 3D FREE3 SURFACE FLOWS

Research paper thumbnail of A Marker-and-Cell Method for Solving Viscoelastic Free Surface Flows of a Second Order Fluid

Research paper thumbnail of APPLICATION OF HIGH-ORDER UPWIND DISCRETIZATIONS FOR CALCULATING INCOMPRESSIBLE FLUID FLOWS

Research paper thumbnail of Numerical Solution of Viscoelastic Free Surface Flows Using the PTT Constitutive Equation

Research paper thumbnail of Exact solution of the SPTT model for fully developed channel flows

Research paper thumbnail of Upwind schemes for convection dominated problems

Research paper thumbnail of Surface Tension Implementation for Gensmac2d

Journal of the Brazilian Society of Mechanical Sciences, 2001

Similarly to MAC (Welch et al., 1965), SMAC (Amsden and Harlow, 1970), and GENSMAC (Tome and McKe... more Similarly to MAC (Welch et al., 1965), SMAC (Amsden and Harlow, 1970), and GENSMAC (Tome and McKee, 1994) methods, in GENSMAC2D, the equations Eqs. (3)–(6) are discretized by finite differences in a staggered grid. However, in GENSMAC2D, the fluid domain is tracked ...

Research paper thumbnail of Numerical Solution of the UCM Model Using the LOG���Conformation Technique

Research paper thumbnail of Numerical Simulation of 3D Multi-fluid Flows

TEMA - Tendências em Matemática Aplicada e Computacional, 2002

Abstract. A method to simulate three-dimensional unsteady multi-fluid flows with free surfaces is... more Abstract. A method to simulate three-dimensional unsteady multi-fluid flows with free surfaces is described. A sharp interface separates incompressible fluids of different density and viscosity. Surface and interface tensions are also considered and the required curvature is approximated at the fronts by a methodology described in [3]. The method is based on the GENSMAC [14] front-tracking method. The velocity field is computed using a finite-difference scheme in an Eulerian grid. The free-surface and the interfaces are represented by an ...

Research paper thumbnail of An Effective Implementation of Surface Tension Using the Marker and Cell Method for Axisymmetric and Planar Flows

SIAM Journal on Scientific Computing, 2005

This work presents a method for simulating axisymmetric and planar free-surface flows dominated b... more This work presents a method for simulating axisymmetric and planar free-surface flows dominated by surface tension forces. The surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is ...

Research paper thumbnail of Application of the log-conformation tensor to three-dimensional time-dependent free surface flows

Journal of Non-Newtonian Fluid Mechanics, 2012

The numerical simulation of flows of highly elastic fluids has been the subject of intense resear... more The numerical simulation of flows of highly elastic fluids has been the subject of intense research over the past decades with important industrial applications. Therefore, many efforts have been made to improve the convergence capabilities of the numerical methods employed to simulate viscoelastic fluid flows. An important contribution for the solution of the High-Weissenberg Number Problem has been presented by Fattal and Kupferman [J. Non-Newton. Fluid. Mech. 123 (2004) 281-285] who developed the matrix-logarithm of the conformation tensor technique, henceforth called log-conformation tensor. Its advantage is a better approximation of the large growth of the stress tensor that occur in some regions of the flow and it is doubly beneficial in that it ensures physically correct stress fields, allowing converged computations at high Weissenberg number flows. In this work we investigate the application of the log-conformation tensor to three-dimensional unsteady free surface flows. The log-conformation tensor formulation was applied to solve the Upper-Convected Maxwell (UCM) constitutive equation while the momentum equation was solved using a finite difference Marker-and-Cell type method. The resulting developed code is validated by comparing the log-conformation results with the analytic solution for fully developed pipe flows. To illustrate the stability of the log-conformation tensor approach in solving three-dimensional free surface flows, results from the simulation of the extrudate swell and jet buckling phenomena of UCM fluids at high Weissenberg numbers are presented.

Research paper thumbnail of A finite difference technique for solving the Oldroyd-B model for 3D-unsteady free surface flows

Journal of Non-Newtonian Fluid Mechanics, 2008

a b s t r a c t This work presents a numerical method for solving three-dimensional (3D) viscoela... more a b s t r a c t This work presents a numerical method for solving three-dimensional (3D) viscoelastic unsteady free surface flows governed by the Oldroyd-B constitutive equation. It is an extension of the two-dimensional (2D) technique introduced by Tomé et al. [M.F. Tomé, N. Mangiavacchi, J.A. Cuminato, A. Castelo, S. McKee, A numerical technique for solving unsteady viscoelastic free surface flows, J. Non-Newt. Fluid Mech. 106 (2002) 61-106]. The governing equations are solved by a finite difference method on a 3D-staggered grid. Marker particles are employed to describe the fluid providing both visualization and the location of the free surface. The numerical technique is validated by using an exact solution of the flow of an Oldroyd-B fluid inside a 3D-pipe. Numerical results include the simulation of the transient extrudate swell and jet buckling.

