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The paper aims at constructing two different solutions to an elliptic system u ⋅ ∇ u + ( − Δ ) m u = λ F defined on the two dimensional torus. It can be viewed as an elliptic regularization of the stationary Burgers 2D system. A motivation to consider the above system comes from an examination of unusual properties of the linear operator λ sin ⁡ y ∂ x w + ( − Δ ) m w arising from a linearization of the equation about the dominant part of F . We argue that the skew-symmetric part of the operator provides in some sense a smallness of norms of the linear operator inverse. Our analytical proof is valid for a particular force F and for λ > λ 0 , m > m 0 sufficiently large. The main steps of the proof concern finite dimension approximation of the system and concentrate on analysis of features of large matrices, which resembles standard numerical analysis. Our analytical results are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analytical study of initial–boundary value problems for a system of hyperbolic balance laws derived from a repulsive chemotaxis model with logarithmic sensitivity. In the first part of the paper we show that, subject to the Dirichlet boundary conditions, classical solutions exist globally in time for large initial data. Asymptotically in time, the solutions are shown to converge to their boundary data at an exponential rate as time goes to infinity. Numerical simulations are supplied to corroborate the analytical results. The analytic approach developed herein can be utilized to handle a family of initial and initial–boundary value problems of the model and related models with similar mathematical structure. As a demonstration of the effectiveness of our approach, in the second part of the paper we show that, subject to the Neumann–Dirichlet boundary conditions, classical solutions exist and converge to constant equilibrium states for large initial data and for arbitrary values of the chemical diffusion coefficient. This improves a previous result obtained in [30] where the smallness of the chemical diffusion coefficient was required. [ABSTRACT FROM AUTHOR]

In this paper we introduce a numerical scheme which preserves the behavior of solutions to the Kolmogorov Equation as time tends to infinity. The method presented is based on a self-similar change of variables technique to transform the Kolmogorov Equation into a new form, such that the problem of designing structure preserving schemes, for the original equation, amounts to building a standard scheme for the transformed equation. This transformation also has the added benefit of allowing for an exact operator splitting scheme, whereas in the original form a standard operator splitting was only second-order. Finally, we verify the preservation of long time behavior through numerical simulations. [ABSTRACT FROM AUTHOR]

An imprecise probability approach based on evidence theory is proposed for squeal instability analysis of uncertain disc brakes in this paper. First, the squeal instability of the finite element (FE) model of a disc brake is investigated and its dominant unstable eigenvalue is detected by running two typical numerical simulations, i.e., complex eigenvalue analysis (CEA) and transient dynamical analysis. Next, the uncertainty mainly caused by contact and friction is taken into account and some key parameters of the brake are described as uncertain parameters. All these uncertain parameters are usually involved with imprecise data such as incomplete information and conflict information. Finally, a squeal instability analysis model considering imprecise uncertainty is established by integrating evidence theory, Taylor expansion, subinterval analysis and surrogate model. In the proposed analysis model, the uncertain parameters with imprecise data are treated as evidence variables, and the belief measure and plausibility measure are employed to evaluate system squeal instability. The effectiveness of the proposed approach is demonstrated by numerical examples and some interesting observations and conclusions are summarized from the analyses and discussions. The proposed approach is generally limited to the squeal problems without too many investigated parameters. It can be considered as a potential method for squeal instability analysis, which will act as the first step to reduce squeal noise of uncertain brakes with imprecise information. [ABSTRACT FROM AUTHOR]

In this paper, a new advance in the application of Artificial Neural Networks (ANNs) to the automated diagnosis of misfires in Internal Combustion engines(IC engines) is detailed. The automated diagnostic system comprises three stages: fault detection, fault localization and fault severity identification. Particularly, in the severity identification stage, separate Multi-Layer Perceptron networks (MLPs) with saturating linear transfer functions were designed for individual speed conditions, so they could achieve finer classification. In order to obtain sufficient data for the network training, numerical simulation was used to simulate different ranges of misfires in the engine. The simulation models need to be updated and evaluated using experimental data, so a series of experiments were first carried out on the engine test rig to capture the vibration signals for both normal condition and with a range of misfires. Two methods were used for the misfire diagnosis: one is based on the torsional vibration signals of the crankshaft and the other on the angular acceleration signals (rotational motion) of the engine block. Following the signal processing of the experimental and simulation signals, the best features were selected as the inputs to ANN networks. The ANN systems were trained using only the simulated data and tested using real experimental cases, indicating that the simulation model can be used for a wider range of faults for which it can still be considered valid. The final results have shown that the diagnostic system based on simulation can efficiently diagnose misfire, including location and severity. [ABSTRACT FROM AUTHOR]

