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Fabricio Sousa

Universidade de São Paulo, ICMC - Instituto de Ciências Matemáticas e de Computação, Faculty Member

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Flávio Awa-Guajá

Universidade Estadual de Santa Cruz

Emilio Kavamura

Universidade Federal do Paraná

Leonardo B L Santos

National Centre for Monitoring and Warning of Natural Disasters

Lourival C Paraiba

PUC-RIO

margarida giestas

LNEG

Instituto Nacional de Pesquisas Espaciais

Fernando Malafaia

Universidade de Brasília - UnB

Universidade Federal de Santa Catarina - UFSC (Federal University of Santa Catarina)

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Papers by Fabricio Sousa

Simula��ao Num��rica do Transporte da Temperatura e de Esp��cies Constituintes em Reservat��rios Hidrel��tricos Utilizando M��todo de Elementos Finitos em Malhas Nao-Estruturadas

Resumo O enchimento de reservat��rios hidrel��tricos provoca impactos ambientais, interferindo no... more Resumo O enchimento de reservat��rios hidrel��tricos provoca impactos ambientais, interferindo nos ecossistemas e nos modos de vida das popula��oes envolvidas, pois durante este processo a biomassa terrestre �� decomposta lan��ando subst��ncias que se concentram nos volumes dos diferentes compartimentos do reservat��rio. Nestas condi��oes, algumas regioes do reservat��rio passam por per��odos em que os teores de oxig��nio dissolvido ea concentra��ao de mat��ria org��nica comprometem o equil��brio da flora e ...

Simulação numérica 2D e 3D de escoamentos com tensão superficial

Palavras-chave: elementos finitos, tensão superficial, formulação variacional, ALE, potência virt... more Palavras-chave: elementos finitos, tensão superficial, formulação variacional, ALE, potência virtual Resumo: O fenômeno de molhamento, estudo de como um líquido se deposita em um sólido, apresenta problemas ainda em aberto tanto do ponto de vista da modelagem física como no da si-mulação numérica. Neste trabalho, são discutidos métodos numéricos para a simulação de linhas de contato dinâmicas formadas da interação fluido-fluido-estrutura. Os efeitos da tensão super-ficial são estudados com a abordagem do princípio do trabalho virtual, o qual leva o problemà a equações na formulação variacional, linguagem natural para o tratamento numérico com o método dos elementos finitos (MEF). São apresentados resultados preliminares de aproximações calculadas através do método de elementos finitos (formulação ALE-FEM) para problemas en-volvendo tensão superficial, bem como aspectos teóricos da modelagem de linhas tríplices nas equações de Navier-Stokes.

Spurious transients of projection methods in microflow simulations

Computer Methods in Applied Mechanics and Engineering, 2015

The temporal behavior of projection methods for viscous incompressible low-Reynolds-number flows ... more The temporal behavior of projection methods for viscous incompressible low-Reynolds-number flows is adressed. The methods considered result from algebraically splitting the linear system corresponding to each time step, in such a way that the computation of velocity is segregated from that of pressure. Each method is characterized by two (possibly equal) approximate inverses (B 1 and B 2 ) of the momentum-equation velocity matrix, plus a parameter γ which renders the method non-incremental (if γ = 0) or incremental (if γ = 1). The classical first-order projection method, together with more sophisticated methods (Perot's second-order method, Yosida method, pseudoexact factorization method) and their incremental variants are put into the same algebraic form and their accuracy numerically tested. Splitting errors of first, second and third order in the time step size δt are obtained, depending on the method.