Research paper thumbnail of A numerical method for solving the Oldroyd-B model for 3D free surface flows

This work presents a numerical method for solving three-dimensional viscoelastic free surface flo... more This work presents a numerical method for solving three-dimensional viscoelastic free surface flows governed by the Oldroyd-B constitutive equation. It is an extension to three dimensions of the technique introduced by Tomé et al. 1 The governing equations are solved by a finite difference method on a 3D-staggered grid. Marker particles are employed to describe the fluid providing the visualization and the location of the fluid free surface. As currently implemented, the numerical method presented in this work can simulate three-dimensional free surface flows of an Oldroyd-B fluid. The numerical technique presented in this paper is validated by using an exact solution of the flow of an Oldroyd-B fluid inside a pipe. Numerical simulation of the extrudated swell is given.

Research paper thumbnail of A finite difference technique for solving the Oldroyd-B model for 3D-unsteady free surface flows

Journal of Non-Newtonian Fluid Mechanics, 2008

This work presents a numerical method for solving three-dimensional (3D) viscoelastic unsteady fr... more This work presents a numerical method for solving three-dimensional (3D) viscoelastic unsteady free surface flows governed by the Oldroyd-B constitutive equation. It is an extension of the two-dimensional (2D) technique introduced by Tomé et al. [M.F. Tomé, N. Mangiavacchi, J.A. Cuminato, A. Castelo, S. McKee, A numerical technique for solving unsteady viscoelastic free surface flows, J. Non-Newt. Fluid Mech. 106 (2002) 61-106]. The governing equations are solved by a finite difference method on a 3D-staggered grid. Marker particles are employed to describe the fluid providing both visualization and the location of the free surface. The numerical technique is validated by using an exact solution of the flow of an Oldroyd-B fluid inside a 3D-pipe. Numerical results include the simulation of the transient extrudate swell and jet buckling.

Research paper thumbnail of The MAC method

Research paper thumbnail of Two studies in process modelling: injection moulding and resin film infusion

Research paper thumbnail of Numerical simulations of 3D free-surface flows with surface tension

… 5th International Meeting …, 2002

Research paper thumbnail of A Study of Numerical Schemes for Incompressible Fluid Flows

TEMA - Tendências em Matemática Aplicada e Computacional, 2005

The present work is concerned with a study of numerical schemes for solving two-dimensional time-... more The present work is concerned with a study of numerical schemes for solving two-dimensional time-dependent incompressible free-surface fluid flow problems. The primitive variable flow equations are discretized by the finite difference method. A projection method is employed to uncouple the velocity components and pressure, thus allowing the solution of each variable separately (a segregated approach). The diffusive terms are discretized by Implicit Backward and Crank-Nicolson schemes, and the non-linear advection terms are approximated by the high order upwind VONOS (Variable-Order Non-oscillatory Scheme) technique. In order to improved numerical stability of the schemes, the boundary conditions for the pressure field at the free surface are treated implicitly, and for the velocity field explicitly. The numerical schemes are then applied to the simulation of the Hagen-Poiseuille flow, and container filling problems. The results show that the semi-implicit techniques eliminate the stability restriction in the original explicit GENSMAC method.

Research paper thumbnail of A Numerical Technique for Solving the Maxwell Model for Free Surface Flows

TEMA - Tendências em Matemática Aplicada e Computacional, 2004

ABSTRACT This work is concerned with the development of a numerical technique for solving free su... more ABSTRACT This work is concerned with the development of a numerical technique for solving free surface flows of a Maxwell fluid. The governing equations for the flow of a Maxwell type fluid together with appropriate boundary conditions are given. The free surface stress conditions are treated in details. A novel formulation for calculating the extra stress components on rigid boundaries is given. The numerical technique presented in this work employs the finite difference method on a staggered grid and employs the ideas of the MAC (Marker-and-Cell) method. Numerical results demonstrating that this numerical technique can solve viscoelastic flows governed by the Maxwell model are presented. Moreover, validation results are presented.

