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We present a scalable two-dimensional Galerkin spectral element method solution to the linearized potential flow radiation problem for wave induced forcing of a floating offshore structure. The pseudo-impulsive formulation of the problem is solved in the time domain using a Gaussian displacement signal tailored to the discrete resolution. The added mass and damping coefficients are then obtained via Fourier transformation. The spectral element method is used to discretize the spatial fluid domain, whereas the classical explicit 4-stage fourth-order Runge–Kutta scheme is employed for the temporal integration. Spectral convergence of the proposed model is established for both affine and curvilinear elements, and the computational effort is shown to scale with (Formula presented.), with (Formula presented.) being the total number of grid points and (Formula presented.). The solver is used to compute the hydrodynamic coefficients for several floating bodies and compared against known public benchmark results. The results show excellent agreement, ultimately validating the solver and emphasizing the geometrical flexibility and high accuracy and efficiency of the proposed solution strategy. Lastly, an extensive investigation of nonresolved energy from the pseudo-impulse is carried out to characterize the induced spurious oscillations of the free surface quantities leading to a robust strategy for tuning the pseudo-impulsive motion to the spatial discretization.

Predicting the spray evolution using simulations requires accurate modeling of the turbulent gas-phase flow field. In this study, the high-order spectral-element method (SEM), implemented in the code Nek5000, was used to provide highly resolved solutions to the turbulent flow field. Spray modeling capabilities were implemented into the Nek5000 code. The spray is modeled in a Lagrangian–Eulerian (LE) framework, where the liquid is represented by discrete parcels of droplets. The method for coupling liquid and gas in the context of SEM is described, which allows for very fine meshes to be used without affecting the stability of the solution. Large-eddy simulations (LES) of the eight-hole ECN Spray G gasoline injector were conducted. Numerical results are compared against experimental data for liquid penetration, droplet size and gas velocity. The morphology of the multiplume spray is compared against experimental data. The effect of different spray injection inputs is analyzed. It was found that using a plume direction of 33 deg and an injection cone angle of 30 deg produced the best results overall. This work shows the applicability of SEM for spray modeling applications, where use of a high-order flow solver can help us understand the multiplume spray aerodynamics and how it leads to plume collapse under certain conditions. Results also highlight the need for tuning spray input parameters in the LE framework, even when high-fidelity gas flow solutions are possible.

When submerged under a liquid, the microstructure of a SuperHydrophobic Surface (SHS) traps a lubricating layer of gas pockets, which has been seen to reduce the skin friction of the overlying liquid flow in both laminar and turbulent regimes. More recently, spatially homogeneous SHS have also been shown to delay laminar–turbulent transition in channel flows, where transition is triggered by modal mechanisms. In this study, we investigate, by means of topology optimization, whether a spatially inhomogeneous SHS can be designed to further delay transition in channel flows. Unsteady direct numerical simulations are conducted using the spectral element method in a 3D periodic wall-bounded channel. The effect of the SHS is modelled using a partial slip length on the walls, forming a 2D periodic optimization domain. Following a density-based approach, the optimization procedure uses the adjoint-variable method to compute gradients and a checkpointing strategy to reduce storage requirements. This methodology is adapted to optimizing over an ensemble of initial perturbations. This study presents the first application of topology optimization to laminar–turbulent transition. We show that this method can design surfaces that delay transition significantly compared to a homogeneous counterpart, by inhibiting the growth of secondary instability modes. By optimizing over an ensemble of streamwise phase-shifted perturbations, designs have been found with comparable mean transition time and lower variance.

Measurement of transient pressure distribution on maritime structures is important for the assessment of the hydrodynamic loads applied. The commonly used pressure sensors are mostly bulky, need to be bolted to the structure, and/or only provide point-wise measurements. In this paper, an elastic matrix layer with a network of embedded piezoelectric sensors is proposed to address these issues. For experimental validation, a 400 × 400 × 5 mm epoxy layer is fabricated embedding 25 piezoelectric sensors on a square grid in accordance with Gauss-Lobatto-Legendre points. A finite element based inverse procedure is developed to reconstruct the pressure field from the electric potentials measured by the piezoelectric transducers. Feasibility of the concept is evaluated by measuring and reconstructing the pressure field generated by a travelling wave in a water tank. Sensitivity of the layer is also investigated through the experiments. The results indicate that the retrofit layer is capable of pressure field reconstruction, and that the presence of disturbances on the sensing surface does not affect the measurements in a notable way, while non-ideal conditions of the mounting can have a significant impact on the accuracy of the measurements. The results highlight the potential of the concept in pressure distribution measurements.