This paper is focused on the numerical simulation of the interaction of an ultrasound wave with a bubble. Our interest is to develop a fully compressible solver in the two phases and to account for surface tension effects. As the volume oscillation of the bubble occurs in a low Mach number regime, a specific care must be paid to the effectiveness of the numerical method which is chosen to solve the compressible Euler equations. Three different numerical solvers, an explicit HLLC (Harten–Lax–van Leer-Contact) solver [48] , a preconditioning explicit HLLC solver [14] and the compressible projection method [21,53,55] , are described and assessed with a one dimensional spherical benchmark. From this preliminary test, we can conclude that the compressible projection method outclasses the other two, whether the spatial accuracy or the time step stability are considered. Multidimensional numerical simulations are next performed. As a basic implementation of the surface tension leads to strong spurious currents and numerical instabilities, a specific velocity/pressure time splitting is proposed to overcome this issue. Numerical evidences of the efficiency of this new numerical scheme are provided, since both the accuracy and the stability of the overall algorithm are enhanced if this new time splitting is used. Finally, the numerical simulation of the interaction of a moving and deformable bubble with a plane wave is presented in order to bring out the ability of the new method in a more complex situation. [ABSTRACT FROM AUTHOR]

This study uses the Rayleigh–Ritz method to derive a dynamic model for the free vibration analysis of a circular cylindrical shell. In particular, explicit expressions for the mass and stiffness matrices are obtained to easily implement a computer simulation under different shell theories and boundary conditions. The dynamic model is constructed according to the Donnell–Mushtari theory, which is fully discussed herein, and then, dynamic models are constructed by using Sanders theory, Love–Timoshenko theory, Reissner theory, Flügge theory, and Vlasov theory. This paper also discusses the use of eigenfunctions of a uniform beam as admissible functions that produce compact expressions for the mass and stiffness matrices. The numerical results indicate that the Donnell–Mushtari theory is not sufficiently accurate to calculate the natural frequencies and that there is no discernible difference between the other shell theories considered in this study. [ABSTRACT FROM AUTHOR]

Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM). [ABSTRACT FROM AUTHOR]

This paper deals with the comparison of Eulerian methods to take into account the capillary contribution in the vicinity of a fluid–fluid interface. Eulerian methods are well-known to produce additional vorticity close to the interface that leads to non-physical spurious currents. Numerical equilibrium between pressure gradient and capillary force for the static bubble test case within a VOF framework has been reached in [35] with the height-function technique [14,35] . However, once the bubble is translated in a uniform flow, spurious currents are maintained by slight errors induced by translation schemes. In this work, two main points are investigated: the ability of Volume of Fluid and Level Set methods to accurately calculate the curvature, and the magnitude of spurious currents due to errors in the calculation of the curvature after advection in both translating and rotating flows. The spurious currents source term is expressed from the vorticity equation and used to discuss and compare the methods. Simulations of gas–liquid Taylor flow at low capillary number show that the flow structure and the bubble velocity can be significantly affected by spurious currents. [ABSTRACT FROM AUTHOR]

The paper investigates elastic waves guided by thick-walled, hollow cylindrical structures. Theoretical, numerical and experimental investigations are presented to facilitate understanding of various wave propagation phenomena in thick-walled cylinders for potential damage detection applications. Semi-analytical analysis of dispersion characteristics is performed, revealing a repetitive pattern of coupled pairs of higher-order longitudinal modes. This behaviour is found to be analogue to terrace-like structures formed by interlacing high-frequency symmetric and antisymmetric plate mode curves. A hyperbolic behaviour of curves and modeshape transitions is observed due to mode coupling. The work presented demonstrates analytically how solutions for a thick-walled hollow cylinder correspond to the Lamb wave theory. The relevant pseudo-symmetry relations for mode displacement patterns are obtained using asymptotic approximations of Bessel functions. Theoretical solutions of dispersion characteristics are compared with numerical simulations that are based on the local interaction simulation approach. The results are validated experimentally using laser vibrometry. [ABSTRACT FROM AUTHOR]

