Numerical Interpolation Scheme Research Articles

An efficient SPH methodology for modelling mechanical characteristics of particulate composites

Particulate composites are one of the widely used materials in producing numerous state-of-the-art components in biomedical, automobile, aerospace including defence technology. Variety of modelling techniques have been adopted in the past to model mechanical behaviour of particulate composites. Due to their favourable properties, particle-based methods provide a convenient platform to model failure or fracture of these composites. Smooth particle hydrodynamics (SPH) is one of such methods which demonstrate excellent potential for modelling failure or fracture of particulate composites in a Lagrangian setting. One of the major challenges in using SPH method for modelling composite materials depends on accurate and efficient way to treat interface and boundary conditions. In this paper, a master-slave method based multi-freedom constraints is proposed to impose essential boundary conditions and interfacial displacement constraints in modelling mechanical behaviour of composite materials using SPH method. The proposed methodology enforces the above constraints more accurately and requires only smaller condition number for system stiffness matrix than the procedures based on typical penalty function approach. A minimum cut-off value-based error criteria is employed to improve the computational efficiency of the proposed methodology. In addition, the proposed method is further enhanced by adopting a modified numerical interpolation scheme along the boundary to increase the accuracy and computational efficiency. The numerical examples demonstrate that the proposed master-slave approach yields better accuracy in enforcing displacement constraints and requires approximately the same computational time as that of penalty method.

Predicting Non-Linear Flow Phenomena through Different Characteristics-Based Schemes

The present work investigates the bifurcation properties of the Navier–Stokes equations using characteristics-based schemes and Riemann solvers to test their suitability to predict non-linear flow phenomena encountered in aerospace applications. We make use of a single- and multi-directional characteristics-based scheme and Rusanov’s Riemann solver to treat the convective term through a Godunov-type method. We use the Artificial Compressibility (AC) method and a unified Fractional-Step, Artificial Compressibility with Pressure-Projection (FSAC-PP) method for all considered schemes in a channel with a sudden expansion which provides highly non-linear flow features at low Reynolds numbers that produces a non-symmetrical flow field. Using the AC method, our results show that the multi-directional characteristics-based scheme is capable of predicting these phenomena while the single-directional counterpart does not predict the correct flow field. Both schemes and also Riemann solver approaches produce accurate results when the FSAC-PP method is used, showing that the incompressible method plays a dominant role in determining the behaviour of the flow. This also means that it is not just the numerical interpolation scheme which is responsible for the overall accuracy. Furthermore, we show that the FSAC-PP method provides faster convergence and higher level of accuracy, making it a prime candidate for aerospace applications.

Experimental Validation of the Simulated Steady-State Behavior of Porous Journal Bearings1

This study deals with a comparison between new experiments on the frictional behavior of porous journal bearings and its prediction by previous numerical simulations. The tests were carried out on bearings lubricated with polyalphaolefin (PAO)-based oils of distinct viscosities. The theoretical model underlying the simulations includes the effects of cavitation by vaporization and accounts for the sinter flow by virtue of Darcy's law. The effective eccentricity ratio corresponding to the experimentally imposed load is estimated by an accurate numerical interpolation scheme. The comparison focuses on the hydrodynamic branches of the Stribeck curve by dimensional analysis (DA), where the variations of the lubricant viscosity with temperature are of main interest. The numerically calculated values of the coefficient of friction are found to reproduce the experimentally obtained ones satisfactorily well in terms of overall trends; yet, the former lie predominantly below the measured ones, which results in a low-positive correlation between the two.

Modelling of transient heat conduction with diffuse interface methods

We present a survey on different numerical interpolation schemes used for two-phase transient heat conduction problems in the context of interface capturing phase-field methods. Examples are general transport problems in the context of diffuse interface methods with a non-equal heat conductivity in normal and tangential directions to the interface. We extend the tonsorial approach recently published by Nicoli M et al (2011 Phys. Rev. E 84 1–6) to the general three-dimensional (3D) transient evolution equations. Validations for one-dimensional, two-dimensional and 3D transient test cases are provided, and the results are in good agreement with analytical and numerical reference solutions.

