Roberto F. Ausas

A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation

A numerical algorithm for fully dynamical lubrication problems based on the Elrod― Adams formulation of the Reynolds equation with mass-conserving boundary conditions is described. A simple but effective relaxation scheme is used to update the solution maintaining the complementarity conditions on the variables that represent the pressure and fluid fraction. The equations of motion are discretized in time using Newmarks scheme, and the dynamical variables are updated within the same relaxation process just mentioned. The good behavior of the proposed algorithm is illustrated in two examples: an oscillatory squeeze flow (for which the exact solution is available) and a dynamically loaded journal bearing. This article is accompanied by the ready-to-compile source code with the implementation of the proposed algorithm.

Optimization tools in the analysis of micro-textured lubricated devices

We address the problem of optimizing the performance of lubricated devices by means of artificial texturing. We consider a slider (or equivalently a thrust bearing) and minimize the friction using optimization tools such as sensitivity analysis and genetic algorithms. We show that textures that perform significantly better than the smooth (untextured) one can be found, and that the optimized texture depends on the working conditions (load, velocity). The GENESIS code that we used, with no fine tuning of algorithmic variables, proved a valuable tool in the identification of improved shapes.

The Multiscale Robin Coupled Method for flows in porous media

Abstract 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 on the skeleton of the decomposition, corresponding to interface pressures and fluxes, that can be chosen with great flexibility to accommodate local features of the underlying permeability fields. The well-posedness of the new domain decomposition procedure is established and its connection with the method of Douglas et al. (1993) [12] , is identified, also allowing us to reinterpret the known procedure as an optimized Schwarz (or Two-Lagrange-Multiplier) method. The multiscale property of the new domain decomposition method is indicated, and its relation with the Multiscale Mortar Mixed Finite Element Method (MMMFEM) and the Multiscale Hybrid-Mixed (MHM) Finite Element Method is discussed. Numerical simulations are presented aiming at illustrating several features of the new method. Initially we illustrate the possibility of switching from MMMFEM to MHM by suitably varying the Robin condition parameter in the new multiscale method. Then we turn our attention to realistic flows in high-contrast, channelized porous formations. We show that for a range of values of the Robin condition parameter our method provides better approximations for pressure and velocity than those computed with either the MMMFEM and the MHM. This is an indication that our method has the potential to produce more accurate velocity fields in the presence of rough, realistic permeability fields of petroleum reservoirs.

Tratamento numérico da mecânica de interfaces lipídicas: modelagem e simulação

A mecanica celular jaz na membrana plasmatica, fundamentalmente uma bicamada fosfolipidica com espessura de dimensoes moleculares. Alem de forcas elasticas, tal material bidimensional tambem experimenta tensoes viscosas devido ao seu comportamento fluido na direcao tangencial, ainda incompreendido do ponto de vista da modelagem computacional. Assim, reportamos aqui a construcao de um esquema numerico variacional capaz de simular a dinamica das membranas celulares. Em posse do operador de Boussinesq-Scriven, introduzimos uma formulacao variacional mista de tres campos para escoamentos viscosos de superficies fechadas curvas. Nela, o fluido circundante e levado em conta considerando-se uma restricao de volume interior a membrana, cuja inextensibilidade e imposta via restricao de area. As incognitas sao a velocidade, o vetor curvatura e a pressao superficial, todas interpoladas com elementos finitos lineares continuos estabilizados. Outro ingrediente numerico inedito aqui reportado e uma forca que mimetiza a acao de uma pinca optica que permite interacao virtual com a membrana, situacao esta na qual a qualidade e o refinamento de malha sao mantidos por remalhagem adaptativa automatica utilizando-se de uma metologia ja existente na literatura. Observamos estabilidade temporal condicional com uma restricao de passo de tempo que varia segundo o quadrado da menor aresta dos triangulos da malha, inclusive fornecendo uma regra pratica para escolhe-lo. Reportamos os limites de estabilidade do metodo e sua capacidade de predizer o equilibrio dinamico de elongacoes cilindricas compridas e finas (tethers) que surgem a partir de pincamentos. Revelamos um efeito dinamico onde ha dependencia da forma da membrana com respeito a uma velocidade imposta de pincamento, de modo que abaixo de um valor limiar de velocidade um tether nao se forma de inicio. O esquema numerico apresentado permite simular a dinamica de membranas elasticas viscosas em geometriais tridimensionais assimetricas e em topologias nao-triviais (e.g., toro).