Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

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.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5]. (C) 2008 Elsevier Inc. All rights reserved.

On state representations of nonlinear implicit systems

This work considers a semi-implicit system A, that is, a pair (S, y), where S is an explicit system described by a state representation (x)over dot(t) = f(t, x(t), u(t)), where x(t) is an element of R(n) and u(t) is an element of R(m), which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) is an element of R(l). An input candidate is a set of functions v = (v(1),.... v(s)), which may depend on time t, on x, and on u and its derivatives up to a Finite order. The problem of finding a (local) proper state representation (z)over dot = g(t, z, v) with input v for the implicit system Delta is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Delta. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Levine, Martin, and Rouchon (1999) (`A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems`, IEEE Transactions on Automatic Control, 44(5), (922-937)).

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

A numerical method for solving the dynamic three-dimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field

A finite difference technique, based on a projection method, is developed for solving the dynamic three-dimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field. The governing equations in this situation are derived using primitive variables and are solved using the ideas behind the GENSMAC methodology (Tome and McKee [32]; Tome et al. [34]). The resulting numerical technique is then validated by comparing the numerical solution against an analytic solution for steady three-dimensional flow between two-parallel plates subject to a strong magnetic field. The validated code is then employed to solve channel flow for which there is no analytic solution. (C) 2009 Elsevier B.V. All rights reserved.

Three-dimensional, fully adaptive simulations of phase-field fluid models

We present an efficient numerical methodology for the 31) computation of incompressible multi-phase flows described by conservative phase-field models We focus here on the case of density matched fluids with different viscosity (Model H) The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time discretization strategy and a linear, multi-level multigrid to relax high order stability constraints and to capture the flow`s disparate scales at optimal cost. Only five linear solvers are needed per time-step. Moreover, all the adaptive methodology is constructed from scratch to allow a systematic investigation of the key aspects of AMR in a conservative, phase-field setting. We validate the method and demonstrate its capabilities and efficacy with important examples of drop deformation, Kelvin-Helmholtz instability, and flow-induced drop coalescence (C) 2010 Elsevier Inc. All rights reserved

A new approach for in vitro bioassay to measure tannin biological effects based on a gas production technique

The aim of this paper was to study a method based on gas production technique to measure the biological effects of tannins on rumen fermentation. Six feeds were used as fermentation substrates in a semi-automated gas method: feed A - aroeira (Astronium urundeuva); feed B - jurema preta (Mimosa hostilis), feed C - sorghum grains (Sorghum bicolor); feed D - Tifton-85 (Cynodon sp.); and two others prepared mixing 450 g sorghum leaves, 450 g concentrate (maize and soybean meal) and 100 g either of acacia (Acacia mearnsii) tannin extract (feed E) or quebracho (Schinopsis lorentzii) tannin extract (feed F) per kg (w:w). Three assays were carried out to standardize the bioassay for tannins. The first assay compared two binding agents (polyethylene glycol - PEG - and polyvinyl polypirrolidone - PVPP) to attenuate the tannin effects. The complex formed by PEG and tannins showed to be more stable than PVPP and tannins. Then, in the second assay, PEG was used as binding agent, and this assay was done to evaluate levels of PEG (0, 500, 750, 1000 and 1250 mg/g DM) to minimize the tannin effect. All the tested levels of PEG produced a response to evaluate tannin effects but the best response was for dose of 1000 mg/g DM. Using this dose of PEG, the final assay was carried out to test three compounds (tannic acid, quebracho extract and acacia extract) to establish a curve of biological equivalent effect of tannins. For this, five levels of each compound were added to I g of a standard feed (Lucerne hay). The equivalent effect showed not to be directly related to the chemical analysis for tannins. It was shown that different sources of tannins had different activities or reactivities. The curves of biological equivalence can provide information about tannin reactivity and its use seems to be important as an additional factor for chemical analysis. (C) 2007 Elsevier B.V. All rights reserved.

