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At least 757 records · Page 42

Study on coalescence dynamics of unequal-sized microbubbles captive on solid substrate

The dynamics of bubble coalescence are of importance for a number of industrial processes, in which the size inequality of the parent bubbles plays a significant role in mass transport, topological change and overall motion. In this study, coalescence of unequal-sized microbubbles captive on a solid substrate was observed from cross-section view using synchrotron high-speed imaging technique and a microfluidic gas generation device. The bridging neck growth and surface wave propagation at the early stage of coalescence were investigated by experimental and numerical methods. The results show that theoretical half-power-law of neck growth rate is still valid when viscous effect is neglected. However, the inertial-capillary time scale is associated with the initial radius of the smaller parent microbubble. Furthermore the surface wave propagation rate on the larger parent microbubble is proportional to the inertial-capillary time scale.

42 ENGINEERING↗

CG-Kit: Code Generation Toolkit for performant and maintainable variants of source code applied to Flash-X hydrodynamics simulations

CG-Kit is a new Code Generation tool-Kit that we have developed as a part of the solution for portability and maintainability for multiphysics computing applications. The development of CG-Kit is rooted in the urgent need created by the shifting landscape of high-performance computing platforms and the algorithmic complexities of a particular large-scale multiphysics application: Flash-X. To efficiently use computing resources on a heterogeneous node, an application must have a map of computation to resources and a mechanism to move the data and computation to the resources according to the map. Most existing performance portability solutions are focussed on abstracting the expression of computations so that a unified source code can be specialized to run on different resources. However, such an approach is insufficient for a code like Flash-X, which has a multitude of code components that can be assembled in various permutations and combinations to form different instances of applications. Similar challenges apply to any code that has composability, where a single specified way of apportioning work among devices may not be optimal. Additionally, use cases arise where the optimal control flow of computation may differ for different devices while the underlying numerics remain identical. This combination leads to unique challenges including handling an existing large code base in Fortran and/or C/C++, subdivision of code into a great variety of units supporting a wide range of physics and numerical methods, different parallelization techniques for distributed and shared memory systems and accelerator devices, and heterogeneity of computing platforms requiring coexisting variants of parallel algorithms. All of these challenges demand that scientific software developers apply existing knowledge about domain applications, algorithms, and computing platforms to determine custom abstractions and granularity for code generation. There is a critical lack of tools to tackle those problems. CG-Kit is designed to fill this gap by providing a user with the ability to express their desired control flow and computation-to-resource map in the form a pseudocode-like recipe. It consists of standalone tools that can be combined into highly specific and, we argue, highly effective portability and maintainability toolchains. Here we present the design of our new tools: parametrized source trees, control flow graphs, and recipes. The tools are implemented in Python. They are agnostic to the programming language of the source code targeted for code generation. In conclusion, we demonstrate the capabilities of the toolkit with two examples, first, multithreaded variants of the basic AXPY operation, and second, variants of parallel algorithms within a hydrodynamics solver, called Spark, from Flash-X that operates on block-structured adaptive meshes.

Algorithmic portability↗

Paleotemperatures at the lunar surfaces from open system behavior of cosmogenic 38 Ar and radiogenic 40 Ar

The simultaneous diffusion of both cosmogenic 38 Ar and radiogenic 40 Ar from solid phases is controlled by the thermal conditions of rocks while residing near planetary surfaces. Combined observations of 38 Ar/ 37 Ar and 40 Ar/ 39 Ar ratios during stepwise degassing analyses of neutron-irradiated Apollo samples can distinguish between diffusive loss of Ar due to solar heating of the rocks and that associated with elevated temperatures during or following impact events; the data provide quantitative constraints on the durations and temperatures of each process. From sequentially degassed 38 Ar/ 37 Ar ratios can be calculated a spectrum of apparent 38 Ar exposure ages versus the cumulative release fraction of 37 Ar, which is particularly sensitive to conditions at the lunar surface typically over ~106–108 year timescales. Due to variable proportions of K- and Ca-bearing glass, plagioclase and pyroxene, with variability in the grain sizes of these phases, each sample will have distinct sensitivity to, and therefore different resolving power on, past near-surface thermal conditions. Furthermore, we present the underlying assumptions, and the analytical and numerical methods used to quantify the Ar diffusion kinetics in multi-phase whole-rock analyses that provide these constraints.