High-order ALE schemes for incompressible capillary flows

Journal of Computational Physics, 2014

The spatial discretization of problems with moving boundaries is considered, incorporating the te... more The spatial discretization of problems with moving boundaries is considered, incorporating the temporal evolution of not just the mechanical variables, but also of the nodal positions of the moving mesh. The outcome is a system of Differential-Algebraic Equations (DAE) of index 2 or, in the case of inertialess flow, just 1. From the DAE formulation it its possible to define strategies to build schemes of arbitrary accuracy. We introduce here several schemes of order 2 and 3 that avoid the solution of a nonlinear system involving simultaneously the mechanical variables and the geometrical ones. This class of schemes has been the one adopted by the majority of practitioners of Computational Fluid Dynamics up to now. The proposed schemes indeed achieve the design accuracy, and further show stability restrictions that are not significantly more severe than those of popular first order schemes. The numerical experimentation is performed on capillary problems, discretized by both div-stable (P 2 /P 1 , P + 1 /P 1 ) and equal-order (P 1 /P 1 , stabilized) finite elements, and incorporating surface tension and triple (contact) line effects.

A Lagrangian level-set approach for the simulation of incompressible two-fluid flows

International Journal for Numerical Methods in Fluids, 2005

A Lagrangian level-set method to solve incompressible two-dimensional two-uid ows is presented. T... more A Lagrangian level-set method to solve incompressible two-dimensional two-uid ows is presented. The Navier-Stokes equations are discretized by a Galerkin ÿnite element method. A projection method is employed to decouple the system of non-linear equations. The interface between uids is represented by the zero level set of a function plus additional marker points of the computational mesh. In the standard Eulerian level-set method, this function is advected through the domain by solving a pure advection equation. To reduce mass conservation errors that can arise from this step, our method employs a Lagrangian technique which moves the nodes of the ÿnite element mesh, and consequently, the information stored in each node. The quality of the mesh is controlled by a remeshing procedure, avoiding bad triangles by ipping edges, inserting or removing vertices from the triangulation. Results of numerical simulations are presented, illustrating the improvements in mass conservation and accuracy of this new methodology.

A numerical method for solving the three-dimensional parabolized Navier-Stokes equations

Computers & Fluids, 1997

A numerical technique that solves the parabolized form of the Navier-Stokes equa-*

Numerical simulations of 3D free-surface flows with surface tension

by Antonio Castelo, Fabricio Sousa, and M. Tomé

… 5th International Meeting …, 2002

A MASS-CONSERVING SMOOTH METHOD

by Antonio Castelo and Fabricio Sousa

Review The MAC method

In this article recent advances in the Marker and Cell (MAC) method will be reviewed. The MAC tec... more In this article recent advances in the Marker and Cell (MAC) method will be reviewed. The MAC technique dates back to the early 1960s at the Los Alamos Laboratories and this article starts with a historical review, and then a brief discussion of related techniques. Improvements since the early days of MAC (and the Simplified MAC - SMAC) include automatic time-stepping, the use of the conjugate gradient method to solve the Poisson equation for the corrected velocity potential, greater efficiency through stripping out the virtual particles (markers) other than those near the free surface, and more accurate approximations of the free surface boundary conditions, the addition of bounded high accuracy upwinding for the convected terms (thereby being able to solve higher Reynolds number flows), and a (dynamics) flow visualization facility. More recently, effective techniques for surface and interfacial flows and, in particular, for accurately tracking the associated surface(s)/interface(s...

Uma técnica de correção de interface para o método "Incompressible Smoothed Particle Hydrodynamics

TEMA (São Carlos), 2013

ABSTRACT The maintainability of a good particle distribution is of prior importance to SPH (Smoot... more ABSTRACT The maintainability of a good particle distribution is of prior importance to SPH (Smoothed Particle Hydrodynamics) simulations, since it affects both stability and accuracy of the numerical results. When using ISPH (Incompressible SPH), the particle distribution can be improved by dislocating particles away from their Lagrangian trajectories. However, when applying this technique to multiphase flows, the correct position of the interface between fluids is disturbed, resulting in unphysical flow behavior. In this work, we propose a correction, based upon a constructed smooth distance function. Numerical tests show that this correction can recover the expected position of the interface. Finally, issues regarding mass conservation are assessed and reported.

Numerical Simulation of 3D Multi-fluid Flows

by Antonio Castelo, M. Tomé, and Fabricio Sousa

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 ...