An improved Monte Carlo method (IMCM) is developed to solve radiative heat transfer in participating media in this work. Monte Carlo method (MCM) as a high-precision method has good applicability f...

This article attempts to enhance the low-frequency vibration suppression performance of corrugated-core sandwich beams. Multiple local resonators are introduced into the corrugated-core sandwich beam to acquire low-frequency bandgaps with broader bandwidth and higher wave attenuation capability. The governing equations for vibration analysis of the local resonator–attached corrugated-core sandwich beam are established based on the spectral element method, which incorporates the locally resonant effect by adding the dynamic stiffness term of one specific resonator to the degree of freedom that it attaches to. The bandgaps of the proposed periodic structure are further derived by imposing the Bloch boundary conditions. After validating the numerical model through finite element simulations as well as experimental investigations, the bandgaps and vibration transmissibility of the corrugated-core sandwich beam are carried out, both with and without attached local resonators. It is found that the vibration reduction capability of the corrugated-core sandwich beam is greatly enhanced, bringing two low-frequency bandgaps with high attenuation factors and wide bandwidths. Meantime, the first bandgap of resonator-free corrugated-core sandwich beam is broadened apparently. An interesting result is that the bandgap with higher frequency is split by a newly generated passband. Furthermore, parametric studies are performed, and it is found that the regulating characteristics of the bandgaps obtained through varying the attachment location of local resonators are similar to those through tuning their inherent parameters.

In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a fully nonlinear potential flow (FNPF) model discretized using a Galerkin spectral element method to serve as a basis for handling both wave propagation and wave-body interaction with high computational efficiency within a single modellingapproach. We design and propose an efficientO(n)-scalable computational procedure based on geometric p-multigrid for solving the Laplace problem in the numerical scheme. The fluid volume and the geometric features of complex bodies is represented accurately using high-order polynomial basis functions and unstructured meshes with curvilinear prism elements. The new p-multigrid spectralelement model can take advantage of the high-order polynomial basis and thereby avoid generating a hierarchy of geometric meshes with changing number of elements as required in geometric h-multigrid approaches. We provide numerical benchmarks for the algorithmic and numerical efficiency of the iterative geometric p-multigrid solver. Results of numerical experiments are presented for wave propagation and for wave-body interaction in an advanced case for focusing design waves interacting with a FPSO. Our study shows, that the use of iterative geometric p-multigrid methods for theLaplace problem can significantly improve run-time efficiency of FNPF simulators.

Large eddy simulation is performed in heat transfer of turbulent pipe flow with NEK5000 code based on spectral element method to study uncertainty quantification by Grid Convergence Index. The turb...

This paper concerns the design of a high-frequency GaN-based rotating transformer confined by conductive materials. The design approach combines the high-order spectral element method for the magnetic modeling, an electronic circuit model, and the finite element method for the thermal modeling. The objective of the design analysis is to minimize the ratio of core inertia to efficiency. Two different transformer topologies are considered, in which the power is either transferred in the axial or radial direction. The resulting designs are compared in terms of efficiency, core inertia, and transferred power. The radial design shows the best performance within the optimization problem.

Vibration response and band gap characteristics of the functionally graded frame structures are investigated based on the first-order shear deformation theory. The material properties of functionally graded material rods vary continuously in thickness direction according to a power law. Spectral stiffness matrix of the periodic functionally graded material frame structure in the global coordinate system is derived in detail. Consequently, the vibration band gap properties of the functionally graded material frame structure can be calculated and analyzed by using the spectral element method. The calculation accuracy for dynamic responses of the functionally graded material frame structure is validated by the finite element method. The results demonstrate that the wider band gaps in the low and medium frequency ranges can be achieved for the functionally graded frame structures comparing with the homogeneous ones. Moreover, the frequency windows and ranges for the band gaps of the functionally graded material frame structure can be effectively adjusted through designing the gradient indexes for the functionally graded material rods, which provide a novel idea for vibration suppression of frame structures.

A non-linear model is developed to capture the transient flow and pressure behaviour of methane-rich gas (MRG) in industrial pipelines for the use in simulation and control applications. Hyperbolic partial differential equations describe the pipe pressure and flow profiles, and composition analyses are used to develop the physical properties of the gas appearing in the pipe segment equations. The spectral element method (SEM) is used to numerically solve the spatial profiles within the pipeline, and a model verification is done on the SEM tuning parameter choices. The model is developed into a compact state–space description for improved usability. Furthermore, the developed model achieves good accuracy when validated on real process data of an industrial MRG network and can be used for simulation and model-based control applications.

