Computational Methods for Parachute Fluid–Structure Interactions

The computational challenges posed by fluid–structure interaction (FSI) modeling of parachutes include the lightness of the parachute canopy compared to the air masses involved in the parachute dynamics, in the case of “ringsail” parachutes the geometric complexities created by the construction of the canopy from “rings” and “sails” with hundreds of ring “gaps” and sail “slits”, and in the case of parachute clusters the contact between the parachutes. The Team for Advanced Flow Simulation and Modeling () has successfully addressed these computational challenges with the Stabilized Space–Time FSI (SSTFSI) technique, which was developed and improved over the years by the and serves as the core numerical technology, and a number of special techniques developed in conjunction with the SSTFSI technique. The quasi-direct and direct coupling techniques developed by the , which are applicable to cases with incompatible fluid and structure meshes at the interface, yield more robust algorithms for FSI computations where the structure is light and therefore more sensitive to the variations in the fluid dynamics forces. The special technique used in dealing with the geometric complexities of the rings and sails is the Homogenized Modeling of Geometric Porosity, which was developed and improved in recent years by the . The Surface-Edge-Node Contact Tracking (SENCT) technique was introduced by the as a contact algorithm where the objective is to prevent the structural surfaces from coming closer than a minimum distance in an FSI computation. The recently-introduced conservative version of the SENCT technique is more robust and is now an essential technology in the parachute cluster computations carried out by the . We provide an overview of the core and special techniques developed by the , present single-parachute FSI computations carried out for design-parameter studies, and report FSI computation and dynamical analysis of two-parachute clusters.     

On the mass and momentum transport in the Navier–Stokes slip layer

The Navier–Stokes slip boundary conditions are considered as conditions following from the mass and momentum balances within a thin, shell-like moving boundary layer. A problem of consistency between different models, that describes the internal and external friction in a viscous fluid, is stated within the framework of a proper form of the layer momentum balance. Appropriate constitutive equations for friction forces are formulated. The common features of the Navier, Stokes, Reynolds, and Maxwell concepts of a boundary slip layer are revalorized and discussed. Different mobility mechanisms connected with the transpiration phenomena, important for flows in micro- and nanochannels, are classified as a part of equations for the external friction.     

On the importance of carrier fluid viscosity and particle–wall interactions in magnetic-guided assembly of quasi-2D systems

We demonstrate the influence of experimental conditions (carrier fluid viscosity and particle–wall interactions—friction) on the quasi-2D deterministic aggregation kinetics of carbonyl iron magnetic suspensions in rectangular microchannels. On the one hand, the carrier fluid viscosity determines the time scale for aggregation. On the other hand, friction strongly determines the aggregation rate and therefore the kinetic exponent (mean cluster size vs. time dependence). When particle–wall interactions are weak, the mean cluster size increases with a power of 0.65 ± 0.06, for open cavities (≥500 microns channel width), in very good agreement with theories and particle-level simulations. However, when the particle–wall interactions are strong, the kinetic exponent decreases and the aggregation is eventually arrested. This work suggests that particle–wall interactions may be one of the reasons for the discrepancies found in the experimental determination of the aggregation kinetic exponents in the literature.     

On the formulation and implementation of geometric and manufacturing constraints in node–based shape optimization

We introduce a novel method to handle geometrical and manufacturing constraints in parameter–free shape optimization. Therefore the design node coordinates are split in two sets where one set is declared as new design variables and the other set is coupled to the new design variables such that the geometrical constraint is fulfilled. Thereby no additional equations are appended to the optimization problem. In contrast the implementation of a demolding constraint is presented by formulating inequality constraints which indeed have to be attached to the optimization problem. In the context of a sensitivity–based shape optimization approach all manufacturing constraints have to be formulated in terms of the finite element node coordinates such that first order gradients with respect to the design node coordinates can be derived.     

A Computational Fluid Dynamics （CFD） Analysis of an Undulatory Mechanical Fin Driven by Shape Memory Alloy

Many fishes use undulatory fin to propel themselves in the underwater environment. These locomotor mechanisms have a popular interest to many researchers. In the present study, we perform a three-dimensional unsteady computation of an undulatory mechanical fin that is driven by Shape Memory Alloy (SMA). The objective of the computation is to investigate the fluid dynamics of force production associated with the undulatory mechanical fin. An unstructured, grid-based, unsteady Navier-Stokes solver with automatic adaptive remeshing is used to compute the unsteady flow around the fin through five complete cycles. The pressure distribution on fin surface is computed and integrated to provide fin forces which are decomposed into lift and thrust. The velocity field is also computed throughout the swimming cycle. Finally,a comparison is conducted to reveal the dynamics of force generation according to the kinematic parameters of the undulatory fin (amplitude, frequency and wavelength).     