A front-tracking/front-capturing method for the simulation of 3D multi-fluid flows with free surfaces

by Antonio Castelo, M. Tomé, S. McKee, and Fabricio Sousa

Journal of Computational Physics, 2004

A method for simulating incompressible, imiscible, unsteady, Newtonian, multi-fluid flows with fr... more A method for simulating incompressible, imiscible, unsteady, Newtonian, multi-fluid flows with free surfaces is described. A sharp interface separates fluids of different density and viscosity. Surface and interfacial tensions are also considered and the required curvature is geometrically approximated at the fronts by a least squares quadratic fitting . To remove small undulations at the fronts, a mass-conserving filter is employed. The numerical method employed to solve the Navier-Stokes equations is based on the GENSMAC-3D [29] front-tracking method. The velocity field is computed using a finite-difference scheme on an Eulerian grid. The free-surface and the interfaces are represented by an unstructured Lagrangian grid moving through an Eulerian grid. The method was validated by comparing the numerical results with analytical results for a number of simple problems. Complex numerical simulations show the capability and emphasize the robustness of this new method.

Numerical simulations of 3D free surface flows by a multilayer Saint-Venant model

International Journal for Numerical Methods in Fluids, 2008

ABSTRACT We present a multilayer Saint-Venant system for the simulation of 3D free surface flows ... more ABSTRACT We present a multilayer Saint-Venant system for the simulation of 3D free surface flows with friction and viscosity effects. A vertical discretization of a Navier–Stokes system approximation deduced from a precise analysis of the shallow water assumption leads to a set of coupled Saint-Venant-type systems. The idea is to obtain an accurate description of the vertical profile of the horizontal velocity while preserving the robustness and the computational efficiency of the usual Saint-Venant system.For each time-dependent layer, a Saint-Venant-type system is solved on the same 2D mesh by a kinetic solver using a finite volume framework. The free surface is directly deduced from the sum of layers water depth.We validate the model with some numerical academic and realistic examples. We present comparisons with simulations computed with the hydrostatic Navier–Stokes solver of the Telemac-3D code developed by Electricité de France. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Local volume-conserving free surface smoothing

by Antonio Castelo and Fabricio Sousa

Communications in Numerical Methods in Engineering, 2006

Abstract Removing high-frequency undulations in surfaces is a problem that appears in different f... more Abstract Removing high-frequency undulations in surfaces is a problem that appears in different fields, such as computer graphics and computational fluid mechanics. This problem is typically handled by surface smoothing techniques, such as Laplacian filters, that eliminate high-frequency undulations but degrade the volume encompassed by the surface. The need for conserving volume (or mass) rules out the use of such techniques in several application, as for example incompressible flows. In this work we present a smoothing ...

by Antonio Castelo, M. Tomé, S. McKee, and Fabricio Sousa

Computers & Fluids, 2008

In this article recent advances in the Marker and Cell (MAC) method will be reviewed. The MAC tec... more In this article recent advances in the Marker and Cell (MAC) method will be reviewed. The MAC technique dates back to the early 1960s at the Los Alamos Laboratories and this article starts with a historical review, and then a brief discussion of related techniques. Improvements since the early days of MAC (and the Simplified MAC -SMAC) include automatic time-stepping, the use of the conjugate gradient method to solve the Poisson equation for the corrected velocity potential, greater efficiency through stripping out the virtual particles (markers) other than those near the free surface, and more accurate approximations of the free surface boundary conditions, the addition of bounded high accuracy upwinding for the convected terms (thereby being able to solve higher Reynolds number flows), and a (dynamics) flow visualization facility. More recently, effective techniques for surface and interfacial flows and, in particular, for accurately tracking the associated surface(s)/interface(s) including moving contact angles have been developed. This article will concentrate principally on a three-dimensional version of the SMAC method. It will eschew both code verification and model validation; instead it will emphasize the applications that the MAC method can solve, from multiphase flows to rheology.

