High-accuracy Simulations Research Articles

Application of metrics in the space of orbits to search for asteroids on close orbits

Here, we apply natural metrics defined in the space of Keplerian orbits to search for asteroids in close orbits. First, we use as a metric the distance between two orbits in the five-dimensional space of Keplerian orbits. Then, we apply the distance in three-dimensional factor-space of positional orbital elements. We have identified new asteroid pairs with a possible common origin. Once the asteroid pairs candidates are identified, we analyze their dynamical evolution. We find that the Yarkovsky effect must be taken into account when carrying out high-accuracy numerical simulations of the orbital evolution of asteroid pairs. Finally, we consider the planning of follow-up astrometric and photometric observations of the candidate asteroid pairs to determine their rotational parameters, needed to modeling the Yarkovsky effect.

Abstract ID: 104 Efficiency improvement in proton dose calculations with an equivalent restricted stopping power formalism

To maintain the dose accuracy of Monte Carlo simulations, the mean energy loss calculation usually requires a step restriction (dmax). It leads to a O(n) algorithmic time complexity, where n is the subdivision number imposed by dmax. A new formalism is proposed to accelerate Monte Carlo dose calculations, allowing the removal of dmax in the step selection leading to a O(1) algorithmic time complexity. In this formalism, the midpoint rule of the Newton–Cotes formulae was used to solve the integral equation relating the mean energy loss to the step. The fractional energy loss was obtained with a secant method and a Gauss–Kronrod quadrature, revealing within the midpoint rule the equivalent restricted stopping power (Leq), used here as a key physical quantity. For any step, the mean energy loss was simply defined as the product of the step with Leq. Proton inelastic collisions with electrons were added to GPUMCD, a GPU-based Monte Carlo dose calculation code. The proton continuous slowing-down was modelled with the Leq formalism. First, the dose and time impacts of dmax were studied within Geant4. Second, in voxelized geometries, GPUMCD was compared to Geant4 using a high accuracy simulation setup (dmax = 10 μm). The ionization processes alone were activated and the energy straggling was first switched off to validate alone the Leq formalism. The default settings (dmax = 1 mm) in Geant4 led to an error of up to 16.5% in the falloff region, up to 4.8% elsewhere and the computation times were inversely proportional to the maximal step length allowed. Dose differences between Geant4 and GPUMCD were smaller than 0.31% in the Bragg peak for the Leq formalism. GPUMCD 80% falloff positions (R80) matched Geant R80 within 1 μm. With the energy straggling, dose agreements were within 2.7% in the falloff, below 0.83% elsewhere and R80 positions matched within 100 μm. The overall computation times per million transported protons with GPUMCD were 31–173 ms. Under similar conditions, Geant4 computation times were 1.4–20 h. The Leq formalism allows larger steps while preserving the accuracy. It significantly accelerates Monte Carlo proton transport. The Leq formalism constitutes a promising variance reduction technique for computing proton dose distributions in a clinical context.

Modeling of transport processes through large-scale discrete fracture networks using conforming meshes and open-source software

Most industrial and field studies of transport processes in Discrete Fracture Networks (DFNs) involve strong simplifying assumptions, especially at the meshing stage. High-accuracy simulations are therefore required for validating these simplified models and their domain of validity. The present paper proposes an efficient workflow based on open-source software to obtain transport simulations. High-quality computational meshes for DFNs are first generated using the conforming meshing approach FraC. Then, a tracer transport model implemented in the open-source code DuMux is used for simulating tracer transport driven by the advection-dispersion equation. We adopt the box method, a vertex-centered finite volume scheme for spatial discretization, which ensures concentration continuity and mass conservation at intersections between fractures. Numerical results on simple networks for validation purposes and on complex realistic DFNs are presented. An a-posteriori convergence study of the discretization method shows an order of convergence O(h) for tracer concentration with h the mesh size.