Sudden bed changes and wave–current interactions in coastal regions

Mean bottom evolutions due to currents and wind waves, even due to wave–current interactions, are easily computed by averaging mean quantities over one or more wave cycles. However, dealing with fine processes, like breaking waves and bar formations in coastal regions, great quantities of sediment are transported and, as a consequence, considerable erosion and deposition can occur quite rapidly. Other phenomena normally associated with earthquakes, like volcanic eruptions, landslides, etc. occur frequently in various coastal regions of the terrestrial globe. Those problems can only be tackled by using a more complete set of equations with improved wave dispersion characteristics, and taking into account time–bed-level changes. Other characteristic non-linearity phenomena in shallow water regions and wave–current interaction become important factors that have to be considered. From the sedimentary point of view, particularly in terms of the wave and current fields, it is not known whether the existing sand transport models are generally valid.The applicability of a computational structure, based on extended Boussinesq-type equations, and two existing sediment transport models are discussed and confirmed through published data. Numerical results obtained at Ria Formosa, Algarve, in the ambit of the European Union INDIA Project are shown.     

Modelling uncertainty in social–natural interactions

Socio-ecological systems can be represented as a complex network of causal interactions. Modelling such systems requires methodologies that are able to take uncertainty into account. Due to their probabilistic nature, Bayesian networks are a powerful tool for representing complex systems where interactions between variables are subject to uncertainty. In this paper, we study the interactions between social and natural subsystems (land use and water flow components) using hybrid Bayesian networks based on the Mixture of Truncated Exponentials model. This study aims to provide a new methodology to model systemic change in a socio-ecological context. Two endogenous changes – agricultural intensification and the maintenance of traditional cropland – are proposed. Intensification of the agricultural practices leads to a rise in the rate of immigration to the area, as well as to greater water losses through evaporation. By contrast, maintenance of traditional cropland hardly changes the social structure, while increasing evapotranspiration rates and improving the control over runoff water. These results indicate that hybrid Bayesian networks are an excellent tool for modelling social–natural interactions.     

Numerical Methods and Simulations for the Dynamics of One-Dimensional Zakharov–Rubenchik Equations

In this paper, we propose and study several accurate numerical methods for solving the one-dimensional Zakharov–Rubenchik equations (ZRE). We begin with a review on the important properties of the ZRE, including the solitary wave solutions and the various conservation laws. Then we propose a very efficient and accurate numerical method based on the time-splitting technique and the Fourier pseudo-spectral (TSFP) method. Next, we propose some conservative and non-conservative types of finite difference time domain methods, including a Crank–Nicolson finite difference method that conserves the mass and the energy of the system in the discrete level. Discrete conservation laws and numerical stability of all the proposed methods are analyzed. Comparisons between different methods in the efficiency, stability and accuracy are carried out, which identifies that the TSFP method is the most efficient and accurate numerical method among all the methods. Lastly, we apply the TSFP method to simulate and study the dynamics of the solitons in the ZRE numerically.     

Explanatory Factors and Causality in the Dynamics of Volatility Surfaces Implied from OTC Asian–Pacific Currency Options

Volatility implied from observed option contracts systematically varies with the contracts’ strike price and time to expiration, giving rise to an instantaneously non-flat implied volatility surface (IVS) that exhibits substantial time variation. We identify a number of latent factors that drive the dynamics of the IVSs from options on 11 Asian–Pacific exchange rates and show that these have a natural interpretation in the law of motion of each surface. We present evidence that these latent factors are related due to their common dependence on exogenous economy-wide variables. Findings suggest that the factors capturing (i) the volatility level of the Japanese yen and the Chinese yuan, (ii) the volatility term structure of the Japanese yen, Taiwanese and Australian dollars and (iii) the risk aversion towards the Australian dollar, Japanese yen and Chinese yuan seem to incorporate first the investors’ expectations regarding the volatility in the region.     

On the formation of intermetallics in rapidly solidifying Al–Fe–Si alloys

It is known from previous experimental observations that a rapid solidification of Al–Fe and Al–Fe–Si alloys results in the formation of various metastable phases. Despite attempts to explain why particular intermetallics form and to accurately predict a sequence of their precipitation, a fully satisfactory and prognostic explanation remains to be found. In this communication, it is conjectured that after the concept of the driving forces for the onset of precipitation is adapted to take into account important differences between the Al-rich FCC solution and all other solid phases, it can be used to identify intermetallics whose formation is thermodynamically permissible for a given supercooling. If the composition of some of the “possible phases” is close to the composition of the remaining liquid, then the precipitation of these particular phases is facilitated, because corresponding nucleation events do not require a long-range diffusion, which might be slow in supercooled melts.     