An improved finite element space for discontinuous pressures

Computer Methods in Applied Mechanics and Engineering, 2010

We consider incompressible Stokes flow with an internal interface at which the pressure is discon... more We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L 2 (Ω)-norm is of order h 1 2 ).

Numerical assessment of stability of interface discontinuous finite element pressure spaces

Computer Methods in Applied Mechanics and Engineering, 2012

The stability of two recently developed pressure spaces has been assessed numerically: The space ... more The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 1019-1031, which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina (Int. can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form.

Numerical Simulation of 3D Multi-fluid Flows doi: 10.5540/tema. 2002.03. 01.0203

by Antonio Castelo, M. Tomé, and Fabricio Sousa

FREE-SURFACE AND TWO-FLUID FLOW SIMULATIONS ON UNSTRUCTURED GRIDS

by Antonio Castelo, M. Tomé, and Fabricio Sousa

Free-surface and two-fluid flow simulations are computationally demanding tasks. The freedom allo... more Free-surface and two-fluid flow simulations are computationally demanding tasks. The freedom allowed when using unstructured grids can be exploited to develop efficient methods for this type of problems. For instance, level-set methods and front tracking methods can be combined onto an unstructured grid method that combines advantages of both methods. In this work, methods to solve incompressible two-dimensional two-fluid flows on unstructured grids are discussed. The Navier-Stokes equations are discretized by suitable finite element methods. The numerical method for the solution is based on the projection method to uncouple the system of non-linear equations. Strategies employed for the representation of the interface between fluids are discussed. For instance, the interface can be represented by the zero level set of a function φ plus additional marker points of the computational mesh. In the standard Eulerian level-set method, this function is advected through the domain by solving a pure advection equation. To reduce mass conservation errors that can arise from this step, a Lagrangian technique, which moves the nodes of the finite element mesh, and consequently, the information stored in each node, can be employed. Due to the large distortion of the mesh that can occur, remeshing procedures are required in order to control de quality of the mesh. Results from some simulations are shown to compare the mass conservation and accuracy of the various discussed methodologies.

A numerical method for solving three-dimensional generalized Newtonian free surface flows

by Antonio Castelo, M. Tomé, S. McKee, Fabricio Sousa, and Fabiano B M Silva

Journal of Non-Newtonian Fluid Mechanics, 2004

A numerical technique that solves the parabolized form of the Navier-Stokes equa-*

Simula��ao Num��rica do Transporte da Temperatura e de Esp��cies Constituintes em Reservat��rios Hidrel��tricos Utilizando M��todo de Elementos Finitos em Malhas Nao-Estruturadas

Resumo O enchimento de reservat��rios hidrel��tricos provoca impactos ambientais, interferindo no... more Resumo O enchimento de reservat��rios hidrel��tricos provoca impactos ambientais, interferindo nos ecossistemas e nos modos de vida das popula��oes envolvidas, pois durante este processo a biomassa terrestre �� decomposta lan��ando subst��ncias que se concentram nos volumes dos diferentes compartimentos do reservat��rio. Nestas condi��oes, algumas regioes do reservat��rio passam por per��odos em que os teores de oxig��nio dissolvido ea concentra��ao de mat��ria org��nica comprometem o equil��brio da flora e ...

Simulação numérica 2D e 3D de escoamentos com tensão superficial

Palavras-chave: elementos finitos, tensão superficial, formulação variacional, ALE, potência virt... more Palavras-chave: elementos finitos, tensão superficial, formulação variacional, ALE, potência virtual Resumo: O fenômeno de molhamento, estudo de como um líquido se deposita em um sólido, apresenta problemas ainda em aberto tanto do ponto de vista da modelagem física como no da si-mulação numérica. Neste trabalho, são discutidos métodos numéricos para a simulação de linhas de contato dinâmicas formadas da interação fluido-fluido-estrutura. Os efeitos da tensão super-ficial são estudados com a abordagem do princípio do trabalho virtual, o qual leva o problemà a equações na formulação variacional, linguagem natural para o tratamento numérico com o método dos elementos finitos (MEF). São apresentados resultados preliminares de aproximações calculadas através do método de elementos finitos (formulação ALE-FEM) para problemas en-volvendo tensão superficial, bem como aspectos teóricos da modelagem de linhas tríplices nas equações de Navier-Stokes.

