# Gustavo BuscagliaUniversity of São Paulo | USP · Department of Applied Mathematics and Statistics (SME) (São Carlos)

Gustavo Buscaglia

Professor

## About

164

Publications

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2,712

Citations

## Publications

Publications (164)

This note extends previous work of the authors modelling the Wheatley valve by using six intersecting and contiguous ellipses to obtain a generalized mathematical representation of the Wheatley valve: this provides a number of free parameters that could be employed to obtain an optimal design. Since optimality is multi-objective with many of the ob...

A three dimensional parallel implementation of Multiscale Mixed Methods based on non-overlapping domain decomposition techniques is proposed for multi-core computers and its computational performance is assessed by means of numerical experiments. As a prototypical method, from which many others can be derived, the Multiscale Robin Coupled Method is...

The coupled problem of hydrodynamics and solute transport for the Najafi-Golestanian three-sphere swimmer is studied, with the Reynolds number set to zero and P\'eclet numbers (Pe) ranging from 0.06 to 60. The adopted method is the numerical simulation of the problem with a finite element code based upon the FEniCS library. For the swimmer executin...

Unresolved pressure fluctuations at the sub-grid scale (SGS) level of large eddy simulation (LES) or Reynolds-averaged Navier–Stokes computations affect cavitation inception predictions, as SGS low pressures are simply ignored. We present a framework to take the unresolved SGS flow into account. Representing the SGS flow as canonical turbulence, in...

In the presence of strong heterogeneities, it is well known that the use of explicit schemes for the transport of species in a porous medium suffers from severe restrictions on the time step. This has led to the development of implicit schemes that are increasingly favoured by practitioners for their computational efficiency. The transport equation...

We propose a finite element method for simulating one-dimensional solid models with finite thickness and finite length that move and experience large deformations while immersed in generalized Newtonian fluids. The method is oriented towards applications involving microscopic devices or organisms in the soft-bio-matter realm. By considering that th...

It is well known that domain-decomposition-based multiscale mixed methods rely on interface spaces, defined on the skeleton of the decomposition, to connect the solution among the non-overlapping subdomains. Usual spaces, such as polynomial-based ones, cannot properly represent high-contrast channelized features such as fractures (high permeability...

We propose a finite element method for simulating one-dimensional solid models moving and experiencing large deformations while immersed in generalized Newtonian fluids. The method is oriented towards applications involving microscopic devices or organisms in the soft-bio-matter realm. By considering that the strain energy of the solid may explicit...

In the presence of strong heterogeneities, it is well known that the use of explicit schemes for the transport of species in a porous medium suffers from severe restrictions on the time step. This has led to the development of implicit schemes that are increasingly favoured by practitioners for their computational efficiency. The transport equation...

A three dimensional parallel implementation of Multiscale Mixed Methods based on non-overlapping domain decomposition techniques is proposed for multi-core computers and its computational performance is assessed by means of numerical experimentation. As a prototypical method, from which many others can be derived, the Multiscale Robin Coupled Metho...

It is well known that domain-decomposition-based multiscale mixed methods rely on interface spaces, defined on the skeleton of the decomposition, to connect the solution among the non-overlapping subdomains. Usual spaces, such as polynomial-based ones, cannot properly represent high-contrast channelized features such as fractures (high permeability...

Two-phase flows in oil reservoirs can be modeled by a coupled system of elliptic and hyperbolic partial differential equations. The transport velocity of the multiphase fluid system is related to the pressure through Darcy’s law and it is coupled to a conservation law for the saturation variable of one of the phases. A time step of the classical IM...

In this work we report for the first time a mathematical approach to model the behaviour of a single oleosome (oil body) within a seed cellular environment. To describe the behaviour of the oleosome membrane, we adopted a dynamical continuum model based on the principle of the virtual work where the intrinsic energy of the lipid membrane is assumed...