Aerosol inorganic composition at a tropical site: Discrepancies between filter-based sampling and a semi-continuous method

The concentrations of the water-soluble inorganic aerosol species, ammonium (NH4+), nitrate (NO3-), chloride (Cl-), and sulfate (SO42-), were measured from September to November 2002 at a pasture site in the Amazon Basin (Rondnia, Brazil) (LBA-SMOCC). Measurements were conducted using a semi-continuous technique (Wet-annular denuder/Steam-Jet Aerosol Collector: WAD/SJAC) and three integrating filter-based methods, namely (1) a denuder-filter pack (DFP: Teflon and impregnated Whatman filters), (2) a stacked-filter unit (SFU: polycarbonate filters), and (3) a High Volume dichotomous sampler (HiVol: quartz fiber filters). Measurements covered the late dry season (biomass burning), a transition period, and the onset of the wet season (clean conditions). Analyses of the particles collected on filters were performed using ion chromatography (IC) and Particle-Induced X-ray Emission spectrometry (PIXE). Season-dependent discrepancies were observed between the WAD/SJAC system and the filter-based samplers. During the dry season, when PM2.5 (D-p <= 2.5 mu m) concentrations were similar to 100 mu g m(-3), aerosol NH4+ and SO42- measured by the filter-based samplers were on average two times higher than those determined by the WAD/SJAC. Concentrations of aerosol NO3- and Cl- measured with the HiVol during daytime, and with the DFP during day- and nighttime also exceeded those of the WAD/SJAC by a factor of two. In contrast, aerosol NO3- and Cl- measured with the SFU during the dry season were nearly two times lower than those measured by the WAD/SJAC. These differences declined markedly during the transition period and towards the cleaner conditions during the onset of the wet season (PM2.5 similar to 5 mu g m(-3)); when filter-based samplers measured on average 40-90% less than the WAD/SJAC. The differences were not due to consistent systematic biases of the analytical techniques, but were apparently a result of prevailing environmental conditions and different sampling procedures. For the transition period and wet season, the significance of our results is reduced by a low number of data points. We argue that the observed differences are mainly attributable to (a) positive and negative filter sampling artifacts, (b) presence of organic compounds and organosulfates on filter substrates, and (c) a SJAC sampling efficiency of less than 100%.

Rapid detection of bovine coronavirus by a semi-nested RT-PCR

Bovine coronavirus (BCoV) is a member of the group 2 of the Coronavirus (Nidovirales: Coronaviridae) and the causative agent of enteritis in both calves and adult bovine, as well as respiratory disease in calves. The present study aimed to develop a semi-nested RT-PCR for the detection of BCoV based on representative up-to-date sequences of the nucleocapsid gene, a conserved region of coronavirus genome. Three primers were designed, the first round with a 463bp and the second (semi-nested) with a 306bp predicted fragment. The analytical sensitivity was determined by 10-fold serial dilutions of the BCoV Kakegawa strain (HA titre: 256) in DEPC treated ultra-pure water, in fetal bovine serum (FBS) and in a BCoV-free fecal suspension, when positive results were found up to the 10-2, 10-3 and 10-7 dilutions, respectively, which suggests that the total amount of RNA in the sample influence the precipitation of pellets by the method of extraction used. When fecal samples was used, a large quantity of total RNA serves as carrier of BCoV RNA, demonstrating a high analytical sensitivity and lack of possible substances inhibiting the PCR. The final semi-nested RT-PCR protocol was applied to 25 fecal samples from adult cows, previously tested by a nested RT-PCR RdRp used as a reference test, resulting in 20 and 17 positives for the first and second tests, respectively, and a substantial agreement was found by kappa statistics (0.694). The high sensitivity and specificity of the new proposed method and the fact that primers were designed based on current BCoV sequences give basis to a more accurate diagnosis of BCoV-caused diseases, as well as to further insights on protocols for the detection of other Coronavirus representatives of both Animal and Public Health importance.

Consolidation of elastic-plastic saturated porous media by the boundary element method

This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic-plastic behavior for the solid. Biot`s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton-Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme. The developments are illustrated through the Drucker-Prager elastic-plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms. (c) 2008 Elsevier B.V. All rights reserved.

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

The applicability of a meshfree approximation method, namely the EFG method, on fully geometrically exact analysis of plates is investigated. Based on a unified nonlinear theory of plates, which allows for arbitrarily large rotations and displacements, a Galerkin approximation via MLS functions is settled. A hybrid method of analysis is proposed, where the solution is obtained by the independent approximation of the generalized internal displacement fields and the generalized boundary tractions. A consistent linearization procedure is performed, resulting in a semi-definite generalized tangent stiffness matrix which, for hyperelastic materials and conservative loadings, is always symmetric (even for configurations far from the generalized equilibrium trajectory). Besides the total Lagrangian formulation, an updated version is also presented, which enables the treatment of rotations beyond the parameterization limit. An extension of the arc-length method that includes the generalized domain displacement fields, the generalized boundary tractions and the load parameter in the constraint equation of the hyper-ellipsis is proposed to solve the resulting nonlinear problem. Extending the hybrid-displacement formulation, a multi-region decomposition is proposed to handle complex geometries. A criterium for the classification of the equilibrium`s stability, based on the Bordered-Hessian matrix analysis, is suggested. Several numerical examples are presented, illustrating the effectiveness of the method. Differently from the standard finite element methods (FEM), the resulting solutions are (arbitrary) smooth generalized displacement and stress fields. (c) 2007 Elsevier Ltd. All rights reserved.

Investigation of a method for predicting AUV derivatives

The paper addresses the problem of autonomous underwater vehicle (AUV) modelling and parameter estimation as a means to predict the dynamic performance of underwater vehicles and thus provide solid guidelines during their design phase. The use of analytical and semi-empirical (ASE) methods to estimate the hydrodynamic derivatives of a popular class of AUVs is discussed. A comparison is done with the results obtained by using computational fluid dynamics to evaluate the bare hull lift force distribution around a fully submerged body. An application is made to the estimation of the hydrodynamic derivatives of the MAYA AUV, an autonomous underwater vehicle developed under a joint Indian-Portuguese project. The estimates obtained were used to predict the turning diameter of the vehicle during sea trials. (C) 2008 Elsevier Ltd. All rights reserved.

Distributed Estimation Over an Adaptive Incremental Network Based on the Affine Projection Algorithm

We study the problem of distributed estimation based on the affine projection algorithm (APA), which is developed from Newton`s method for minimizing a cost function. The proposed solution is formulated to ameliorate the limited convergence properties of least-mean-square (LMS) type distributed adaptive filters with colored inputs. The analysis of transient and steady-state performances at each individual node within the network is developed by using a weighted spatial-temporal energy conservation relation and confirmed by computer simulations. The simulation results also verify that the proposed algorithm provides not only a faster convergence rate but also an improved steady-state performance as compared to an LMS-based scheme. In addition, the new approach attains an acceptable misadjustment performance with lower computational and memory cost, provided the number of regressor vectors and filter length parameters are appropriately chosen, as compared to a distributed recursive-least-squares (RLS) based method.

Ultra-thin films of alternating semi-interpenetrating layers of a conducting polymer with thermosetting phenolic resins for sensor application

In this work a new method for crosslinking ultra-thin films with potential applications in sensor systems is proposed. The films were produced by layer-by-layer (LbL) assembly using a conducting polymer, poly(o-ethoxyaniline) (POEA), alternated with a thermosetting resin, novolac-type phenolformaldehyde (PF), crosslinked by a simple thermal treatment. The PF resin served as both alternating and crosslinking agents. The films were characterized by Fourier transform infrared (FTIR) and ultraviolet-visible (UV-Vis) spectroscopy, thermogravimetry (TG), desorption, doping/dedoping cycling and electrical measurements. The results showed that film architecture and crosslinking degree can be controlled by the conditions used for film deposition (number of bilayers, polymer concentration, pH, and deposition time), and crosslinking time. Moreover, this approach offers several advantages such as fast curing time and low cost, indicating that these films can be used to produce sensors with improved stability.