Spurious transients of projection methods in microflow simulations

Computer Methods in Applied Mechanics and Engineering, 2015

The temporal behavior of projection methods for viscous incompressible low-Reynolds-number flows ... more The temporal behavior of projection methods for viscous incompressible low-Reynolds-number flows is adressed. The methods considered result from algebraically splitting the linear system corresponding to each time step, in such a way that the computation of velocity is segregated from that of pressure. Each method is characterized by two (possibly equal) approximate inverses (B 1 and B 2 ) of the momentum-equation velocity matrix, plus a parameter γ which renders the method non-incremental (if γ = 0) or incremental (if γ = 1). The classical first-order projection method, together with more sophisticated methods (Perot's second-order method, Yosida method, pseudoexact factorization method) and their incremental variants are put into the same algebraic form and their accuracy numerically tested. Splitting errors of first, second and third order in the time step size δt are obtained, depending on the method.

High-order ALE schemes for incompressible capillary flows

Journal of Computational Physics, 2014

The spatial discretization of problems with moving boundaries is considered, incorporating the te... more The spatial discretization of problems with moving boundaries is considered, incorporating the temporal evolution of not just the mechanical variables, but also of the nodal positions of the moving mesh. The outcome is a system of Differential-Algebraic Equations (DAE) of index 2 or, in the case of inertialess flow, just 1. From the DAE formulation it its possible to define strategies to build schemes of arbitrary accuracy. We introduce here several schemes of order 2 and 3 that avoid the solution of a nonlinear system involving simultaneously the mechanical variables and the geometrical ones. This class of schemes has been the one adopted by the majority of practitioners of Computational Fluid Dynamics up to now. The proposed schemes indeed achieve the design accuracy, and further show stability restrictions that are not significantly more severe than those of popular first order schemes. The numerical experimentation is performed on capillary problems, discretized by both div-stable (P 2 /P 1 , P + 1 /P 1 ) and equal-order (P 1 /P 1 , stabilized) finite elements, and incorporating surface tension and triple (contact) line effects.

A Lagrangian level-set approach for the simulation of incompressible two-fluid flows

International Journal for Numerical Methods in Fluids, 2005

A Lagrangian level-set method to solve incompressible two-dimensional two-uid ows is presented. T... more A Lagrangian level-set method to solve incompressible two-dimensional two-uid ows is presented. The Navier-Stokes equations are discretized by a Galerkin ÿnite element method. A projection method is employed to decouple the system of non-linear equations. The interface between uids is represented by the zero level set of a function plus additional marker points of the computational mesh. In the standard Eulerian level-set method, this function is advected through the domain by solving a pure advection equation. To reduce mass conservation errors that can arise from this step, our method employs a Lagrangian technique which moves the nodes of the ÿnite element mesh, and consequently, the information stored in each node. The quality of the mesh is controlled by a remeshing procedure, avoiding bad triangles by ipping edges, inserting or removing vertices from the triangulation. Results of numerical simulations are presented, illustrating the improvements in mass conservation and accuracy of this new methodology.

A numerical method for solving the three-dimensional parabolized Navier-Stokes equations

Computers & Fluids, 1997

A numerical technique that solves the parabolized form of the Navier-Stokes equa-*

Numerical simulations of 3D free-surface flows with surface tension

by Antonio Castelo, Fabricio Sousa, and M. Tomé

… 5th International Meeting …, 2002

A MASS-CONSERVING SMOOTH METHOD

by Antonio Castelo and Fabricio Sousa

Review The MAC method

In this article recent advances in the Marker and Cell (MAC) method will be reviewed. The MAC tec... more In this article recent advances in the Marker and Cell (MAC) method will be reviewed. The MAC technique dates back to the early 1960s at the Los Alamos Laboratories and this article starts with a historical review, and then a brief discussion of related techniques. Improvements since the early days of MAC (and the Simplified MAC - SMAC) include automatic time-stepping, the use of the conjugate gradient method to solve the Poisson equation for the corrected velocity potential, greater efficiency through stripping out the virtual particles (markers) other than those near the free surface, and more accurate approximations of the free surface boundary conditions, the addition of bounded high accuracy upwinding for the convected terms (thereby being able to solve higher Reynolds number flows), and a (dynamics) flow visualization facility. More recently, effective techniques for surface and interfacial flows and, in particular, for accurately tracking the associated surface(s)/interface(s...

Uma técnica de correção de interface para o método "Incompressible Smoothed Particle Hydrodynamics

TEMA (São Carlos), 2013

ABSTRACT The maintainability of a good particle distribution is of prior importance to SPH (Smoot... more ABSTRACT The maintainability of a good particle distribution is of prior importance to SPH (Smoothed Particle Hydrodynamics) simulations, since it affects both stability and accuracy of the numerical results. When using ISPH (Incompressible SPH), the particle distribution can be improved by dislocating particles away from their Lagrangian trajectories. However, when applying this technique to multiphase flows, the correct position of the interface between fluids is disturbed, resulting in unphysical flow behavior. In this work, we propose a correction, based upon a constructed smooth distance function. Numerical tests show that this correction can recover the expected position of the interface. Finally, issues regarding mass conservation are assessed and reported.

Numerical Simulation of 3D Multi-fluid Flows

by Antonio Castelo, M. Tomé, and Fabricio Sousa

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 ...

A front-tracking/front-capturing method for the simulation of 3D multi-fluid flows with free surfaces

by Antonio Castelo, M. Tomé, S. McKee, and Fabricio Sousa

Journal of Computational Physics, 2004

A method for simulating incompressible, imiscible, unsteady, Newtonian, multi-fluid flows with fr... more A method for simulating incompressible, imiscible, unsteady, Newtonian, multi-fluid flows with free surfaces is described. A sharp interface separates fluids of different density and viscosity. Surface and interfacial tensions are also considered and the required curvature is geometrically approximated at the fronts by a least squares quadratic fitting . To remove small undulations at the fronts, a mass-conserving filter is employed. The numerical method employed to solve the Navier-Stokes equations is based on the GENSMAC-3D [29] front-tracking method. The velocity field is computed using a finite-difference scheme on an Eulerian grid. The free-surface and the interfaces are represented by an unstructured Lagrangian grid moving through an Eulerian grid. The method was validated by comparing the numerical results with analytical results for a number of simple problems. Complex numerical simulations show the capability and emphasize the robustness of this new method.

Numerical simulations of 3D free surface flows by a multilayer Saint-Venant model

International Journal for Numerical Methods in Fluids, 2008

ABSTRACT We present a multilayer Saint-Venant system for the simulation of 3D free surface flows ... more ABSTRACT We present a multilayer Saint-Venant system for the simulation of 3D free surface flows with friction and viscosity effects. A vertical discretization of a Navier–Stokes system approximation deduced from a precise analysis of the shallow water assumption leads to a set of coupled Saint-Venant-type systems. The idea is to obtain an accurate description of the vertical profile of the horizontal velocity while preserving the robustness and the computational efficiency of the usual Saint-Venant system.For each time-dependent layer, a Saint-Venant-type system is solved on the same 2D mesh by a kinetic solver using a finite volume framework. The free surface is directly deduced from the sum of layers water depth.We validate the model with some numerical academic and realistic examples. We present comparisons with simulations computed with the hydrostatic Navier–Stokes solver of the Telemac-3D code developed by Electricité de France. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Local volume-conserving free surface smoothing

by Antonio Castelo and Fabricio Sousa

Communications in Numerical Methods in Engineering, 2006

Abstract Removing high-frequency undulations in surfaces is a problem that appears in different f... more Abstract Removing high-frequency undulations in surfaces is a problem that appears in different fields, such as computer graphics and computational fluid mechanics. This problem is typically handled by surface smoothing techniques, such as Laplacian filters, that eliminate high-frequency undulations but degrade the volume encompassed by the surface. The need for conserving volume (or mass) rules out the use of such techniques in several application, as for example incompressible flows. In this work we present a smoothing ...