Mechanical structures often consist of active and passive parts, the former containing the sources, the latter the transfer paths and the targets. The active and passive parts are connected to each other by means of links. In this paper, an innovative theoretical model has been developed to achieve the mathematical decoupling of such structures without disassembling the substructures, when the links connecting the structures are resilient enough. This procedure is required to identify components causing a specific Noise, Vibration and Harsh-ness (NVH) problem. The links are regarded as a parallel connection of springs and dampers, ignoring some physical properties. However, the new procedure will provide a powerful construction in which different link models can be investigated. Therefore, this procedure will be called the Link-Preserving, Decoupling Method (LPD method). The absence of a time-consuming physical decoupling procedure distinguishes the LPD method from all known methods such as the classical TPA method. The LPD method is validated by two numerical simulations using linear and nonlinear lumped parameter models and by an experimental case study. [ABSTRACT FROM AUTHOR]

This paper discusses an inverse source problem for time-dependent linear Maxwell's equations. We propose a numerical procedure to compute a current density source that gives a specified electromagnetic field. The efficiency of our method is shown by numerical tests, first in 1D and then we move on to a 3D example with antennas. In that case, we show potential applications for fault detection. [ABSTRACT FROM AUTHOR]

The paper focuses on a theoretical description and numerical evaluation of active and reactive components of sound intensity in enclosed spaces. As the study was dedicated to low-frequency room responses, a modal expansion of the sound pressure was used. Numerical simulations have shown that the presence of energy vortices whose size and distribution depend on the character of the room response is a distinctive feature of the active intensity field. When several modes with frequencies close to a source frequency are excited, the vortices within the room are positioned irregularly. However, if the response is determined by one or two dominant modes, a regular distribution of vortices in the room can be observed. The irrotational component of the active intensity was found using the Helmholtz decomposition theorem. As was evidenced by numerical simulations, the suppression of the vortical flow of sound energy in the nearfield permits obtaining a clear image of the sound source. [ABSTRACT FROM AUTHOR]

A numerical scheme is developed for two- and three-dimensional time-dependent diffusion equations in numerical simulations involving mixed cells. The focus of the development is on the formulations for both transient and steady states, the property for large time steps, second-order accuracy in both space and time, the correct treatment of the discontinuity in material properties, and the handling of mixed cells. For a mixed cell, interfaces between materials are reconstructed within the cell so that each of resulting sub-cells contains only one material and the material properties of each sub-cell are known. Diffusion equations are solved on the resulting polyhedral mesh even if the original mesh is structured. The discontinuity of material properties between different materials is correctly treated based on governing physics principles. The treatment is exact for arbitrarily strong discontinuity. The formulae for effective diffusion coefficients across interfaces between materials are derived for general polyhedral meshes. The scheme is general in two and three dimensions. Since the scheme to be developed in this paper is intended for multi-physics code with adaptive mesh refinement (AMR), we present the scheme on mesh generated from AMR. The correctness and features of the scheme are demonstrated for transient problems and steady states in one-, two-, and three-dimensional simulations for heat conduction and radiation heat transfer. The test problems involve dramatically different materials. [ABSTRACT FROM AUTHOR]

• The piezo-metastructure is shunted with a one-way electrical transmission line. • Local-resonance bandgaps are maintained in opposite directions. • Nonreciprocal wave attenuation behaviors exist in the bandgap. • The presented nonreciprocal system is linear, adaptive and easily implemented. • Theoretical and experimental results verify nonreciprocity of the system. In contrary to elastic media, it is easy to attain one-way coupling feature among electrical elements, which enables unidirectional transmission of electrical wave. In this paper, we explore and exploit the interaction of a piezoelectric beam with a one-way electrical transmission line to facilitate nonreciprocal transmission of elastic wave in the linear fashion. Theoretical dispersion analysis and numerical simulations are performed to reveal transmission behaviors of elastic wave in the presented piezoelectric metastructure. It is uncovered that, when the one-way electrical coupling feature is introduced, local-resonance bandgaps are maintained in opposite directions of the piezoelectric metastructure. However, the bandgap attenuation capability in one direction is increased compared to conventional local-resonance metastructures, in which no electrical coupling exists between cells, while that in the other direction is decreased. Therefore, nonreciprocal transmission of elastic wave emerges in this system due to the distinct bandgap attenuation capability in opposite directions. It is also revealed that this sort of nonreciprocal wave attenuation capability is adaptive with the one-way electrical coupling coefficient and the resistance of electrical cells. An experimental set-up of the piezoelectric metastructure is built and experimental results verify the nonreciprocity property and its adaptiveness. Overall, the presented piezoelectric metastructure provides a linear and concise approach to realize adaptive nonreciprocal transmission of elastic wave. [ABSTRACT FROM AUTHOR]