Damage model for simulating chloride concentration in reinforced concrete with internal cracks

We present a method to simulate, in three dimensions, the concentration of chloride ions that penetrate into concrete with internal cracks. The method comprises the crack-propagation analysis of concrete and the diffusion analysis of chloride ions. A finite-element model with a damage model that is based on fracture mechanics for concrete was applied in the crack-propagation analysis, and we were able to reproduce the three-dimensional geometry of the internal cracks. Chloride-ion transfer through internal cracks was simulated by diffusion analysis with the simultaneous consideration of damage, and a diffusion coefficient that was expressed as a function of the damage variable obtained from crack-propagation analysis. We present a formulation of crack-propagation analysis by using the damage model and unsteady-diffusion analysis in consideration of damage. We also present a verification analysis of internal cracking in concrete to demonstrate that the crack width and the chloride concentration can be evaluated without mesh dependency. This is followed by a validation analysis. A comparison between the numerical and experimental results shows that the proposed method enables the high-accuracy simulation of chloride penetration into concrete with internal cracks.

Advanced EUV mask and imaging modeling

The exploration and optimization of image formation in partially coherent EUV projection systems with complex source shapes requires flexible, accurate, and efficient simulation models. This paper reviews advanced mask diffraction and imaging models for the highly accurate and fast simulation of EUV lithography systems, addressing important aspects of the current technical developments. The simulation of light diffraction from the mask employs an extended rigorous coupled wave analysis (RCWA) approach, which is optimized for EUV applications. In order to be able to deal with current EUV simulation requirements, several additional models are included in the extended RCWA approach: a field decomposition and a field stitching technique enable the simulation of larger complex structured mask areas. An EUV multilayer defect model including a database approach makes the fast and fully rigorous defect simulation and defect repair simulation possible. A hybrid mask simulation approach combining real and ideal mask parts allows the detailed investigation of the origin of different mask 3-D effects. The image computation is done with a fully vectorial Abbe-based approach. Arbitrary illumination and polarization schemes and adapted rigorous mask simulations guarantee a high accuracy. A fully vectorial sampling-free description of the pupil with Zernikes and Jones pupils and an optimized representation of the diffraction spectrum enable the computation of high-resolution images with high accuracy and short simulation times. A new pellicle model supports the simulation of arbitrary membrane stacks, pellicle distortions, and particles/defects on top of the pellicle. Finally, an extension for highly accurate anamorphic imaging simulations is included. The application of the models is demonstrated by typical use cases.

Numerical simulation of azimuth electromagnetic wave tool response based on self-adaptive FEM

Azimuth electromagnetic wave is a new type of electromagnetic prospecting technology. It can detect weak electromagnetic wave signal and realize real-time formation conductivity imaging. For effectively optimizing measurement accuracy of azimuth electromagnetic wave imaging tool, the efficient numerical simulation algorithm is required. In this paper, self-adaptive finite element method (FEM) has been used to investigate the azimuth electromagnetic wave logging tool response by adjusting antenna array system in different geological conditions. Numerical simulation examples show the accuracy and efficiency of the method, and provide physical interpretation of amplitude attenuation and phase shift of electromagnetic wave signal. Meanwhile, the high-accuracy numerical simulation results have great value to azimuth electromagnetic wave imaging tool calibration and data interpretation.

A new stationary droplet evaporation model and its validation

The liquid droplet evaporation character is important for not only combustion chamber design process but also high-accuracy spray combustion simulation. In this paper, the suspended droplets’ evaporation character was measured in a quiescent high-temperature environment by micro high-speed camera system. The gasoline and kerosene experimental results are consistent with the reference data. Methanol, common kerosene and aviation kerosene droplet evaporation characteristics, as well as their evaporation rate changing with temperature, were obtained. The evaporation rate experimental data were compared with the prediction result of Ranz-Marshall boiling temperature model (RMB), Ranz-Marshall low-temperature model (RML), drift flux model (DFM), mass analogy model (MAM), and stagnant film model (SFM). The disparity between the experimental data and the model prediction results was mainly caused by the neglect of the natural convection effect, which was never introduced into the droplet evaporation concept. A new droplet evaporation model with consideration of natural convection buoyancy force effect was proposed in this paper. Under the experimental conditions in this paper, the calculation results of the new droplet evaporation model were agreed with the experimental data for kerosene, methanol and other fuels, with less than 20% relative deviations. The relative deviations between the new evaporation model predictions for kerosene and the experimental data from the references were within 10%.