by Antonio Castelo, M. Tomé, S. McKee, and Fabricio Sousa

Computers & Fluids, 2008

In this article recent advances in the Marker and Cell (MAC) method will be reviewed. The MAC tec... more In this article recent advances in the Marker and Cell (MAC) method will be reviewed. The MAC technique dates back to the early 1960s at the Los Alamos Laboratories and this article starts with a historical review, and then a brief discussion of related techniques. Improvements since the early days of MAC (and the Simplified MAC -SMAC) include automatic time-stepping, the use of the conjugate gradient method to solve the Poisson equation for the corrected velocity potential, greater efficiency through stripping out the virtual particles (markers) other than those near the free surface, and more accurate approximations of the free surface boundary conditions, the addition of bounded high accuracy upwinding for the convected terms (thereby being able to solve higher Reynolds number flows), and a (dynamics) flow visualization facility. More recently, effective techniques for surface and interfacial flows and, in particular, for accurately tracking the associated surface(s)/interface(s) including moving contact angles have been developed. This article will concentrate principally on a three-dimensional version of the SMAC method. It will eschew both code verification and model validation; instead it will emphasize the applications that the MAC method can solve, from multiphase flows to rheology.

An improved finite element space for discontinuous pressures

Computer Methods in Applied Mechanics and Engineering, 2010

We consider incompressible Stokes flow with an internal interface at which the pressure is discon... more We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L 2 (Ω)-norm is of order h 1 2 ).

Numerical assessment of stability of interface discontinuous finite element pressure spaces

Computer Methods in Applied Mechanics and Engineering, 2012

The stability of two recently developed pressure spaces has been assessed numerically: The space ... more The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 1019-1031, which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina (Int. can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form.

Numerical Simulation of 3D Multi-fluid Flows doi: 10.5540/tema. 2002.03. 01.0203

by Antonio Castelo, M. Tomé, and Fabricio Sousa

FREE-SURFACE AND TWO-FLUID FLOW SIMULATIONS ON UNSTRUCTURED GRIDS

by Antonio Castelo, M. Tomé, and Fabricio Sousa

Free-surface and two-fluid flow simulations are computationally demanding tasks. The freedom allo... more Free-surface and two-fluid flow simulations are computationally demanding tasks. The freedom allowed when using unstructured grids can be exploited to develop efficient methods for this type of problems. For instance, level-set methods and front tracking methods can be combined onto an unstructured grid method that combines advantages of both methods. In this work, methods to solve incompressible two-dimensional two-fluid flows on unstructured grids are discussed. The Navier-Stokes equations are discretized by suitable finite element methods. The numerical method for the solution is based on the projection method to uncouple the system of non-linear equations. Strategies employed for the representation of the interface between fluids are discussed. For instance, the interface can be represented by the zero level set of a function φ plus additional marker points of the computational mesh. In the standard Eulerian level-set method, this function is advected through the domain by solving a pure advection equation. To reduce mass conservation errors that can arise from this step, a Lagrangian technique, which moves the nodes of the finite element mesh, and consequently, the information stored in each node, can be employed. Due to the large distortion of the mesh that can occur, remeshing procedures are required in order to control de quality of the mesh. Results from some simulations are shown to compare the mass conservation and accuracy of the various discussed methodologies.

A numerical method for solving three-dimensional generalized Newtonian free surface flows

by Antonio Castelo, M. Tomé, S. McKee, Fabricio Sousa, and Fabiano B M Silva

Journal of Non-Newtonian Fluid Mechanics, 2004

A numerical technique that solves the parabolized form of the Navier-Stokes equa-*