58 GEOSCIENCES↗

Growth of Jupiter: Formation in disks of gas and solids and evolution to the present epoch

The formation of Jupiter is modeled via core-nucleated accretion, and the planet's evolution is simulated up to the present epoch. Throughout the phases when the planet acquires most of its heavy-element content, the calculation of solids' accretion accounts for interactions with an evolving disk of planetesimals. The phase of growth from an embryo of a few hundred kilometers in radius until the time when the accretion of gas overtakes solids' accretion was presented by D'Angelo et al., and the same numerical methods are applied here. Those calculations followed the formation for about 4 × 10 5 years, until the epoch when the heavy-element and hydrogen/helium masses were $M_Z ≈ 7.3$ and $M_{XY} ≈ 0.15$ Earth's masses ($M_⊕$), respectively, and $\dot {M} _{XY} ≈ $$\dot {M}_Z$. In this work, the calculation is continued through the phase when $M_{XY}$ grows to equal $M_Z$ , at which age, about 2.4 × 10 6 years, the total mass of the planet is $M_p ≈ 20 M_⊕$. About 9 × 10 5 years later, $M_p$ is approximately $60 M_⊕$ and $M_Z ≈ 16 M_⊕$, three-quarters of which are delivered by planetesimals larger than 10 km in radius. Around this epoch, the contraction of the envelope dictates gas accretion rates a few times 10 –3 $M_⊕$ per year, initiating the regime of disk-limited accretion, whereby the planet can accrete all the gas provided by the disk, and its evolution is therefore tied to disk's evolution. Growth is continued by constructing simplified models of protosolar accretion disks that evolve through viscous diffusion, winds, and accretion on the planet. Jupiter's formation ends after ≈ 3.4–4.2 Myr, depending on the applied disk viscosity parameter, when nebula gas disperses. The young Jupiter is 4.5–5.5 times as voluminous as it is presently and thousands of times as luminous, ~10 –5 $L_⊙$. The heavy-element mass is ≈ 20 $M_⊕$. The evolution proceeds through the cooling and contraction phase, in isolation except for solar irradiation. After 4570 Myr, the age of the solar system, radius and luminosity of the planet are within 10$\%$ of current values, accounting also for uncertainties in the power absorbed from the Sun. During formation, and soon thereafter, the planet exhibits features, e.g., luminosity and effective temperature, that may probe aspects of the latter stages of formation, if observable. These possibly distinctive features, however, seem to disappear within a few tens of Myr.

79 ASTRONOMY AND ASTROPHYSICS↗

Heat transfer augmentation of natural convection heat sink through notched fin design

A novel notched fin heat sink with a central opening is proposed in the present study to augment the heat transfer performance of the natural convection heat sink under horizontal configuration. Thermal and airflow behavior in the heat sinks were studied using both experimental and numerical methods. The results showed that the performance of the conventional heat sink can be enhanced by optimizing its fin design. The basic heat sink model provided a 17% reduction in thermal resistance when its fin height and fin spacing were doubled, and it was accompanied by a 21% increase in surface area. The heat sink with a notched fin design with a less surface area offered a 13% lower thermal resistance compared to the basic model by entraining more airflow into the interior fin region. Providing a central opening in the notched fin heat sink can further reduce the thermal resistance by about 13%. Further, this study also analyzed the influence of emissivity of the heat sink on natural convection conditions. The findings demonstrated that the heat sink with an emissivity of 0.9 can reduce the thermal resistance by nearly 23% compared to one with an emissivity of 0.15.

42 ENGINEERING↗

Heat transfer and pseudo phase transition for low-Reynolds, mixed-convection channel flow in the supercritical thermodynamic regime

Fluids at supercritical thermodynamic conditions are inherently complex due to the large variations in thermodynamic and transport properties. Multiple recent numerical and experimental investigations indicate ongoing interest for these fluids, especially supercritical CO and supercritical water, for a variety of applications. The potential heat transfer benefits in this regime are directly influenced by the extreme variations in thermodynamic and transport properties, which occur at, and above, the critical point. Limited studies have been conducted for low-Reynolds/intermediate-Rayleigh numbers mixed-convection channel flow of supercritical water, which is the focus of this study. To investigate the thermally driven hydrodynamic instabilities in this regime, we use a high-order fully-implicit numerical method. As expected, in this channel configuration and flow regime, a competition arises between the forced and the natural convection. Buoyancy, driven by the thermal gradient at the wall, pushes the fluid upwards in the channel, while inertial forces drive the fluid from inlet to outlet. We observe significant differences in the heat transfer coefficient between the top and bottom walls of the channel flow, due to natural convection, and unstable plumes. We further quantify the buoyancy forces along the channel flow through evaluation of the Richardson number. Simulations show that with a higher negative Richardson number, there are more unstable structures along the channel, resulting in enhanced mixing. Furthermore, we demonstrate the existence of gas-like, liquid-like, and the possibility of pseudo-two-phase regimes in the supercritical fluid. The pseudo-two-phase regime occurs when the range of fluid temperatures is crossing the pseudo-critical line, also known as the Widom line. The density of the fluid varies significantly near the Widom line, and further influences the natural convection and heat transfer in the flow.