A novel active elastic metamaterial plate is proposed, with tunable vibration band-gap characteristics is by using the periodically placed piezoelectric actuator and sensor pairs along one direction of the plate. Active control strategies are employed to actively adjust the band-gap properties of the metamaterial plate. Displacement and acceleration feedback control methods are applied to design the controllers so that the positive active stiffness and inertia for the elastic metamaterial plate can be provided. The dynamic responses of the finite plate with periodic piezoelectric actuator/sensor pairs are calculated using the spectral element method (SEM), and the calculation accuracy of the SEM is validated by the finite element method. The present results reveal that zero-frequency band gaps can be generated for the elastic metamaterial plate, and the band-gap characteristics in the medium and high frequency ranges can be significantly enhanced by using the acceleration feedback control. Moreover, very wide band gaps for the elastic metamaterial plate can be obtained by using the active acceleration control, and the starting frequencies of the first band gap under the acceleration control can be reduced by increasing the acceleration control gain. The widths of the zero-frequency and Bragg-type band gaps for the elastic metamaterial plate can be amplified by increasing the displacement feedback control gain. The control voltages to be applied on the actuators for the elastic metamaterial plate are also calculated and discussed.

In this work, a combination of the spectral stochastic finite element method (SSFEM) and the time-domain spectral element method (TSEM), referred to as the stochastic time domain spectral element m...

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

Vibration-based damage detection techniques usually focus on the changes in the modal properties as a result of any structural damage. For the last three decades, varying levels of success ...

This paper presents a novel numerical framework based on the accurate spectral element method (SEM) for electro-thermo-hydrodynamics (ETHD), in which the coupled electric, flow, and heat fields are solved simultaneously. The electric field potential is estimated by the classic Galerkin variation with the electric field vectors evaluated by the spectral approximation, and the streamline upwind Petrov-Galerkin variation and consistent approximate upwind technique are applied to stabilize the numerical simulation of charge density transport. As for the flow and heat transfer, the improved time-splitting method developed in our previous work is applied to deal with the coupled pressure and velocity in the momentum equations. Three carefully selected cases of analytical solution, pure thermal and pure electric convection, and electro-thermo-convection are performed to validate the algorithm. Then, the electro-thermo-convection in an enclosure with uniform temperature distribution is simulated and the average Nusselt numbers at different electric Rayleigh numbers are presented accurately. Additionally, the sinusoidal temperature boundary conditions are considered that the contours for stream function, temperature, and charge density are analyzed in detail to depict the heat transfer enhancement with ETHD effects.

In this paper, single material beams as the basic structural members in the traditional periodic frame structure were extended to the ones of multi-material composite beam with locally resonant (LR) unit. Based on the spectral element method and the topological characteristics of structure, an assembly method of the stiffness matrix for virtual full component model is presented. This method can be applied not only to the periodic structures, but also to the aperiodic structures, because the whole stiffness matrix of the structure is assembled by its topological information. The effects of the rest design parameters on the band gap behavior of two-dimension (2D) periodic frame structure were studied when the lattice constant was fixed. The results show that the Bragg band gaps can be adjusted by changing the lengths of structural members and the length ratio of the subunit A to the structural members. The results also show that the LR band gaps can be adjusted by adding LR units with different parameters into different members. The results in this work enrich and expand the modulatory pathway of the band gaps of periodic frame structure, and provide a modified approach to the design and correction of the passive vibration suppression system.

Spectral element method (SEM) is an accurate and efficient frequency domain-based method which has been frequently used in different analyses of various structures. In the present research, for the first time, this method is employed to deal with the wave propagation analysis of moderately thick rectangular plates with two piezoelectric layers attached on the top and bottom surfaces. The equations of motion are derived by taking into account the Mindlin plate theory assumptions and using the Hamilton's principle. The Maxwell's equation is employed to obtain the governing equation of electric potential in the piezoelectric layers. The differential equations are transformed into the frequency domain by employing the discrete Fourier transform and then a closed-form solution for the Levy type plate attached to piezoelectric layers is introduced. The dynamic stiffness matrix for the smart plate is obtained by applying the exact dynamic shape functions. Accurate and efficient numerical algorithms are introduced to extract the natural frequencies and the dynamic response of the structure under impact loading. The validation of the presented method is accomplished by comparing the obtained natural frequencies and dynamic response with the existing results in the literature and also the results obtained by the Abaqus software. Also, the effects of boundary condition and thickness of the plate and piezoelectric layers on the results are investigated. Independence to the mesh structure and less computational time are the most important advantages of the SEM compared with similar numerical methods like the finite element method.