Research paper thumbnail of UM MÉTODO SEMI-IMPLÍCITO PARA RESOLVER ESCOAMENTOS IN-COMPRESSÍVEIS COM SUPERFÍCIE LIVRE

Research paper thumbnail of A NEW APPROACH FOR SOLVING THE OLDROYD-B MODEL FOR 3D FREE3 SURFACE FLOWS

Research paper thumbnail of A Marker-and-Cell Method for Solving Viscoelastic Free Surface Flows of a Second Order Fluid

Research paper thumbnail of APPLICATION OF HIGH-ORDER UPWIND DISCRETIZATIONS FOR CALCULATING INCOMPRESSIBLE FLUID FLOWS

Research paper thumbnail of Numerical Solution of Viscoelastic Free Surface Flows Using the PTT Constitutive Equation

Research paper thumbnail of Exact solution of the SPTT model for fully developed channel flows

Research paper thumbnail of Upwind schemes for convection dominated problems

Research paper thumbnail of Surface Tension Implementation for Gensmac2d

Journal of the Brazilian Society of Mechanical Sciences, 2001

Similarly to MAC (Welch et al., 1965), SMAC (Amsden and Harlow, 1970), and GENSMAC (Tome and McKe... more Similarly to MAC (Welch et al., 1965), SMAC (Amsden and Harlow, 1970), and GENSMAC (Tome and McKee, 1994) methods, in GENSMAC2D, the equations Eqs. (3)–(6) are discretized by finite differences in a staggered grid. However, in GENSMAC2D, the fluid domain is tracked ...

Research paper thumbnail of Numerical Solution of the UCM Model Using the LOG���Conformation Technique

Research paper thumbnail of Numerical Simulation of 3D Multi-fluid Flows

TEMA - Tendências em Matemática Aplicada e Computacional, 2002

Abstract. A method to simulate three-dimensional unsteady multi-fluid flows with free surfaces is... more Abstract. A method to simulate three-dimensional unsteady multi-fluid flows with free surfaces is described. A sharp interface separates incompressible fluids of different density and viscosity. Surface and interface tensions are also considered and the required curvature is approximated at the fronts by a methodology described in [3]. The method is based on the GENSMAC [14] front-tracking method. The velocity field is computed using a finite-difference scheme in an Eulerian grid. The free-surface and the interfaces are represented by an ...

Research paper thumbnail of An Effective Implementation of Surface Tension Using the Marker and Cell Method for Axisymmetric and Planar Flows

SIAM Journal on Scientific Computing, 2005

This work presents a method for simulating axisymmetric and planar free-surface flows dominated b... more This work presents a method for simulating axisymmetric and planar free-surface flows dominated by surface tension forces. The surface tension effects are incorporated into the free surface boundary conditions through the computation of the capillary pressure. The required curvature is ...

Research paper thumbnail of Application of the log-conformation tensor to three-dimensional time-dependent free surface flows

Journal of Non-Newtonian Fluid Mechanics, 2012

The numerical simulation of flows of highly elastic fluids has been the subject of intense resear... more The numerical simulation of flows of highly elastic fluids has been the subject of intense research over the past decades with important industrial applications. Therefore, many efforts have been made to improve the convergence capabilities of the numerical methods employed to simulate viscoelastic fluid flows. An important contribution for the solution of the High-Weissenberg Number Problem has been presented by Fattal and Kupferman [J. Non-Newton. Fluid. Mech. 123 (2004) 281-285] who developed the matrix-logarithm of the conformation tensor technique, henceforth called log-conformation tensor. Its advantage is a better approximation of the large growth of the stress tensor that occur in some regions of the flow and it is doubly beneficial in that it ensures physically correct stress fields, allowing converged computations at high Weissenberg number flows. In this work we investigate the application of the log-conformation tensor to three-dimensional unsteady free surface flows. The log-conformation tensor formulation was applied to solve the Upper-Convected Maxwell (UCM) constitutive equation while the momentum equation was solved using a finite difference Marker-and-Cell type method. The resulting developed code is validated by comparing the log-conformation results with the analytic solution for fully developed pipe flows. To illustrate the stability of the log-conformation tensor approach in solving three-dimensional free surface flows, results from the simulation of the extrudate swell and jet buckling phenomena of UCM fluids at high Weissenberg numbers are presented.

Research paper thumbnail of A finite difference technique for solving the Oldroyd-B model for 3D-unsteady free surface flows

Journal of Non-Newtonian Fluid Mechanics, 2008

a b s t r a c t This work presents a numerical method for solving three-dimensional (3D) viscoela... more a b s t r a c t This work presents a numerical method for solving three-dimensional (3D) viscoelastic unsteady free surface flows governed by the Oldroyd-B constitutive equation. It is an extension of the two-dimensional (2D) technique introduced by Tomé et al. [M.F. Tomé, N. Mangiavacchi, J.A. Cuminato, A. Castelo, S. McKee, A numerical technique for solving unsteady viscoelastic free surface flows, J. Non-Newt. Fluid Mech. 106 (2002) 61-106]. The governing equations are solved by a finite difference method on a 3D-staggered grid. Marker particles are employed to describe the fluid providing both visualization and the location of the free surface. The numerical technique is validated by using an exact solution of the flow of an Oldroyd-B fluid inside a 3D-pipe. Numerical results include the simulation of the transient extrudate swell and jet buckling.