Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model

We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen–Cahn/Cahn–Hilliard/Navier–Stokes–Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.

Two-Phase Mapping for Projecting Massive Data Sets

Most multidimensional projection techniques rely on distance (dissimilarity) information between data instances to embed high-dimensional data into a visual space. When data are endowed with Cartesian coordinates, an extra computational effort is necessary to compute the needed distances, making multidimensional projection prohibitive in applications dealing with interactivity and massive data. The novel multidimensional projection technique proposed in this work, called Part-Linear Multidimensional Projection (PLMP), has been tailored to handle multivariate data represented in Cartesian high-dimensional spaces, requiring only distance information between pairs of representative samples. This characteristic renders PLMP faster than previous methods when processing large data sets while still being competitive in terms of precision. Moreover, knowing the range of variation for data instances in the high-dimensional space, we can make PLMP a truly streaming data projection technique, a trait absent in previous methods.

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures

We design and investigate a sequential discontinuous Galerkin method to approximate two-phase immiscible incompressible flows in heterogeneous porous media with discontinuous capillary pressures. The nonlinear interface conditions are enforced weakly through an adequate design of the penalties on interelement jumps of the pressure and the saturation. An accurate reconstruction of the total velocity is considered in the Raviart-Thomas(-Nedelec) finite element spaces, together with diffusivity-dependent weighted averages to cope with degeneracies in the saturation equation and with media heterogeneities. The proposed method is assessed on one-dimensional test cases exhibiting rough solutions, degeneracies, and capillary barriers. Stable and accurate solutions are obtained without limiters. (C) 2010 Elsevier B.V. All rights reserved.

Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows

We consider Discontinuous Galerkin approximations of two-phase, immiscible porous media flows in the global pressure/fractional flow formulation with capillary pressure. A sequential approach is used with a backward Euler step for the saturation equation, equal-order interpolation for the pressure and the saturation, and without any limiters. An accurate total velocity field is recovered from the global pressure equation to be used in the saturation equation. Numerical experiments show the advantages of the proposed reconstruction. To cite this article: A. Ern et al., C R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Levenberg-Marquardt application to two-phase nonlinear parameter estimation for finned-tube coil evaporators

A procedure for calculation of refrigerant mass flow rate is implemented in the distributed numerical model to simulate the flow in finned-tube coil dry-expansion evaporators, usually found in refrigeration and air-conditioning systems. Two-phase refrigerant flow inside the tubes is assumed to be one-dimensional, unsteady, and homogeneous. In themodel the effects of refrigerant pressure drop and the moisture condensation from the air flowing over the external surface of the tubes are considered. The results obtained are the distributions of refrigerant velocity, temperature and void fraction, tube-wall temperature, air temperature, and absolute humidity. The finite volume method is used to discretize the governing equations. Additionally, given the operation conditions and the geometric parameters, the model allows the calculation of the refrigerant mass flow rate. The value of mass flow rate is computed using the process of parameter estimation with the minimization method of Levenberg-Marquardt minimization. In order to validate the developed model, the obtained results using HFC-134a as a refrigerant are compared with available data from the literature.

Mathematical modeling of the ester oil-refrigerant R134A mixture two-phase flow with foam formation through a small diameter tube

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Plasmid DNA partitioning and separation using poly(ethylene glycol)/poly(acrylate)/salt aqueous two-phase systems

Phase diagrams of poly(ethylene glycol)/polyacrylate/Na2SO4 systems have been investigated with respect to polymer size and pH. Plasmid DNA from Escherichia coil can depending on pH and polymer molecular weight be directed to a poly(ethylene glycol) or to a polyacrylate-rich phase in an aqueous two-phase system formed by these polymers. Bovine serum albumin (BSA) and E. coil homogenate proteins can be directed opposite to the plasmid partitioning in these systems. Two bioseparation processes have been developed where in the final step the pDNA is partitioned to a salt-rich phase giving a total process yield of 60-70%. In one of them the pDNA is partitioned between the polyacrylate and PEG-phases in order to remove proteins. In a more simplified process the plasmid is partitioned to a PEG-phase and back-extracted into a Na2SO4-rich phase. The novel polyacrylate/PEG system allows a strong change of the partitioning between the phases with relatively small changes in composition or pH. (C) 2012 Elsevier B.V. All rights reserved.

Phase Diagrams of the Aqueous Two-Phase Systems of Poly(ethylene glycol)/Sodium Polyacrylate/Salts

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity

We establish universal behaviour in the temperature dependencies of some observables in (s + id)-wave BCS superconductivity in the presence of a weak a wave. We find also a second second-order phase transition. As temperature is lowered-past the usual critical temperature T-c, a less ordered superconducting phase is created in the d wave, which changes to a more ordered phase in a (s + id) wave at T-c1 (