This paper presents a state-vector equation method (SVEM)-based spectral element method (SEM) to formulate frequency domain spectral element models for non-uniform 1-D structures. In the SVEM-based SEM, the frequency domain homogeneous governing differential equations for non-uniform 1-D structures are first transformed into state-vector equations. The system matrix and state-vector are represented with power series. These power series representations are then substituted into the state-vector equation, and the differential transformation method is used to efficiently derive a recurrence formula for the coefficients of the power series solution of the state-vector equation. By computing these coefficients from the recurrence formula, the transfer function that relates the state-vector at an arbitrary position to that at the initial position of a finite element is derived. The transfer matrix is then obtained from the transfer function. Finally, the spectral element matrix or exact dynamic stiffness matrix is obtained from the transfer matrix. The accuracy and computational efficiency of the proposed SVEM-based SEM are verified in due course through comparisons with other solution methods for non-uniform axial rods, Bernoulli−Euler beams, and Timoshenko beams with different spatial variations.

Turbulent mixing is an important thermal hydraulic phenomenon in the reactor core rod bundles and it leads to strong momentum and energy transfer among adjacent subchannels in fuel assembly. Generally, turbulent mixing coefficient is usually referred to describe turbulent effect, which commonly sets to a constant or calculated utilizing Reynolds number dependent fitting correlations based on experimental data. In this paper, a high-scalable and high-performance spectral element method combining with high passed filtered Large Eddy Simulation (LES) model has been proposed to simulate the turbulent flow through parallel wall channel and square channel with a cylindrical rod for single-phase flow. In the parallel wall channel case, mesh sensitivity analysis and model validation were accomplished by comparing the simulation data with DNS references utilizing key parameters such as velocity profile and stresses in the near wall region. Meanwhile, for the square channel with a cylindrical rod case, instantaneous lateral velocity monitored in the gap center has been compared with the experimental data with different Reynolds numbers and geometric conditions. From the simulation approach, both the absolute oscillation amplitude and the oscillation frequency increase with the pitch diameter ratio. Finally, the simulation results of turbulent mixing coefficient dependent on Reynolds number were validated with both experimental and theoretic references to demonstrate the feasibility of spectral element method combining with LES model. The root mean square (RMS) value of lateral fluctuating velocity was adopted to reflect the effective mixing capability, predicting the turbulent mixing phenomena with a reasonable degree of accuracy from the specific calculation strategy. Fast Fourier Transform (FFT) also performed and got an agreement with reference data.

A 3D fully nonlinear potential flow (FNPF) model based on an Eulerian formulation is presented. The model is discretizedusing high-order prismatic – possibly curvilinear – elements using a spectral ...

The exact solution of structural dynamic related problems can be achieved by using the frequency-dependent spectral method. The exact solution is thought to be accurate while reducing the number of degree-of-freedom to resolve the cost and computational drawbacks. This paper investigates the vibrational characteristics of a Levy-type solution of thick plates considering shear deformation based on the two-variable Refined Plate Theory (RPT). The plates, which are modeled by an isotropic Levy-type rectangular plate, were solved by using the Spectral Element Method (SEM). The SEM for RPT Levy-type in the frequency domain is derived to formulate the free vibration problems of the plates. Transcendental stiffness matrices are well established in vibration, formulated from the exact solutions of the differential equations of the RPT Levy-type plate element. The present spectral element model has four line-type degree-of-freedoms (DOF) on each edge of the Levy-type rectangular plate. Natural frequencies of the plate are computed by means of the Wittrick-Williams algorithm. Numerical comparisons are given to show the effectiveness, efficiency, and accuracy of the SEM by using one element. Unlike the FEM, the SEM gives exact solutions of the natural frequencies of plates without element discretization procedures.

Thermocapillary flow instabilities in annular pool with different aspect ratios were investigated by the linear stability analysis based on the Legendre spectral element method. The energy analysis was applied to explore the underlying physical mechanism for the instability of thermocapillary flow. The results reveal two types of instability for different aspect ratios. The onset of instability is an oscillatory bifurcation in the cases of small aspect ratio whereas a stationary bifurcation in the cases of large aspect ratio. Moreover, the energy analysis indicates that the bifurcation of the flow is caused by the hydrodynamic (inertial) instability mechanism for low Prandtl number (Pr = 0.011), while by the coupled hydrodynamic effect and Marangoni effect for moderate Prandtl number (Pr = 1.4).

In this paper, a new series of differential equations which can predict the propagation and dispersive behavior of first symmetric and antisymmetric Lamb wave modes in functionally graded material (FGM) thick plates are developed. Then, given the accuracy and cost effectiveness of Legendre spectral element method in combination with central difference method, these methods are utilized to set up the numerical models and solving the dynamic discretized differential equations. Finally, based on the wave front velocity, the percentage of error is estimated and it is shown that considering some limitations which are inherently included in the utilized method of error estimation, the proposed equations and the numerical procedure can predict the behavior of first symmetric and antisymmetric Lamb wave modes in FGM thick plates precisely.

In the present work, a new dynamic homogenization model is developed to investigate the long-wavelength wave propagation in a corrugated sandwich plate. With the harmonic motion assumption and using a shifting operator, the governing equations of the plate are firstly represented in a state-space form. Then, a dynamic homogenization model is developed via the two-scale homogenization method. Based on this model and considering the propagation of sinusoidal waves, the dispersion relations and corresponding wave modes can be easily obtained. In order to validate the developed homogenization model, the obtained dispersion relations are compared with those predicted by the spectral element method. It is found that the present method gives accurate results in low frequency range. Furthermore, the effects of some geometric and material parameters on the dispersion relations for the corrugated sandwich plate are also discussed. The developed homogenization model is expected to be helpful in the prediction and control of dynamic responses of corrugated or even lattice sandwich structures.

Herein, a circular cylinder with a slit is implemented as an effective passive flow control technique for flow control and other relevant industrial practices. Two-dimensional incompressible Navier–Stokes equations are numerically solved using the high-resolution spectral element method at a Reynolds number of 200. The slit width ratio s/d is varied from 0 to 0.3, and the slit attack angle is between 0° to 90°. The findings show that, for attack angle 0° ≤ β ≤ 45°, a larger slit width ratio and a smaller attack angle tend to induce a lower time-mean drag coefficient and root-mean-square lift coefficient. The relative reduction ratio of the time-mean drag coefficient reaches a maximum of 28.6% at s/d = 0.30 and β = 0°. For attack angle 45°

In this work, a stochastic time domain spectral element method (STSEM) is proposed for stochastic modeling and uncertainty quantification of engineering structures. To perform the analysis, both an isotropic Timoshenko beam (TB) and a sandwich beam are considered. The sandwich beam is modeled considering higher-order sandwich panel theory which is capable of addressing the core flexibility. The material properties are considered as 1D non-Gaussian random fields, and optimal linear estimation (OLE) is used for the discretization of the random fields. The OLE-based discretization of a random field allows simulating the random fields numerically, resulting in realizations of the stiffness, mass matrix, and dynamic stiffness matrix. In the current work, the computationally efficient time domain spectral element method (TSEM) is used to develop the STSEM formulation. The STSEM reduces the CPU time significantly as the number of degrees of freedom (dof) is much smaller than in FEM. TSEM also provides a consistent diagonal mass matrix which reduces the computation cost in case of dynamic problems. The deflection statistics of the beam for static, free vibration and dynamic cases are investigated for both TB and sandwich beam. The computational efficiency of the proposed method and the effect of material variability on the response statistics are also discussed. Moreover, the effect of different correlation lengths on the response statistics is studied.

Direct numerical simulation (DNS) of turbulent flow in a periodic channel is performed to study the effect of the wall-normal spatial resolution near the wall on the calculations of turbulence statistics using multidomain Chebyshev grids. A discontinuous spectral element method (DSEM) is employed to calculate the first- and second-order statistics of the flow near the wall. The effect of the spectral approximation order on the resolution requirement is also studied by considering three approximation orders of P = 2 , 5 , and 7. The Reynolds number based on the bulk density, bulk velocity, and channel half-height is Re = 3266 , which corresponds to a friction Reynolds number of Re τ ≈ 204 based on the wall friction velocity and the channel half-height. It is observed that the near-wall resolution requirement strongly depends on the spectral approximation order. For the same total number of grid points, a higher approximation order provides more accurate results. For approximation orders of P = 5 and 7, grids with respectively 11 and 8 points inside y + = 10 are sufficient to resolve the turbulent statistics near the wall, while a grid with P = 2 requires more than 11 points in the same region to achieve the same level of accuracy.

Damage detection in structures and systems is essential for monitoring parameters that can affect their integrity. This paper evaluates the efficiency of four damage indices (DIs) commonly used with temporal wave signals. The root mean square deviation, mean absolute percentage deviation, covariance, and correlation coefficient deviation DIs are presented, and a normalization is then proposed. An Euler-Bernoulli beam is used as a guided wave modelled with the spectral element method and excited by a toneburst signal. It includes the theoretical background of the throw-off beam, undamaged and cracked beam spectral elements. The DIs for a single crack position and a map varying crack depth and positions are calculated with deterministic and random temporal signal responses derived from noise addition. Results showed that DIs could identify and quantify the damage conditioned to the pulse location point and the influence of noise in the estimation, which leads in an analysis comparable to practical applications.

The compressibility effects on energy exchange mechanisms in a three-dimensional, spatially developing plane free shear layer are investigated via data produced by direct numerical simulation. The compressible shear layer is simulated using a high-order discontinuous spectral element method for convective Mach numbers increases.

In this work, a method for the simulation of guided wave propagation in solids defined by implicit surfaces is presented. The method employs structured grids of spectral elements in combination with a fictitious domain approach to represent complex geometrical features through signed distance functions. A novel approach, based on moment fitting, is introduced to restore the diagonal mass matrix property in elements intersected by interfaces, thus enabling the use of explicit time integrators. Since this approach can lead to significantly decreased critical time steps for intersected elements, a "leap-frog" algorithm is employed to locally comply with this condition, thus introducing only a small computational overhead. The resulting method is tested through a series of numerical examples of increasing complexity, where it is shown that it offers increased accuracy compared to other similar approaches. Due to these improvements, components of interest for structural health monitoring-related tasks can be effectively discretized, while maintaining a performance comparable or only slightly worse than the standard spectral element method. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)., Computer Methods in Applied Mechanics and Engineering, 398, ISSN:0045-7825, ISSN:1879-2138

Construction of drilled shafts for transportation infrastructure presents quality assurance challenges related to structural anomalies, including voids and degraded concrete. Efforts to evaluate anomalies often use stress-wave non-destructive testing (NDT) techniques such as the crosshole sonic logging (CSL) method. CSL relies on the propagation of stress waves between access tubes inserted alongside the reinforcement cage. Differences in travel time and amplitudes can be used to estimate concrete quality within the source-receiver ray paths. Crosshole tomography (CT) advances this approach further and models ray paths to solve an inverse problem based on first arrival times. However, both stress-wave methods cannot typically evaluate anomalies smaller than 10% to 15% of the shaft cross sectional area. Recent advances in wave propagation modeling have led to the development of full waveform inversion (FWI) approaches. FWI attempts to generate a more detailed tomographic model that matches the entire waveform recordings. This paper presents findings from a numerical study where full waveform tomography was performed on a portion of a drilled shaft with a structural anomaly. Crosshole stress-wave propagation was simulated using a spectral element method (SEM) forward modeler. The resulting waveforms were then used as inputs into a CT travel-time inversion algorithm using ray-path modeling and into a FWI algorithm using the entire recorded signals. The results highlighted that FWI estimated concrete velocities and the geometry of the anomaly more accurately than CT in the idealized numerical model. This was the case even though information from more sources and receiver pairs was used for the CT inversion.

We investigate the free convection processes in the vicinity of a spherical 1 kg mass standard by two- and three-dimensional direct numerical simulations using a spectral element method. Our focus is on the determination and suppression of updraft forces in a high-precision mass comparator which are caused by temperature differences between mass standard and its environment in the millikelvin range - a source of systematic uncertainties in the high-precison mass determination. A two-dimensional model is presented first, which obtains a good agreement with previous laboratory measurements for the smaller temperature differences up to 15 mK. The influence of different boundary conditions and side lengths of the square domain is discussed for the mass standard positioned in the center of the chamber. The complexity is increased subsequently in configurations with additional built-ins for counter heating in form of planar plates or hemispherical shells above the mass standard. The latter ones lead to a full compensation of the updraft force. Three-dimensional simulations in a closed cubic chamber confirm the two-dimensional findings and additionally reveal complex secondary flow pattern in the vicinity of the mass standard. The reduction of the heat transfer due to the built-ins is also demonstrated by a comparison of the Nusselt numbers as a function of the Rayleigh number in the chosen parameter range. Our simulations suggest that such additional constructive measures can enhance the precision of the mass determination by suppression of free convection and related systematic uncertainties., 29 pages, 20 figures

The primary instability of thermocapillary flow in a liquid bridge between two coaxial disks with different radii is investigated under microgravity for silicon melt with Prandtl number Pr=0.011 via two heating strategies. The static deformation of the free surface is considered by solving the Young-Laplace equation. The physical instability mechanisms are explored by analyzing the energy budgets of the critical modes, which are determined by linear stability analysis based on the Legendre spectral element method. With the decrease of radius ratio Γr, the stability of thermocapillary flow is significantly improved. In contrast to typical cylindrical liquid bridges (Γr=1), the instability is an oscillatory bifurcation for small radius ratios (Γr≤0.672) when the liquid bridge is heated from the bottom disk. Furthermore, the instabilities for all radius ratios and heating strategies are found to be purely hydrodynamic, but the specific instability mechanisms are different.

