Three-dimensional numerical simulations of viscoelastic flows – predictability and accuracy

In this paper, fully three-dimensional (3-D) numerical simulations of viscoelastic flows using an implicit finite volume method are discussed with the focus on the predictability and accuracy of the method. The viscoelastic flow problems involving the stress singularity, including plane stick–slip flow, the flow past a junction in a channel, and the 3-D edge flow, are used to test the ability of the method to predict the singularity features with accuracy. The accuracy of the numerical predictions is judged by comparing with the known asymptotic behaviour for Newtonian fluids and some viscoelastic fluids, and the investigations are extended to the viscoelastic cases with unknown singular behaviour. The Phan-Thien–Tanner (PTT) model, and in some cases, the upper-convected Maxwell (UCM) model, are used to describe viscoelastic fluids. The numerical results with mesh refinement show that the accuracy is quite satisfactory, especially for Newtonian flows. For viscoelastic flows, the asymptotic results for the flow around a re-entrant corner for the UCM as well as the PTT fluid are reproduced numerically. In the stick–slip flow, a Newtonian-like asymptotic behaviour is predicted for the UCM fluid. In edge flow, it is verified numerically that the kinematics are Newtonian for viscoelastic fluids described by models with a constant viscosity and a zero second normal stress difference. For viscoelastic fluids described by the models with a shear-thinning viscosity and zero second normal stress difference, the fluid behaves like a power-law fluid, and the difference from its Newtonian kinematics is localized in the region near the singularity, and to capture the asymptotic behaviour, a parameter-dependent mesh has to be used. With the 3-D simulations, it is confirmed that in edge flow, the flow around the edge could not be rectilinear, and some secondary flows on the plane normal to the primary flow direction are expected for viscoelastic fluids described by the models with a shear-dependent second normal stress difference, such as the full PTT model. The strength of the secondary flows will depend on the level of the departure of the second normal stress difference from a fixed constant multiple of viscosity of the fluid.     

The simpler GMRES method combined with finite volume method for simulating viscoelastic flows on triangular grid

An efficient solver integrating the restarted simpler generalized minimal residual method (SGMRES(m)) with finite volume method (FVM) on triangular grid is developed to simulate the viscoelastic fluid flows. In particular, the SGMRES(m) solver is used to solve the large-scale sparse linear systems, which arise from the course of FVM on triangular grid for modeling the Newtonian and the viscoelastic fluid flows. To examine the performance of the solver for the nonlinear flow equations of viscoelastic fluids, we consider two types of numerical tests: the Newtonian flow past a circular cylinder, and the Oldroyd-B fluid flow in a planar channel and past a circular cylinder. It is shown that the numerical results obtained by the SGMRES(m) are consistent with the analytical solutions or empirical values. By comparing CPU time of different solvers, we find our solver is a highly efficient one for solving the flow equations of viscoelastic fluids.     

A local adaptive Catmull–Rom to reduce numerical dissipation of semi‐Lagrangian advection

We propose an adaptive Catmull–Rom interpolation to improve accuracy of semi‐Lagrangian advection for smoke simulation. Original Catmull–Rom improves numerical accuracy but overshoot violates global stability. Monotonic Catmull–Rom is unconditionally stable, whereas it sweeps out detail features due to overly suppression operations. Our method modifies original Catmull–Rom to obtain second‐order accuracy and unconditional stability. It flattens locations where interpolations might break through global bounds but maintains local overshoots to conserve diversity of fluid flow. The scheme is easy to collaborate with existing fluid simulators to improve small features. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimal error estimates of the penalty method for the linearized viscoelastic flows

In this article, optimal error estimates of the penalty method for the linearized viscoelastic flows equations arising in the Oldroyd model are derived. Furthermore, error estimates for the backward Euler time discretization scheme in L ² and H ¹-norms are obtained.     