Two phase transitions in (d(x2-y2)+is)-wave superconductors

We study numerically the temperature dependencies of specific heat, susceptibility, penetration depth, and thermal conductivity of a coupled (d(x2-y2) + is)-wave Bardeen-Cooper-Schrieffer (BCS) superconductor in the presence of a weak s-wave component (1) on square lattice and (2) on a lattice with orthorhombic distortion. As the temperature is lowered past the critical temperature T-c, a less ordered superconducting phase is created in d(x2-y2) wave, which changes to a more ordered phase in (d(x2-y2) + is) wave at T-c1. This manifests in two second-order phase transitions. The two phase transitions are identified by two jumps in specific heat at T-c and T-c1. The temperature dependencies of the superconducting observables exhibit a change from power-law to exponential behavior as temperature is lowered below T-c1 and confirm the new phase transition. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Cassava wastewater (manipueira) treatment using a two-phase anaerobic biodigestor

Um biodigestor anaeróbio de duas fases foi utilizado para se analisar a produção de metano com diferentes cargas de entrada de manipueira. A fase acidogênica foi realizada em processo de batelada e a metanogênica em biodigestor anaeróbio de fluxo ascendente e leito fixo com alimentação contínua. As cargas orgânicas de entrada variaram de 0,33 a 8,48 gDQO (Demanda Química de Oxigênio)/L.dia. A maior porcentagem de metano encontrada foi de 80,9%, com carga orgânica de 0,33g e a menor, 56,8%, obtida com 8,49gDQO/L.d. A maior taxa de redução de DQO foi de 88,89%, obtida com carga orgânica de 2,25g e a menor, 54,95%, com 8,48gDQO/L.d. Analisando-se os dados apresentados verificou-se que a biodigestão anaeróbia pode ser conduzida, pelo menos, de duas maneiras, ou seja, para produção de energia (metano) ou para redução de carga orgânica. A carga orgânica de entrada deve ser calculada em função do objetivo a ser alcançado com a biodigestão anaeróbia.

Two-phase separation observed in thermally treated pellets of ClO4- doped poly(3-methylthiophene) from electron spin resonance measurements

A pressed pellet of CIO (-)(4) poly (3-methylthiophene) (P3MT) was heated for two hours at 85 degrees C and suddenly dropped in liquid nitrogen. A change was observed around 220 K in the Electron Spin Resonance (ESR) spectra when the sample was slowly cooled from room temperature. ESR line asymmetry parameter (A/B) showed two spatially separated phases. One was identified as a small metallic-like phase. The other phase, the larger one, makes a transition to a semiconducting Charge-Density Wave (CDW) state.

A two phase flow nonlinear parameter estimation for capillary tube-suction line heat exchanger

Here we present two-phase flow nonlinear parameter estimation for HFC's flow through capillary tube-suction line heat exchangers, commonly used as expansion devices in small refrigeration systems. The simplifying assumptions adopted are: steady state, pure refrigerant, one-dimensional flow, negligible axial heat conduction in the fluid, capillary tube and suction line walls. Additionally, it is considered that the refrigerant is free from oil and both phases are assumed to be at the same pressure, that is, surface tension effects are neglected. Metastable flow effects are also disregarded, and the vapor is assumed to be saturated at the local pressure. The so-called homogeneous model, involving three, first order, ordinary differential equations is applied to analyze the two-phase flow region. Comparison is done with experimental measurements of the mass flow rate and temperature distribution along capillary tubes working with refrigerant HFC-134a in different operating conditions.

Partitioning the relative contribution of one-phase and two-phase seed dispersal when evaluating seed dispersal effectiveness

Seed dispersal effectiveness (SDE) is a conceptual framework that aims at quantifying the contribution of seed dispersal vectors to plant fitness. While it is well recognized that diplochorous dispersal systems, characterized by two successive dispersal steps performed by two different vectors (Phase I=primary seed dispersal and Phase II=secondary seed dispersal) which are common in temperate and tropical regions, little attention has been given to distinguishing the relative contribution of one-phase and two-phase dispersal to overall SDE. This conceptual gap probably results from the lack of a clear methodology to include Phase II dispersal into the calculation of SDE and to quantify its relative contribution. We propose a method to evaluate the relative contribution of one-phase and two-phase dispersal to SDE and determine whether two seed dispersers are better than one. To do so, we used the SDE landscape and an extension of the SDE landscape, the Phase II effect landscape, which measures the direction and magnitude of the Phase II dispersal effect on overall SDE. We used simulated and empirical data from a diplochorous dispersal system in the Peruvian Amazon to illustrate this new approach. Our approach provides the relative contribution of one-phase SDE (SDE1) and two-phase SDE (SDE2) to overall SDE and quantifies how much SDE changes with the addition of Phase II dispersal. Considering that the seed dispersal process is context dependent so that Phase II depends on Phase I, we predict the possible range of variation of SDE according to the variation of the probability of Phase II dispersal. In our specific study system composed of two primate species as primary dispersal vectors and different species of dung beetles as secondary dispersal vectors, the relative contribution of SDE1 and SDE2 to overall SDE varied between plant species. We discuss the context dependency of the Phase II dispersal and the potential applications of our approach. This extension to the conceptual framework of SDE enables quantitative evaluation of the effect of Phase II dispersal on plant fitness and can be easily adapted to other biotic and/or abiotic diplochorous dispersal systems.