The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines, wheels and fan blades) or sliding components (e.g. in compressor or turbine cascade simulations). With an increasing trend towards the high-fidelity modelling of these cases, in particular combined with the use of high-order discontinuous Galerkin methods, there is therefore a requirement to understand how different numerical treatments of the interfaces between the static mesh and the sliding/rotating part impact on overall solution quality. In this article, we compare two different approaches to handle this non-conformal interface. The first is the so-called mortar approach, where flux integrals along edges are split according to the positioning of the non-conformal grid. The second is a less-documented point-to-point interpolation method, where the interior and exterior quantities for flux evaluations are interpolated from elements lying on the opposing side of the interface. Although the mortar approach has significant advantages in terms of its numerical properties, in that it preserves the local conservation properties of DG methods, in the context of complex 3D meshes it poses notable implementation difficulties which the point-to-point method handles more readily. In this paper we examine the numerical properties of each method, focusing not only on observing convergence orders for smooth solutions, but also how each method performs in under-resolved simulations of linear and nonlinear hyperbolic problems, to inform the use of these methods in implicit large-eddy simulations., Comment: 37 pages, 15 figures, 5 tables, submitted to Computer Methods in Applied Mechanics and Engineering, revision 1

The explicit semi-Lagrangian method for solution of Lagrangian transport equations as developed in Natarajan and Jacobs (2020) is adopted for the solution of stochastic differential equations that is consistent with Discontinuous Spectral Element Method (DSEM) approximations of Eulerian conservation laws. The method extends the favorable properties of DSEM that include its high-order accuracy, its local and boundary fitted properties and its high performance on parallel platforms for the concurrent Monte-Carlo, semi-Lagrangian and Eulerian solution of a class of time-dependent problems that can be described by coupled Eulerian–Lagrangian formulations. Such formulations include the probabilistic models used for the simulation of chemically reacting turbulent flows or particle-laden flows. Consistent with an explicit, DSEM discretization, the semi-Lagrangian method seeds particles at Gauss quadrature collocation nodes within a spectral element. The particles are integrated explicitly in time according to a drift velocity and a Wiener increment forcing and form the nodal basis for an advected interpolant. This interpolant is mapped back in a semi-Lagrangian fashion to the Gauss quadrature points through a least squares fit using constraints for element boundary values. Stochastic Monte-Carlo samples are averaged element-wise on the quadrature nodes. The stable explicit time step Wiener increment is sufficiently small to prevent particles from leaving the element’s bounds. The semi-Lagrangian method is hence local and parallel and does not have the grid complexity, and parallelization challenges of the commonly used Lagrangian particle solvers in particle-mesh methods for solution of Eulerian–Lagrangian formulations. Formal proof is presented that the semi-Lagrangian algorithm evolves the solution according to the Eulerian Fokker–Planck equation. Numerical tests in one and two dimensions for drift–diffusion problems show that the method converges exponentially for constant and non-constant advection and diffusion velocities.

This paper presents a new parameter identification (PI) algorithm for estimating effective and detailed thermal parameters of ground source heat pump systems using data obtained from the well-known thermal response test. The PI comprises an iterative scheme coupling a semi-analytical forward model to an inverse model. The forward model is formulated based on the spectral element method to simulate transient 3D heat flow in ground source heat pump (GSHP) systems, and the inverse model is formulated based on the interior-point optimization method to minimize the system objective function. Compared to existing interpretation tools for the thermal response test, the proposed PI algorithm has several advanced features, including: it can handle fluctuating heat pump power and inlet temperatures; interpret data obtained from multiple heat injection or extraction signals; produce accurate backcalculation for short and long duration experiments; and handle multilayer systems. The PI algorithm is tested against synthesized data, using a wide range of random noise, and versus an available laboratory experiment. The computational results show that the PI algorithm is accurate, stable and exhibiting relatively high convergence rate.

In this paper, a contact problem between two bodies, discretized by finite elements, is solved by adding an auxiliary NURBS layer between the bodies. The advantages of a smooth contact formulation in a NURBS approach are combined with simple mesh generation procedures for the bodies discretized with finite elements. Mesh tying conditions are used to couple the NURBS layer with the finite element discretization. The NURBS layer is the master side for contact and mesh tying. Mesh tying is enforced either using pointwise or mortar type approaches. Frictionless 2D and 3D contact problems are considered using small deformations. The contact problem is discretized with the mortar method and a penalty approach is used to enforce the contact constraints. A robust element-based quadrature is applied for mortar tying and contact discretizations, thus avoiding computationally expensive segmentation.