Simulating electric field interactions with polar molecules using spectroscopic databases

Ro-vibrational Stark-associated phenomena of small polyatomic molecules are modelled using extensive spectroscopic data generated as part of the ExoMol project. The external field Hamiltonian is built from the computed ro-vibrational line list of the molecule in question. The Hamiltonian we propose is general and suitable for any polar molecule in the presence of an electric field. By exploiting precomputed data, the often prohibitively expensive computations associated with high accuracy simulations of molecule-field interactions are avoided. Applications to strong terahertz field-induced ro-vibrational dynamics of PH3 and NH3, and spontaneous emission data for optoelectrical Sisyphus cooling of H2CO and CH3Cl are discussed.

A High-Order Time Domain Discontinuous Galerkin Method with Orthogonal Tetrahedral Basis for Electromagnetic Simulations in 3-D Heterogeneous Conductive Media

AbstractWe present a high-order discontinuous Galerkin (DG) method for the time domain Maxwell's equations in three-dimensional heterogeneous media. New hierarchical orthonormal basis functions on unstructured tetrahedral meshes are used for spatial discretization while Runge-Kutta methods for time discretization. A uniaxial perfectly matched layer (UPML) is employed to terminate the computational domain. Exponential convergence with respect to the order of the basis functions is observed and large parallel speedup is obtained for a plane-wave scattering model. The rapid decay of the out-going wave in the UPML is shown in a dipole radiation simulation. Moreover, the low frequency electromagnetic fields excited by a horizontal electric dipole (HED) and a vertical magnetic dipole (VMD) over a layered conductive half-space and a high frequency ground penetrating radar (GPR) detection for an underground structure are investigated, showing the high accuracy and broadband simulation capability of the proposed method.

Aeroacoustic source mechanisms of a wavy leading edge undergoing vortical disturbances

High-accuracy numerical simulations are performed to study aeroacoustic source mechanisms of wavy leading edges (WLEs) on a thin aerofoil undergoing vortical disturbances. This canonical study is based on a prescribed spanwise vortex travelling downstream and creating secondary vortices as it passes through the aerofoil’s leading edge. The primary aim of the study is to precisely understand the relationships between the vortex-induced velocity perturbation and the wall pressure fluctuation on the WLE geometry. It is observed that by increasing the size (amplitude) of the WLE the source strength at the peak region is reduced rapidly to a certain point, followed by a saturation stage, while at the root (trough) it remains fairly consistent regardless of the WLE size. This observation is demonstrated to be the consequence of three-dimensional vortex dynamics taking place along the WLE. One of the most profound features is that a system of horseshoe-like secondary vortices are created from the WLE peak region upon the impingement of the prescribed vortex. It is found that the horseshoe vortices produce a significantly non-uniform velocity perturbation in front of the WLE leading to the disparity in the source characteristics between the peak and root. The alterations to the impinging velocity perturbation are carefully analysed and related to the wall pressure fluctuation in this study. In addition, a semi-analytic model based on Biot–Savart’s law is developed to better understand and explain the role of the horseshoe vortex systems and the source mechanisms.