Mathematical models for the growth of tumours in the presence of stem cells (CSCs) and differentiated tumour cells (CCs) are presented and discussed. The CSCs are assumed to be immortal and multipotent, i.e. capable of generating several possible lineages of CCs that may undergo ageing and apoptosis. Each CC is characterised by two indexes, related...

This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton...

Squirmers are models of a class of microswimmers that self-propel in fluids without significant deformation of their body shape, such as ciliated organisms and phoretic particles. Available techniques for their simulation are based on the boundary element method and do not contemplate nonlinearities such as those arising from the inertia of the flu...

The behavior of the pressure along the trajectories of finite-sized nuclei in isotropic homogeneous turbulence is investigated using direct numerical simulations at Reλ = 150. The trajectories of nuclei of different sizes are computed by solving a modified Maxey–Riley equation under different buoyancy conditions. Results show that larger nuclei are...

We propose two postprocessing procedures (Patch method and Stitch method) to recover local conservation of velocity fields produced by multiscale approximations that are only conservative in coarse scales. These procedures operate on small overlapping regions and are designed to be implemented in parallel, which makes them relatively inexpensive. W...

The study of bubble’s behavior in turbulent flows is fundamental to the understanding of many engineering applications that are concerned with bubbly/two-phase flow. In turbomachinery, for example, tiny gas nuclei present in the liquid may grow to macroscopic size if the instantaneous pressure dips below the vapor pressure for a time long enough to...

Full article access before April 10: https://authors.elsevier.com/a/1ac4I508Hm3jf

This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton...

We propose a finite element method for the solution of viscous incompressible flow problems with singular forces at immersed interfaces. The method combines the algebraic subgrid scale method with a pressure jump stabilization. It consists of the addition, to the continuity equation, of a term weighting the residual of the pressure jump. This term...

Homogeneous and isotropic turbulent fields obtained from two direct numerical simulation databases (with Reλ equal to 150 and 418) were seeded with point particles that moved with the local fluid velocity to obtain Lagrangian pressure histories. Motivated by cavitation inception modeling, the statistics of events in which such particles undergo low...

The Piston-Ring-Liner system is the main tribological component of internal combustion engines. Hydrodynamic models are customarily used to numerically assess the performance of different ring designs and liner surface treatments. However, available models do not properly incorporate the backpressure boundary condition, which corresponds to the com...

Homogeneous and isotropic turbulent fields obtained from two DNS databases (with $\Re_\lambda$ equal to 150 and 418) were seeded with point particles that moved with the local fluid velocity to obtain Lagrangian pressure histories. Motivated by cavitation inception modeling, the statistics of events in which such particles undergo low-pressure fluc...

The Piston-Ring-Liner system is the main tribological component of internal combustion engines. The Elrod-Adams model is customarily used to numerically assess the hydrodynamics of different ring designs and liner surface treatments. However, that model does not incorporate the backpressure boundary condition, which in this case corresponds to the...

A novel methodology for the prediction of cavitation inception based on a probabilistic approach is presented along with a limited validation. The simulation of a cavitating flow is a challenging and evolving area of investigation, complicated by the requirement of accurately solving a complex multiphase flow. However, for many practical applicatio...

Squirmers are models of a class of microswimmers, such as ciliated organisms and phoretic particles, that self-propel in fluids without significant deformation of their body shape. Available techniques for their simulation are based on the boundary-element method and do not contemplate nonlinearities such as those arising from the fluid's inertia o...

Many important microfluid applications require the control and transport of particles immersed in a fluid. We propose a model for automatically planning good trajectories from an arbitrary point to a target in the presence of obstacles. It can be used for the manipulation of particles using actuators of mechanical or electrical type. We present the...

Many important microfluidic applications require the control and transport of particles immersed in a fluid. We propose a model for automatically planning good trajectories from an arbitrary point to a target in the presence of obstacles. It can be used for the manipulation of particles using actuators of mechanical or electrical type. We present t...