Interpolating compact binary waveforms using the singular value decomposition

Compact binary systems with total masses between tens and hundreds of solar masses will produce gravitational waves during their merger phase that are detectable by second-generation ground-based gravitational-wave detectors. In order to model the gravitational waveform of the merger epoch of compact binary coalescence, the full Einstein equations must be solved numerically for the entire mass and spin parameter space. However, this is computationally expensive. Several models have been proposed to interpolate the results of numerical relativity simulations. In this paper we propose a numerical interpolation scheme that stems from the singular value decomposition. This algorithm shows promise in allowing one to construct arbitrary waveforms within a certain parameter space given a sufficient density of numerical simulations covering the same parameter space. We also investigate how similar approaches could be used to interpolate waveforms in the context of parameter estimation.

Influence of Discretization of Permeability Term and Mesh Size on the Prediction of Channel Segregations

Macro- and meso-segregations correspond to compositional heterogeneities at the scale of a casting. They develop during the solidification process. One of the parameters that have an essential effect on these segregations is the mush permeability, which is highly nonlinear, and varies over a wide range of magnitudes. We present simulation results for solidification of a Sn-Pb alloy in a two-dimensional cavity, highlighting the role of (i) the numerical interpolation schemes used for the finite-volume discretization of the highly-nonlinear permeability term and (ii) of the mesh size on the prediction of mesosegregations and macrosegregation. We observe that solute-rich liquid flowing through the mushy zone due to thermo-solutal convection results in patches of thin channel structures, which develop into mesosegregations. We notice little sensitivity of the predicted macrosegregation to different discretization schemes for the permeability term. However, we found their influence on the prediction of channel segregates to be significant when using coarse computational grids, customary in the simulation of industrial castings. Mesh refinement is crucial for capturing the complex phenomena in the formation of channel segregates. With a very fine mesh channels have been captured with more than one grid point along their width, allowing the determination of their width.

Comparison of numerical interpolation schemes for one-dimensional electrostatic Vlasov code

We discuss numerical interpolation schemes used in Vlasov codes. An improved conservative semi-Lagrangian scheme is compared with the latest non-conservative and conservative schemes for a long run-time nonlinear problem of the beam–plasma interaction with respect to the mass and energy conservation.

Robotic 3D SQUID imaging system for practical nondestructive evaluation applications

A robotic three-dimensional (3D) scanning superconducting quantum interference device (SQUID) imaging system was developed for practical nondestructive evaluation (NDE) applications. The major feature of this SQUID–NDE system is that the SQUID sensor itself scans in 3D by traveling over the surface of an object during testing without the need for magnetic shielding. This imaging system consists of (i) DC-SQUID gradiometer for effective movement of the sensor, (ii) SQUID sensor manipulator utilizing an articulated-type robot used in industry, (iii) laser charge-coupled-device (CCD) displacement sensor to measure the 3D coordinates of points on the surface of the object, and (iv) computer-aided numerical interpolation scheme for 3D surface reconstruction of the object. The applicability of this system for NDE was demonstrated by successfully detecting artificial damage of cylindrical-shaped steel tubes.

Characterization of dynamic three-dimensional strain fields in the canine radius

This note describes a method to approximate the 3-D mechanical environment of a long bone during a normal daily activity. Our specific goal was to characterize the temporal and spatial strain distributions in the mid-shaft region of the canine radius during gait. Direct measurement of strains along the entire surface of in vivo bone is not feasible, so we employed a combination of experimental measurements and numerical interpolation techniques to approximate the time-varying longitudinal strain distribution. Using standard in vivo strain gauging techniques, we measured dynamic strains at nine locations (three locations on each of three cross sections, data pooled from two experimental animals) on the canine radius during trotting gait. These in vivo strain measurements were then used to approximate the time course of the strain field for the entire radius mid-shaft region using a 3-D numerical interpolation scheme using finite element basis functions. Despite limitations in the present implementation of the method, the results show that there are considerable time-dependent variations in the strain distribution occurring at different transverse sections along the length of the diaphysis with substantial anteroposterior bending and rotation of neutral axis locations during the gait cycle.