Stencil adaptive diffuse interface method for simulation of two-dimensional incompressible multiphase flows

Diffuse interface method is becoming a more and more popular approach for simulation of multiphase flows. As compared to other solvers, it is easy to implement and can keep conservation of mass and momentum. In the diffuse interface method, the interface is not considered as a sharp discontinuity. Instead, it treats the interface as a diffuse layer with a small thickness. This treatment is similar to the shock-capturing method. To have a fine resolution around the interface, one has to use very fine mesh in the computational domain. As a consequence, a large computational effort will be needed. To improve the computational efficiency, this paper incorporates the efficient 5-points stencil adaptive algorithm [1] into the diffuse interface method with local refinement around the interface and then applies the developed method to simulate two-dimensional incompressible multiphase flows. Three cases are chosen to test the performance of the method, including Young-Laplace law for a 2D drop, drop deformation in the shear flow and viscous finger formation. The method is well validated through the comparison with theoretical analysis or earlier results available in the literature. It is shown that the method can obtain accurate results at much lower cost, even for problems with moving contact lines. The improvement of computational efficiency by the stencil adaptive algorithm is demonstrated obviously.     

A FE/BE coupling for the 3D time-dependent eddy current problem. Part II: a posteriori error estimates and adaptive computations

The discontinuous Galerkin method in time for the coupling of conforming finite element and boundary element methods was established in Part I of this paper, where quasi-optimal a priori error estimates are provided. In the second part, we establish a posteriori error estimates and so justify an adaptive space/time-mesh refinement algorithm for the efficient numerical treatment of the time-dependent eddy current problem.     

The identification and adaptive prediction of urban sewer flows

The input raw material to a waste-water treatment plant exhibits large, and generally poorly quantified, variations with time. In particular, rainfall run-off can cause gross overloading of the treatment processes of the plant. For a proper operational control of the plant, and hence the quality of the receiving river's water, it would be extremely useful to have advance (short-term) estimates of the effluent flow from the sewer network, i.e. the influent to the plant. This paper studies the feasibility of using an on-line adaptive predictor in such a capacity. The procedure is divided into two steps : (i) the parameters of a multiple input/single output time-series model are recursively estimated at each time-step by the method of least squares ; (ii) a forecast of the plant influent flow is then made on the basis of the newly updated prediction model. Results are presented for data from a treatment plant in Stockholm, Sweden. These demonstrate the adaptability of the predictor to unknown changes in the process dynamics when no information is assumed to be available for rainfall events occurring over the urban land surface,     

An efficient and robust method for Lagrangian magnetic particle tracking in fluid flow simulations on unstructured grids

In this paper we report on a newly developed particle tracking scheme for fluid flow simulations on 3D unstructured grids, aiming to provide detailed insights in the particle behaviour in complex geometries. A possible field of applications is the magnetic drug targeting (MDT) technique, on which this paper will be focused. MDT is a promising medical technique that uses locally applied magnetic fields to capture magnetic drug carriers at the desired locations in the human body, strongly increasing the efficiency of medical drugs. The new particle tracking scheme combines the advantages of existing methods and is easy for implementation in a generic numerical code. The scheme is tested and validated for simple MDT cases that include effects of a non-homogeneous magnetic field on deposition of magnetic particles in laminar flow. The first test case is a validation study of the magnetic particle trajectories released in a horizontal circular pipe flow with a current-carrying wire parallel to the flow, for which analytical solutions are reported in literature. The second test case involves particle capture efficiencies in a 90° bent tube for different configurations of the imposed magnetic field. This configuration corresponds more closely to the conditions inside blood vessels, because of the presence of secondary motions. These results are compared with numerical studies from literature too. The obtained results demonstrate that the developed particle tracking scheme is a very robust, efficient and accurate method, which can give detailed insights in particle behaviour in complex geometries. As such it is a good candidate for future applications and optimisations of MDT technique for loco-regional cancer treatment or treatment of cardiovascular diseases.     

The constant‐Jacobian method for kinematics of a three‐DOF planar micro‐motion stage

This paper concerns the development of a class of devices that generate end‐effector motion in the range of less than 100 μm and with sub‐nanometer resolution; in particular, a parallel manipulator configuration that generates a planar x‐y‐γ motion is considered. The parallel manipulator is implemented as a compliant mechanism. A problem with parallel manipulators is that the forward kinematics is usually too complex, which can hinder the implementation of advanced control algorithms. The contribution of this paper is that a simple method, called the constant‐Jacobian (CJ) method, is developed based on the pseudo‐rigid body (PRB) approach to compliant mechanisms. The experiment validates the CJ method. © 2002 John Wiley & Sons, Inc.     

Set-theoretic solutions of the Yang–Baxter equation, graphs and computations

We extend our recent work on set-theoretic solutions of the Yang–Baxter or braid relations with new results about their automorphism groups, strong twisted unions of solutions and multipermutation solutions. We introduce and study graphs of solutions and use our graphical methods for the computation of solutions of finite order and their automorphisms. Results include a detailed study of solutions of multipermutation level 2.     

Development and sensitivity analysis of a Lagrangian particle model for long range dispersion

A new long range dispersion model of Lagrangian particle type (MILORD) has been recently developed at the “Istituto di Cosmogeofisica”. Its capabilities have been tested by comparing its predictions with the Cs-137 air concentrations recorded over Europe by many laboratories during the Chernobyl accident. MILORD sensitivity to variations in its parametrizations has been studied and, in order to ascertain the accuracy of the simulations, some widely used statistical indexes and graphs have been computed. The study has made possible the accomplishment of a set of model input parameters able to produce the best agreement between observations and predictions. It is shown that this model was able to reconstruct with a good accuracy the main characteristics of the radioactive cloud spread over Europe.     

The method of fundamental solutions for oscillatory and porous buoyant flows

Accurate solutions of oscillatory Stokes flows in convection and convective flows in porous media are studied using the method of fundamental solutions (MFS). In the solution procedure, the flows are represented by a series of fundamental solutions where the intensities of these sources are determined by the collocation on the boundary data. The fundamental solutions are derived by transforming the governing equation into the product of harmonic and Helmholtz-type operators, which can be classified into three types depending on the oscillatory frequencies of temperature field. All the velocities, the pressure, and the stresses corresponding to the fundamental solutions are expressed explicitly in tensor forms for all the three cases. Three numerical examples were carried out to validate the proposed fundamental solutions and numerical schemes. Then, the method was also applied to study exterior flows around a sphere. In these studies, we derived the MFS formulas of drag forces. Numerical results were compared accurately with the analytical solutions, indicating the ability of the MFS for obtaining accurate solutions for problems with smooth boundary data. This study can also be treated as a preliminary research for nonlinear convective thermal flows if the particular solutions of the operators can be supplied, which are currently under investigations.     

An immersed boundary method on Cartesian adaptive grids for the simulation of compressible flows around arbitrary geometries

In this article, we present an immersed boundary method for the simulation of compressible flows of complex geometries encountered in aerodynamics. The immersed boundary methods allow the mesh not to conform to obstacles, whose influence is taken into account by modifying the governing equations locally (either by a source term within the equation or by imposing the flow variables or fluxes locally, similarly to a boundary condition). A main feature of the approach which we propose is that it relies on structured Cartesian grids in combination with a dedicated HPC Cartesian solver, taking advantage of their low memory and CPU time requirements but also the automation of the mesh generation and adaptation. Turbulent flow simulations are performed by solving the Reynolds-averaged Navier–Stokes equations or by a Large-Eddy simulation approach, in combination with a wall function at high Reynolds number, to mitigate the cell count resulting from the isotropic nature of Cartesian cells. The objective of this paper is to demonstrate that this automatic workflow is fast and robust and enables to get quantitative aerodynamics results on geometrically complex configurations. Results obtained are in good agreement with classical body-fitted approaches but with a significant reduction of the time of the whole process, that is a day for RANS simulations, including the mesh generation.

     

Wafer‐scale monolithic hybrid integration of Si‐based IC and III–V epi‐layers—A mass manufacturable approach for active matrix micro‐LED micro‐displays

Hybridization of silicon integrated circuits (ICs) with compound semiconductor device arrays are crucial for making functional hybrid chips, which are found to have enormous applications in many areas. Although widely used in manufacturing hybrid chips, the flip‐chip technology suffers from several limitations that are difficult to overcome, especially when the demand is raised to make functional hybrid chips with higher device array density without sacrificing the chip footprint. To address those issues, Beida Jade Bird Display Limited has developed its unique wafer‐level monolithic hybrid integration technology and demonstrated its advantages in making large‐scale hybrid integration of functional device arrays on Si IC wafers. Active matrix micro‐light‐emitting diode micro‐displays with a resolution of 5000+ pixel per inch were successfully fabricated using Beida Jade Bird Display Limited's monolithic hybrid integration technology. The general fabrication method is described, and the result is presented in this paper. The fabricated monochromatic micro‐light‐emitting diode micro‐displays exhibit improved device performance than do other micro‐display technologies and have great potentials in applications such as portable projectors and near‐to‐eye projection for augmented reality. More importantly, the wafer‐scale monolithic hybrid integration technology offers a clear path for low‐cost mass production of hybrid optoelectronic IC chips.     

Sufficient stability conditions in the calculations of steady supersonic flows using the marching technique and time-dependent flows with account for viscosity

The sufficient conditions for the stability and monotonicity in calculating supersonic steady flows by means of the marching technique are derived. The sufficient stability conditions are also obtained for constructing the solutions of time-dependent conservation laws with account for viscosity by explicit difference schemes. With increase in the viscosity coefficient, the conditions derived go over continuously from the hyperbolic to the parabolic constraints on the time step.     

Design method considering human satisfaction: Development of adaptive human–machine interface based on satisfaction measures

We are part of a sociotechnical system consisting of individual persons, organizations, and technology. Therefore, a methodology of synthesizing and balancing technological, organizational, and human factors becomes necessary as a discipline. The authors have proposed a design method that takes human satisfaction into consideration, and to this end, have developed a satisfaction measurement system using a neural network that estimates human satisfaction from electroencephalogram measurements. This article discusses the design method and the satisfaction measurement system, and describes the development of a real-time adaptive human–machine interface based on satisfaction measures as an example of the design method proposed. © 1999 John Wiley & Sons, Inc.     

New non‐synthetic method to modify properties of liquid crystals using micro‐ and nano‐particles

Abstract— The modification of the properties of existing LCs by doping them with ferroelectric micro‐ and nano‐particles will be reported. This approach, in contrast to the conventional time‐consuming and expensive chemical synthetic methods, enriches and enhances the electro‐optical performance of many liquid‐crystal materials. The effect of the ferroelectric particles on the nematic, smectic, and cholesteric phases will be discussed. The performance of these new composite systems in various devices, including displays, light modulators, and beam‐steering devices, will be reported.     

Forward‐adaptive method for context‐based compression of large binary images

A method for compressing large binary images is proposed for applications where spatial access to the image is required. The proposed method is a two‐stage combination of forward‐adaptive modeling and backward‐adaptive context based compression with re‐initialization of statistics. The method improves compression performance significantly in comparison to a straightforward combination of JBIG and tiling. Only minor modifications to the QM‐coder are required, and therefore existing software implementations can be easily utilized. Technical details of the modifications are provided. Copyright © 1999 John Wiley & Sons, Ltd.     

Directed spanning tree–based adaptive protocols for second‐order consensus of multiagent systems

This paper discusses the consensus problem of second‐order multiagent systems with nonlinear dynamics. A directed spanning tree–based adaptive control protocol is developed, which overcomes the drawback that the spectrum of the Laplacian matrix must be known a priori. A scheme for reordering the nodes is proposed. Applying the developed method and the Lyapunov stability theory, some distributed adaptive laws are designed in the directed network. It is found that the consensus can be achieved by randomly choosing a directed spanning tree and using the developed distributed adaptive law. Finally, an example is presented to illustrate the theoretical analysis.     

A method of time–time analysis: The TT-transform

A novel technique of analysis of an arbitrary primary time series into a set of secondary, time-limited, local, constituent time series, the TT-transform, is presented. The time–time representation is derived from the S-transform, a method of representation of a real time series as a set of complex, time-localized spectra. When integrated over time, the S-transform becomes the Fourier transform of the primary time series. Similarly, when summed over the primary time variable, the TT-transform reverts to the primary time series. The invertibility of the TT-transform points to the possibility of filtering and signal to noise improvements in the time domain, and some insight into the localized spectra of the S-transform.