The Multiscale Robin Coupled Method (MRCM) is a recent multiscale numerical method based on a non-overlapping domain decomposition procedure. One of its hallmarks is that the MRCM allows for the independent definition of interface spaces for pressure and flux over the skeleton of the decomposition. The accuracy of the MRCM depends on the choice of...

The coupling of Reynolds and Rayleigh-Plesset equations has been used in several works to simulate lubricated devices considering cavitation. The numerical strategies proposed so far are variants of a staggered strategy where Reynolds equation is solved considering the bubble dynamics frozen, and then the Rayleigh-Plesset equation is solved to upda...

A multiscale mixed method aiming at the accurate approximation of velocity and pressure fields in heterogeneous porous media is proposed. The procedure is based on a new domain decomposition method in which the local problems are subject to Robin boundary conditions. The domain decomposition procedure is defined in terms of two independent spaces o...

The effects of surface roughness in hydrodynamic bearings been accounted for through several approaches, the most widely used being averaging or stochastic techniques. With these the surface is not treated "as it is", but by means of an assumed probability distribution for the roughness. The so called direct, deterministic or measured-surface simul...

When simulating numerically the hydrodynamical lubrication of tribological devices, a common assumption is that the boundary pressure and the cavitation pressure are equal (and taken equal to zero). This allows to include cavitation effects through some of the available algorithms, like the mass-conserving Elrod-Adams cavitation model. However, tri...

The most widely adopted model to treat thin film (lubrication) problems with cavitation is
the Elrod-Adams model. An efficient numerical solution is by no means trivial, as the classical Newton-
Raphson method is not suitable for this problem. The best approach so far is to solve it with a Jacobi
or Gauss-Seidel type algorithm, as done by Ausas (R....

This paper presents an extension of the Kurganov and Tadmor central scheme [A. Kurganov and E. Tadmor, J. Comput. Phys., 160 (2000), pp. 241–282] to work with solvers based on conservative face fluxes, which are usual in the solution of incompressible flows by the Finite Volume method. The proposed scheme retains the desirable properties of simplic...

Models of the friction force are assessed by direct comparison with two-dimensional Navier-Stokes results. A three-term formula obtained from asymptotic expansion provides a reasonable estimate of the hydrodynamic friction of rough runners even at sub-micron clearances. Simulations of a measured honed surface are then reported using the conservativ...

In this paper we prove an existence result for a variety of rotor-bearing systems, namely journal bearing, piston ring-liner and mechanical seal systems. These results are shown for a fixed geometry for different boundary conditions. The mathematical model considered is the mass-conserving Elrod-Adams in presence of cavitation and in the unsteady c...

Numerical results are presented for three fully dynamical lubrication devices (piston ring–liner, journal bearing and mechanical
seals) based on the Elrod–Adams model for the Reynolds equation and Newmark scheme for the motion equations. For each
lubricated system we give the mathematical model, the corresponding non-dimensional problem and numeric...

Surface incompressibility, also called inextensibility, imposes a
zero-surface-divergence constraint on the velocity of a closed deformable
material surface. The well-posedness of the mechanical problem under such
constraint depends on an inf-sup or stability condition for which an elementary
proof is provided. The result is also shown to hold in c...

A finite element formulation to approximate the behavior of lipid membranes is proposed. The mathematical model incorporates tangential viscous stresses and bending elastic forces, together with the inextensibility constraint and the enclosed volume constraint. The membrane is discretized by a surface mesh made up of planar triangles, over which a...

The temporal behavior of projection methods for viscous incompressible low-Reynolds-number flows is addressed. 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...

Surface tension in multi-phase fluid flow engenders pressure discontinuities on phase interfaces. In this work we present a finite element method to solve viscous incompressible flows problems, especially designed to cope with such a situation. Taking as a model the Stokes system we study a finite element solution method based on a classical Galerk...

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienk...