On the cost–effectiveness of PRAMs

We introduce a formalism which allows to treat computer architecture as a formal optimization problem. We apply this to the design of shared memory parallel machines. While present parallel computers of this type only support the programming model of a shared memory but often process simultaneous access by several processors to the shared memory sequentially, theoretical computer science offers solutions for this problem that are provably fast and asymptotically optimal. But the constants in these constructions seemed to be too large to let them be competitive. We modify these constructions under engineering aspects and improve the price/performance ratio by roughly a factor of 6. The resulting machine has surprisingly good price/performance ratio even if compared with distributed memory machines. For almost all access patterns of all processors into the shared memory, access is as fast as the access of only a single processor. Received: 29 June 1993 / 22 June 1999     

Accounting for surface–groundwater interactions and their uncertainty in river and groundwater models: A case study in the Namoi River,Australia

Surface–groundwater (SW–GW) interactions constitute a critical proportion of the surface and groundwater balance especially during dry conditions. Conjunctive management of surface and groundwater requires an explicit account of the exchange flux between surface and groundwater when modelling the two systems. This paper presents a case study in the predominantly gaining Boggabri–Narrabri reach of the Namoi River located in eastern Australia. The first component of the study uses the Upper Namoi numerical groundwater model to demonstrate the importance of incorporating SW–GW interactions into river management models. The second component demonstrates the advantages of incorporating groundwater processes in the Namoi River model.Results of the numerical groundwater modelling component highlighted the contrasting groundwater dynamics close to, and away from the Namoi River where lower declines were noted in a near-field well due to water replenishment sourced from river depletion. The contribution of pumping activities to river depletion was highlighted in the results of the uncertainty analysis, which showed that the SW–GW exchange flux is the most sensitive to pumping rate during dry conditions. The uncertainty analysis also showed that after a drought period, the 95% prediction interval becomes larger than the simulated flux, which implies an increasing probability of losing river conditions. The future prospect of a gaining Boggabri–Narrabri reach turning into losing was confirmed with a hypothetical extended drought scenario during which persistent expansion of groundwater pumping was assumed. The river modelling component showed that accounting for SW–GW interactions improved the predictions of low flows, and resulted in a more realistic calibration of the Namoi River model.Incorporating SW–GW interactions into river models allows explicit representation of groundwater processes that provides a mechanism to account for the impacts of additional aquifer stresses that may be introduced beyond the calibration period of the river model. Conventional river models that neglect the effects of such future stresses suffer from the phenomenon of non-stationarity and hence have inferior low flow predictions past the calibration period of the river model. The collective knowledge acquired from the two modelling exercises conducted in this study leads to a better understanding of SW–GW interactions in the Namoi River thus leading to improved water management especially during low flow conditions.     

Dynamics of quantum correlation for a qubit–qutrit system in the presence of the dephasing environments

We analytically study the dynamic behaviors of quantum correlation measured by three kinds of measures including quantum discord (QD), geometric quantum discord (GQD) and one-norm GQD for a qubit–qutrit system under the influence of dephasing environments with Ohmic-like spectral densities at nonzero temperature. It is shown that the similar evolution behaviors may be obtained for sub-Ohmic and Ohmic reservoirs. By properly choosing the system’s initial states and reservoir temperature, quantum correlation can take on some interesting results, such as the frozen and double sudden transition as well as the “revival” phenomenon, etc. Meanwhile, the remarkable similarities and differences among these correlation measures are also analyzed in detail and some significant results are presented. Our results provide some important information for the application of quantum correlation in hybrid qubit–qutrit systems in quantum information.     

Applicability of the three-parameter Kozeny–Carman generalized equation to the description of viscous fingering in simulations of waterflood in heterogeneous porous media

This article discusses the applicability of the three-parameter Kozeny–Carman generalized equation to trigger immiscible viscous fingers and describe it in fractal heterogeneous porous media, during numerical simulations of waterflood operations in oil reservoirs. For that purpose, for the first time this equation was incorporated into a model that describes immiscible flows of incompressible two-phase fluids in porous media. Results were generated from intensive simulations, and viscous fingers were visualized graphically for three different well patterns, typical of oil fields: Line-Drive, Five-Spot and Inverted Five-Spot. Such results suggest that this generalization of the Kozeny–Carman equation can be used in numerical simulations of oil recovery processes susceptible to hydrodynamic instability phenomena.     

On Unitary and Forward–Backward MODE

A new unitary (real-valued) formulation of the popular MODE direction-of-arrival (DOA) estimator is considered. Our unitary MODE algorithm has a reduced computational complexity because it is based on the eigendecomposition of a real-valued covariance matrix. We prove its exact equivalence to the forward-backward MODE (FB-MODE) estimator derived by Stoica and Jansson. This property sheds a new light on the usefulness of FB-MODE.     

On leaders’ presence: interactions and influences within online communities

By conceptualising presence as a behavioural construct, this study explores how online leaders’ presence exerts an influence on online communities and their members. Drawing on qualitative research where five online communities were examined, the findings show that online leaders’ presence is identified in different forms which ultimately may have different impacts on the community and its members. Articulations of leaders’ presence online included interactive, instructive, stimulating and silent and for each the leader was found to exert a different influence on online community members. The theoretical and practical implications of the study are discussed and areas for further research are identified.     

On reference solutions and the sensitivity of the 2D Kelvin–Helmholtz instability problem

Two-dimensional Kelvin–Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin–Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2D turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed.