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.     

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.     

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 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,     

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.     

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.     

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.

     

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.     

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.     

The ALE/Lagrangian Particle Finite Element Method: A new approach to computation of free-surface flows and fluid-object interactions

The Particle Finite Element Method (PFEM) is a well established numerical method [Aubry R, Idelsohn SR, Oñate E, Particle finite element method in fluid mechanics including thermal convection-diffusion, Comput Struct 2004;83:1459-75; Idelsohn S, Oñate E, Del Pin F, A Lagrangian meshless finite element method applied to fluid-structure interaction problems, Comput Struct 2003;81:655-71; Idelsohn SR, Oñate E, Del Pin F, The particle finite element method a powerful tool to solve incompressible flows with free-surfaces and breaking waves, Int J Num Methods Eng 2004;61:964-84] where critical parts of the continuum are discretized into particles. The nodes treated as particles transport their momentum and physical properties in a Lagrangian way while the rest of the nodes may move in an Arbitrary Lagrangian-Eulerian (ALE) frame. In order to solve the governing equations that represent the continuum, the particles are connected by means of a Delaunay Triangulation [Idelsohn SR, Oñate E, Calvo N, Del Pin F, The meshless finite element method, Int J Num Methods Eng 2003;58(4)]. The resulting partition is a mesh where the Finite Element Method is applied to solve the equations of motion. The application of a fully Lagrangian formulation on the particles provides a natural and simple way to track free surfaces as well as to compute contacts in an accurate and robust fashion. Furthermore, the usage of an ALE formulation allows large mesh deformation with larger time steps than the full Lagrangian scheme.     

An extension of MacCormack's method for flows with higher-order equations and in different configurations

The numerical scheme for the computation of a shock discontinuity developed by MacCormack has been extended to solve a number of differential equations, including cases explicitly containing higher-order derivatives: (1) Korteweg-de Vries equation with a term of third-order derivative, (2) a system of nonlinear equations governing nonsteady one-dimensional plasma flow in cylindrical coordinate, (3) equations of solar wind. Comparisons with previous results are made, if available, to illustrate the advantages of the present method. The question of convergence of the numerical calculation is discussed.     

Multi-basin particle swarm intelligence method for optimal calibration of parametric Lévy models

In this paper, we propose a novel intelligent method to improve the calibration quality of parametric exponential Lévy models that have recently emerged as alternative option pricing models. The method based on so-called multi-basin systems consists of three sequential phases to expedite the search for a good parameter set and to reduce the burden of selecting proper initial set of particles for particle swarm intelligence techniques. We conduct simulations on model-generated option prices and real data of option prices to verify the performance of the proposed method and show that the method can significantly improve the calibration quality in a systematic and automatic way.     

Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows

We present a review of the semi-Lagrangian method for advection-diffusion and incompressible Navier-Stokes equations discretized with high-order methods. In particular, we compare the strong form where the departure points are computed directly via backwards integration with the auxiliary form where an auxiliary advection equation is solved instead; the latter is also referred to as Operator Integration Factor Splitting (OIFS) scheme. For intermediate size of time steps the auxiliary form is preferrable but for large time steps only the strong form is stable.     

Construction of modified embedded atom method potentials for the study of the bulk phase behaviour in binary Pt–Rh, Pt–Pd, Pd–Rh and ternary Pt–Pd–Rh alloys

A first attempt is made to simulate the solid part of the phase diagram of the ternary Pt–Pd–Rh system. To this end, Monte Carlo (MC) simulations are combined with the Modified Embedded Atom Method (MEAM) and optimised parameters entirely based on Density Functional Theory (DFT) data. This MEAM potential is first validated by calculating the heat of mixing or the demixing phase boundary for the binary subsystems Pt–Rh, Pt–Pd and Pd–Rh. For the disordered alloy systems Pt–Rh and Pt–Pd, the MC/MEAM simulation results show a slightly exothermic heat of mixing, thereby contradicting any demixing behaviour, in agreement with other theoretical results. For the Pd–Rh system the experimentally observed demixing region is very well reproduced by the MC/MEAM simulations. The extrapolation of the MEAM potentials to ternary systems is next validated by comparing DFT calculations for the energy of formation of ordered Pt–Pd–Rh compounds with the corresponding MEAM energies. Finally, the validated potential is used for the calculation of the ternary phase diagram at 600 K.