Numerical simulations of the ring/liner contact in which the liner exhibits a periodic texture (pockets) are reported. The mass-conservative Elrod–Adams model is used to treat cavitation, and the dynamics of the ring is considered with a linear mass that corresponds to actual engine compression rings. The results, computed at a Stribeck number of 1...

A thrust bearing consisting of an infinitely wide pad, subject to a constant load and sliding at constant speed on a runner with transverse sinusoidal textures is considered. The analysis method consists of time- and mesh-resolved simulations with a finite volume approximation of the Elrod-Adams model. Friction and clearance contours as functions o...

A generalization of the Elrod–Adams model of cavitation in lubricated devices is proposed, such that the translation velocity
$V$
V
for the saturation field
$\theta $
θ
can be given any value between
$S/2$
S
/
2
and
$S$
S
, with
$S$
S
being the relative speed of the surfaces. The lack of uniqueness of the classical model when...

The method of asymptotic partial decomposition of a domain aims at replacing a 3D or 2D problem by a hybrid problem 3D − 1D; or 2D − 1D, where the dimension of the problem decreases in part of the domain. The location of the junction between the heterogeneous problems is asymptotically estimated in certain circumstances, but for numerical simulatio...

Surface tension in multi-phase fluid flow engender pressure
discontinuities on phase interfaces. In this work we present two finite
element methods to solve viscous incompressible flows problems,
especially designed to cope with such a situation. Taking as a model the
two-dimensional Stokes system, we consider stable solution methods based
on piece...

An in‐house fully three‐dimensional general‐purpose finite element model is applied to solve the hydrodynamic structure in a periodic Kinoshita‐generated meandering channel. The numerical model solves the incompressible Reynolds‐averaged Navier–Stokes equations for mass and momentum, while solving the k − ε equations for turbulence. The free surfac...

This work presents a generic and efficient black-box approach for the strong iterative coupling of dimensionally heterogeneous flow models in computational hemodynamics. A heterogeneous model of the cardiovascular system is formed by several vascular black-box components, which are connected through coupling equations. The associated system of equa...

The simulation of biological interfaces at the Living Cell scale relies on membrane models that are a combination of a finite–strain elastic part, typically modeling the contribution of a cytoskeleton, and a viscous part that models the contribution of the lipidic bilayer. The motion of these membranes is driven by a shape-dependent energy, modeled...

This paper presents a conservative numerical implementation of a new cavitation model that is well suited for lubrication problems with cavitated regions in which the fluid film is attached to just one of the participating surfaces, as happens for instance in piston–ring assemblies. This new model was recently proposed by Buscaglia et al. (2011) an...

Surface tension in multi phase fluid flow engenders pressure discontinuities on phase interfaces. In this work we present
two finite element methods to solve viscous incompressible flows problems, especially designed to cope with such a situation.
Taking as a model the two-dimensional Stokes system, we consider solution methods based on piecewise l...

In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds two degrees of freedom per element that can be eliminated by means of static condensation. The new space is tested and compared with the classical P1 space and to the space propo...

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019–1031], which is capable of representing discontinuous pressures, and the s...

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across
a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite
element methodologies, the space is a variant of the standard conforming space that can be implemente...

The interest in the simulation of flows with significant surface tension effects has grown significantly in recent years. This has been driven by the substantial advances made in the measurement and manufacturing of microscopic systems, since at small length scales surface phenomena are dominant. In this article, surface tension, capillarity and we...

In this work an iterative strategy is developed to tackle the problem of coupling dimensionally- heterogeneous models in the context of fluid mechanics. The procedure proposed here makes use of a reinterpretation of the original problem as a nonlinear interface problem for which classical nonlinear solvers can be applied. Strong coupling of the par...

In this paper we describe and evaluate a geometric mass-preserving redistancing procedure for the level set function on general structured grids. The proposed algorithm is adapted from a recent finite element-based method and preserves the mass by means of a localized mass correction. A salient feature of the scheme is the absence of adjustable par...