DYNAMICS OF TIDALLY CAPTURED PLANETS IN THE GALACTIC CENTER

ABSTRACT Recent observations suggest ongoing planet formation in the innermost parsec of the Galactic center. The supermassive black hole (SMBH) might strip planets or planetary embryos from their parent star, bringing them close enough to be tidally disrupted. Photoevaporation by the ultraviolet field of young stars, combined with ongoing tidal disruption, could enhance the near-infrared luminosity of such starless planets, making their detection possible even with current facilities. In this paper, we investigate the chance of planet tidal captures by means of high-accuracy N-body simulations exploiting Mikkola's algorithmic regularization. We consider both planets lying in the clockwise (CW) disk and planets initially bound to the S-stars. We show that tidally captured planets remain on orbits close to those of their parent star. Moreover, the semimajor axis of the planetary orbit can be predicted by simple analytic assumptions in the case of prograde orbits. We find that starless planets that were initially bound to CW disk stars have mild eccentricities and tend to remain in the CW disk. However, we speculate that angular momentum diffusion and scattering by other young stars in the CW disk might bring starless planets into orbits with low angular momentum. In contrast, planets initially bound to S-stars are captured by the SMBH on highly eccentric orbits, matching the orbital properties of the clouds G1 and G2. Our predictions apply not only to planets but also to low-mass stars initially bound to the S-stars and tidally captured by the SMBH.

Growth rates of dry thermal oxidation of 4H-silicon carbide

We provide a full set of growth rate coefficients to enable high-accuracy two- and three-dimensional simulations of dry thermal oxidation of 4H-silicon carbide. The available models are insufficient for the simulation of complex multi-dimensional structures, as they are unable to predict oxidation for arbitrary crystal directions because of the insufficient growth rate coefficients. By investigating time-dependent dry thermal oxidation kinetics, we obtain temperature-dependent growth rate coefficients for surfaces with different crystal orientations. We fit experimental data using an empirical relation to obtain the oxidation growth rate parameters. Time-dependent oxide thicknesses at various temperatures are taken from published experimental findings. We discuss the oxidation rate parameters in terms of surface orientation and oxidation temperature. Additionally, we fit the obtained temperature-dependent growth rate coefficients using the Arrhenius equation to obtain activation energies and pre-exponential factors for the four crystal orientations. The thereby obtained parameters are essential for enabling high-accuracy simulations of dry thermal oxidation and can be directly used to augment multi-dimensional process simulations.

Land use scenarios and projections simulation using an integrated GIS cellular automata algorithms

Over the years, urban growth models have proven to be effective in describing and estimating urban development and have consequently proven to be valuable for informed urban planning decision. Therefore, this paper investigates the implementation of an urban growth Cellular automata (CA) model using a GIS platform as a support tool for city planners, economists, urban ecologists and resource managers to help them establish decision making strategies and planning towards urban sustainable development. The area used as a test case is the River Shannon Basin in Ireland. This paper investigates the spatio-temporally varying effects of urbanization using a combined method of CA and GIS rasterization. The results generated from Cellular automata model indicated that the historical urban growth patterns in the River Shannon Basin area, in considerable part, be affected by distance to district centres, distance to roads, slope, neighbourhood effect, population density, and environmental factors with relatively high levels of explanation of the spatial variability. The optimal factors and the relative importance of the driving factors varied over time, thus, providing a valuable insight into the urban growth process. The developed model for Shannon catchment has been calibrated, validated, and used for predicting the future land use scenarios for the future time intervals 2020, 2050 and 2080. By involving natural and socioeconomic variables, the developed Cellular automata (CA) model had proved to be able to reproduce the historical urban growth process and assess the consequence of future urban growth. This paper presented as a novel application to the integrated CA-GIS model using a complicated land use dynamic system for Shannon catchment. The major conclusion from this paper was that land use simulation and projection without GIS rasterization formats cannot perform a multi-class, multi factors analysis which makes high accuracy simulation is impossible.

A high-accuracy Eulerian gyrokinetic solver for collisional plasmas

We describe a new approach to solve the electromagnetic gyrokinetic equations which is optimized for accurate treatment of multispecies Fokker–Planck collisions including both pitch-angle and energy diffusion. The new algorithm is spectral/pseudospectral in four of the five phase space dimensions, and in the fieldline direction a novel 5th-order conservative upwind scheme is used to permit high-accuracy electromagnetic simulation even in the limit of very high plasma β and vanishingly small perpendicular wavenumber, k⊥→0. To our knowledge, this is the first pseudospectral implementation of the collision operator in a gyrokinetic code. We show that the new solver agrees closely with GYRO in the limit of weak Lorentz collisions, but gives a significantly more realistic description of collisions at high collision frequency. The numerical methods are also designed to be efficient and scalable for multiscale simulations that treat ion-scale and electron–scale turbulence simultaneously.