A frequency-domain spectral element method (SEM) is proposed for the vibration analysis of thin plate structures subjected to a moving point force. The thin plate structures may consist of multiple rectangular thin plates with arbitrary boundary conditions that form multispan thin plate structures, such as bridges. The time-domain point force moving on a thin rectangular plate with arbitrary trajectory is transformed into a series of stationary point forces in the frequency domain. The vibration responses induced by the moving point force are then obtained by superposing all vibration responses excited by each stationary point force. For the vibration response of a specific stationary point force, the plate subjected to the specific stationary point force is represented by four spectral finite plate elements, which were developed in the authors’ previous work. The SEM-based vibration analysis technique is first presented for single-span thin plate structures and then extended to the multispan thin plate structures. The high accuracy and computational efficiency of the proposed SEM-based vibration analysis technique are verified by comparison with other well-known solution methods, such as the exact theory, integral transform method, finite element method, and the commercial finite element analysis package ANSYS.

Initiated by the problem of the coupled vibration of three-dimensional pipes conveying fluid, a spectral element method is proposed to address its dynamic characteristics. Based on a more comprehensive fluid-filled beam model than previous studies, not only the shear deformation, gravity, initial tension and fluid friction, but also the fluid–structure coupling is analyzed so as to obtain more reasonable results. The present method is validated by comparing numerical results of a T-shaped branched pipe with data from the literature, as well as from finite element software. It is shown that the spectral element method (SEM) has remarkable advantages over finite element method in computational efficiency and accuracy. In addition, through experiments on the vibrations of an L-shaped water-filled pipe, the in-plane and out-plane acceleration responses by SEM are also verified. This method would have great potential in modeling the vibrations of complex pipelines conveying fluid in a variety of engineering applications.

Non Uniform Rational B-spline (NURBS) patches are a standard way to describe complex geometries in Computer Aided Design tools, and have gained a lot of popularity in recent years also for the approximation of partial differential equations, via the Isogeometric Analysis (IGA) paradigm. However, spectral accuracy in IGA is limited to relatively small NURBS patch degrees (roughly p, 33 pages, 15 figures, 3 tables, to appear on "Computer Methods in Applied Mechanics and Engineering"

An accurate Chebyshev spectral element method is developed to simulate the natural convection in a porous cavity using the local thermal non-equilibrium model. Two horizontal walls of the cavity are adiabatic, while the left vertical wall is heated and the right side wall is cooled. The non-dimensional governing equations are derived based on the Darcy model and Boussinesq assumption. The validation test with exact solution verifies the high accuracy of the algorithm, and the numerical results for natural convection in porous square cavity reach an excellent agreement with reported solutions. Two physical problems are investigated: (1) Natural convection in porous cavity at different aspect ratios with fixed temperature on two vertical walls; (2) Natural convection in porous square cavity with temporal sinusoidal temperature on the hot wall and fixed temperature on the cold wall. The effects of aspect ratio and non-dimensional heat transfer characteristic parameters are analyzed.

In this paper, a boundary spectral element method (BSEM) for solving the problem of three-dimensional wave propagation is introduced. In the new formulation, elastodynamics of structures is computed by the Laplace transformed boundary element method (BEM), and boundaries of structures are discretised into high-order isoparametric spectral elements. Three types of spectral elements – Lobatto, Gauss–Legendre and Chebyshev elements – have been implemented. With a significantly higher computational efficiency than the conventional BEM, the BSEM provides a competitive alternative for modelling high-frequency wave propagation in engineering applications.

Inspired by the hierarchical structures of butterfly wing surfaces, a new kind of lattice structures with a two-order hierarchical periodicity is proposed and designed, and the band-gap properties are investigated by the spectral element method (SEM). The equations of motion of the whole structure are established considering the macro and micro periodicities of the system. The efficiency of the SEM is exploited in the modeling process and validated by comparing the results with that of the finite element method (FEM). Based on the highly accurate results in the frequency domain, the dynamic behaviors of the proposed two-order hierarchical structures are analyzed. An original and interesting finding is the existence of the distinct macro and micro stop-bands in the given frequency domain. The mechanisms for these two types of band-gaps are also explored. Finally, the relations between the hierarchical periodicities and the different types of the stop-bands are investigated by analyzing the parametrical influences.

This paper concerns the comparison of the performance of the Spectral Element Method (SEM) and the Finite Element Method (FEM) for modeling a magnetostatic problem. The convergence of the vector magnetic potential, the magnetic flux density, and the total stored energy in the system is compared with the results of FEM. Two simulation scenarios are examined which are distinct by a large and a small rounding radius of the corner. SEM shows comparable convergence to FEM for field computations and faster convergence for energy calculations.

In this paper, the time-domain dynamic response of a thick hollow cylinder made of two-dimensional functionally graded material is studied. An axisymmetric solid spectral finite element mod...

A hybrid Spectral Element Method (SEM)–Symplectic Method(SM) method for high-efficiency computation of the high-frequency random vibrations of a high-speed vehicle–track system with the frequency-d...