Advances in the Spherical Harmonic–Boltzmann–Wigner approach to device simulation

Recent advances in the Spherical Harmonic Boltzmann method of device modeling are presented. A new surface scattering model and improved numerical interpolation schemes have been developed. The method is shown to be capable of calibrating an entire deep submicron process to provide I–V characteristics and substrate current self-consistently. Substrate currents agree with experiment over a complete process without any fitting parameters. Applications to a 50 nm MOSFET predict well-behaved device operation. The method requires approximately ten minutes to self-consistently calculate a MOSFET bias point and provide the device distribution function. The spherical harmonic method has been extended to account for quantum mechanical effects by applying it to the Wigner equation. We treat the Wigner equation as a quantum correction to the Boltzmann equation thereby making the spherical harmonic approach a natural method of solution.

An assessment of the role of the North Atlantic as a CO 2 sink

A numerical interpolation scheme based upon the lateral diffusive and advective transport of ocean surface waters has been developed to interpolate measurements made in irregular time and space over the oceans. This has been applied to about 2700 surface ocean P CO 2 measurements observed during the period 1972-1992 in the North Atlantic to give the distribution of sea-air P CO 2 difference (Δ P CO 2 ) over the Atlantic. Although the atmospheric CO 2 concentration has increased by about 28 ppm over this period, the P CO 2 values in the surface waters of subarctic regions have increased little because they are dictated primarily by the properties of underlying deep waters through vertical mixing. Accordingly, Δ P CO 2 values measured north of 50° N have been corrected to the year 1990 using the secular increase of atmospheric CO 2 . Because the surface water P CO 2 value in temperate waters tracks the secular increase in atmospheric CO 2 with a time lag of about two years, no correction was applied to the warm water Δ p CO 2 data. It has been assumed that seasonal variations are the same for each year. The net CO2 flux across the sea surface has been computed over a 4° latitude x 5° longitude grid using the mean monthly A p CO 2 values and the gas transfer coefficients estimated using the mean monthly wind speed. It has been found that the areas of the high latitude North Atlantic and the adjacent seas north of 42° N are net CO 2 sinks of 0.2 to 0.5 Gt G a -1 . The total sink flux of CO 2 over the temperate North Atlantic areas between 18° N and 42° N is balanced approximately by the source flux over the tropical Atlantic between 18° N and 18° S.

Bremsstrahlung spectra from electron interactions with screened atomic nuclei and orbital electrons

Through the synthesis of various theoretical results, a comprehensive set of bremsstrahlung cross sections (differential in the energy of the emitted photons) has been prepared. The set includes results for electrons with energies from 1 keV to 10 GeV incident on neutral atoms with atomic numbers Z = 1 to 100. For bremsstrahlung in the Coulomb field of the atomic nucleus, use was made of (a) results of Pratt, Tseng, and collaborators based on numerical phase-shift calculations for the screened Coulomb potential at energies below 2 MeV, and (b) the analytical high-energy theory (with Coulomb corrections) of Davies, Bethe, Maximon and Olsen at energies above 50 MeV, supplemented by the Elwert Coulomb correction factor and the theory of the high-frequency limit given by Jabbur and Pratt. In the high-energy region, the effect of screening was included with use of Hartree-Fock atomic form factors. A numerical interpolation scheme, applied to suitably scaled cross sections, was used to bridge the gap between the low-energy and high-energy theoretical results, and thus to obtain improved cross sections in the intermediate-energy region 2 to 50 MeV. Bremsstrahlung in the field of the atomic electrons was calculated according to the theory of Haug, combined with screening corrections derived from Hartree-Fock incoherent scattering factors. The paper also contains numerous comparisons between calculated and measured bremsstrahlung spectra, which indicate generally good agreement.