Numerical analysis on the effect of angle of attack on evaluating radio-frequency blackout in atmospheric reentry

A three-dimensional numerical simulation model that considers the effect of the angle of attack was developed to evaluate plasma flows around reentry vehicles. In this simulation model, thermochemical nonequilibrium of flowfields is considered by using a four-temperature model for high-accuracy simulations. Numerical simulations were performed for the orbital reentry experiment of the Japan Aerospace Exploration Agency, and the results were compared with experimental data to validate the simulation model. A comparison of measured and predicted results showed good agreement. Moreover, to evaluate the effect of the angle of attack, we performed numerical simulations around the Atmospheric Reentry Demonstrator of the European Space Agency by using an axisymmetric model and a three-dimensional model. Although there were no differences in the flowfields in the shock layer between the results of the axisymmetric and the three-dimensional models, the formation of the electron number density, which is an important parameter in evaluating radio-frequency blackout, was greatly changed in the wake region when a non-zero angle of attack was considered. Additionally, the number of altitudes at which radio-frequency blackout was predicted in the numerical simulations declined when using the three-dimensional model for considering the angle of attack.

Accuracy of binary black hole waveform models for aligned-spin binaries

Coalescing binary black holes are among the primary science targets for second generation ground-based gravitational wave (GW) detectors. Reliable GW models are central to detection of such systems and subsequent parameter estimation. This paper performs a comprehensive analysis of the accuracy of recent waveform models for binary black holes with aligned spins, utilizing a new set of $84$ high-accuracy numerical relativity simulations. Our analysis covers comparable mass binaries ($1\le m_1/m_2\le 3$), and samples independently both black hole spins up to dimensionless spin-magnitude of $0.9$ for equal-mass binaries and $0.85$ for unequal mass binaries. Furthermore, we focus on the high-mass regime (total mass $\gtrsim 50M_\odot$). The two most recent waveform models considered (PhenomD and SEOBNRv2) both perform very well for signal detection, losing less than 0.5\% of the recoverable signal-to-noise ratio $\rho$, except that SEOBNRv2's efficiency drops mildly for both black hole spins aligned with large magnitude. For parameter estimation, modeling inaccuracies of SEOBNRv2 are found to be smaller than systematic uncertainties for moderately strong GW events up to roughly $\rho\lesssim 15$. PhenomD's modeling errors are found to be smaller than SEOBNRv2's, and are generally irrelevant for $\rho\lesssim 20$. Both models' accuracy deteriorates with increased mass-ratio, and when at least one black hole spin is large and aligned. The SEOBNRv2 model shows a pronounced disagreement with the numerical relativity simulation in the merger phase, for unequal masses and simultaneously both black hole spins very large and aligned. Two older waveform models (PhenomC and SEOBNRv1) are found to be distinctly less accurate than the more recent PhenomD and SEOBNRv2 models. Finally, we quantify the bias expected from all GW models during parameter estimation for recovery of binary's masses and spins.

Star–disc interaction in galactic nuclei: orbits and rates of accreted stars

We examine the effect of an accretion disc on the orbits of stars in the central star cluster surrounding a central massive black hole by performing a suite of 39 high-accuracy direct N-body simulations using state-of-the art software and accelerator hardware, with particle numbers up to 128k. The primary focus is on the accretion rate of stars by the black hole (equivalent to their tidal disruption rate for black holes in the small to medium mass range) and the eccentricity distribution of these stars. Our simulations vary not only the particle number, but disc model (two models examined), spatial resolution at the centre (characterised by the numerical accretion radius) and softening length. The large parameter range and physically realistic modelling allow us for the first time to confidently extrapolate these results to real galactic centres. While in a real galactic centre both particle number and accretion radius differ by a few orders of magnitude from our models, which are constrained by numerical capability, we find that the stellar accretion rate converges for models with N > 32k. The eccentricity distribution of accreted stars, however, does not converge. We find that there are two competing effects at work when improving the resolution: larger particle number leads to a smaller fraction of stars accreted on nearly-circular orbits, while higher spatial resolution increases this fraction. We scale our simulations to some nearby galaxies and find that the expected boost in stellar accretion (or tidal disruption, which could be observed as X-ray flares) in the presence of a gas disc is about a factor of 10. Even with this boost, the accretion of mass from stars is still a factor of ~ 100 slower than the accretion of gas from the disc. Thus, it seems accretion of stars is not a major contributor to black hole mass growth.

Development of a flow based dynamic gridding approach for fluid flow modeling in heterogeneous reservoirs

The non-uniform flow based gridding is a well-known approach to create coarse-scale dynamic model to obtain results with high accuracy and low computation cost. In this approach, the grid refinement is performed only in the flow feature regions. Since the flow features will change during the reservoir life, the dynamic gridding method makes it possible to capture the accuracy. In this study, the combination of the grid generation and the reservoir simulation sciences has been used to create the coarse-scale dynamic mesh model with high accuracy and low simulation running time. In this model, the mesh will be updated based on the dynamic interest regions during the simulation time. The simulation results of the presented methodology have been compared with the conventional static gridding models and fine-scale models for oil–water and gas–water flows in the heterogeneous oil and gas reservoirs.

Integrated control design for driver assistance systems based on LPV methods

ABSTRACTThe paper proposes a control design method for a driver assistance system. In the operation of the system, a predefined trajectory required by the driver with a steering command is followed. During manoeuvres the control system generates differential brake moment and the auxiliary front-wheel steering angle and changes the camber angles of the wheels in order to improve the tracking of the road trajectory. The performance specifications are guaranteed by the local controllers, i.e. the brake, the steering, and the suspension systems, while the coordination of these components is provided by the supervisor. The advantage of this architecture is that local controllers are designed independently, which is ensured by the fact that the monitoring signals are taken into consideration in the formalisation of their performance specifications. The fault-tolerant control can be achieved by incorporating the detected fault signals in their performance specifications. The control system also uses a driver model, with which the reference signal can be generated. In the control design, the parameter-dependent linear parameter-varyingmethod, which meets the performance specifications, is used. The operation of the control system is illustrated through different normal and emergency vehicle manoeuvres with a high-accuracy simulation software.

Third-order symplectic integration method with inverse time dispersion transform for long-term simulation

The symplectic integration method is popular in high-accuracy numerical simulations when discretizing temporal derivatives; however, it still suffers from time-dispersion error when the temporal interval is coarse, especially for long-term simulations and large-scale models. We employ the inverse time dispersion transform (ITDT) to the third-order symplectic integration method to reduce the time-dispersion error. First, we adopt the pseudospectral algorithm for the spatial discretization and the third-order symplectic integration method for the temporal discretization. Then, we apply the ITDT to eliminate time-dispersion error from the synthetic data. As a post-processing method, the ITDT can be easily cascaded in traditional numerical simulations. We implement the ITDT in one typical exiting third-order symplectic scheme and compare its performances with the performances of the conventional second-order scheme and the rapid expansion method. Theoretical analyses and numerical experiments show that the ITDT can significantly reduce the time-dispersion error, especially for long travel times. The implementation of the ITDT requires some additional computations on correcting the time-dispersion error, but it allows us to use the maximum temporal interval under stability conditions; thus, its final computational efficiency would be higher than that of the traditional symplectic integration method for long-term simulations. With the aid of the ITDT, we can obtain much more accurate simulation results but with a lower computational cost. We use the inverse time dispersion transform to the 3rd-order symplectic integration.It can greatly reduce the time-dispersion error, especially for long travel times.It is superior to the conventional 2nd- and high-order finite-difference methods.It allows the maximum temporal interval under stability conditions thus is efficient.We can obtain more accurate simulation results but with a lower computational cost.