42 ENGINEERING↗

Numerical simulations of a horizontal axis water turbine designed for underwater mooring platforms

In order to extend the operational life of Underwater Moored Platforms (UMPs), a horizontal axis water turbine is designed to supply energy for the UMPs. The turbine, equipped with controllable blades, can be opened to generate power and charge the UMPs in moored state. Three-dimensional Computational Fluid Dynamics (CFD) simulations are performed to study the characteristics of power, thrust and the wake of the turbine. Particularly, the effect of the installation position of the turbine is considered. Simulations are based on the Reynolds Averaged Navier-Stokes (RANS) equations and the shear stress transport k-ω turbulent model is utilized. The numerical method is validated using existing experimental data. The simulation results show that this turbine has a maximum power coefficient of 0.327 when the turbine is installed near the tail of the UMP. The flow structure near the blade and in the wake are also discussed.

13 HYDRO ENERGY↗

A crystal plasticity finite element model embedding strain-rate sensitivities inherent to deformation mechanisms: Application to alloy AZ31

We report the fundamental power-law relationship representing the flow rule in crystal visco-plasticity ensures uniqueness in the selection of slip systems accommodating imposed plastic strain-rates. The power-law relationship also introduces an artificially high strain-rate sensitivity in crystal plasticity simulations, unless a high value of the power-law exponent is used. However, the use of high values for the exponent is limited by numerical tractability. This paper presents a numerical method implemented in a crystal plasticity finite element (CPFE) model for embedding any value of the power-law exponent reflecting the true material strain-rate sensitivity. Importantly, the method does not increase computation time involved in the simulations. The enhanced CPFE model is used to interpret and predict a complex strain-rate sensitive response and microstructural evolution of AZ31 Mg alloy. Measured values of strain-rate sensitivity for slip and twinning modes are used in the simulations. Calculations show that the model successfully captures the phenomena pertaining to the effect of changing applied strain-rate on the mechanical response including flow stress and evolution of texture and twinning for a broad range of strain-rates ranging from 10 -3 s -1 to 10 3 s -1 and loading orientations in tension and compression. It is shown that such predictions are a consequence of not only relative amounts of slip and twinning activities driven by a set of accurately characterized hardening law parameters but also values of the strain-rate sensitivities inherent to individual deformation mechanisms. Besides, the model validates the measured strain-rate dependency of deformation mechanisms while accurately reproducing the mechanical data. Hence, the model can be used to verify and further refine or infer measured strain-rate sensitivity per deformation mechanism by reproducing experimental data.

36 MATERIALS SCIENCE↗

Prediction of the thermal-hydraulic-mechanical response of a geological repository at large scale and sensitivity analyses

To better understand the Thermal-Hydraulic-Mechanical (THM) response of the rock caused by the high-level radioactive waste (HLW) released heat in the Callovo-Oxfordian formation (COx) in the near-field and far-field areas, a series of coupled THM modelling is performed. This study presents a case study based on the French geological repository for HLW (Cigéo project) to better assess modelling of deep geological repositories (DGR) within the DECOVALEX-2019 framework. In this study, the proposed coupled THM model, implemented in the platform of COMSOL, is validated by comparing the modelled THM results for a point heat source in an infinite rock mass with an analytical solution. It is also validated by comparing its thermal component for the Base Case with accurate results calculated using another numerical method. To shorten the calculation time, the DGR is modelled using six cuboid blocks representing 162 HLW cells and only six central HLW cells of interest modelled in detail. This simplification is validated. This model can easily be used to model not only the near-field THM response of the rock but also the far-field THM response. The influence of the boundary conditions applied on the gallery wall, HLW cell walls, and external surfaces of the model and the influence of different vertical dimensions of the geometry are studied. The sensitivity analyses of the THM parameters of COx on the THM response at different locations are performed. Finally, the influence of using a 2-dimensional (2D) model to represent a 3-dimensional (3D) repository is also investigated.

58 GEOSCIENCES↗

Reduced discretization error in HZETRN

The deterministic particle transport code HZETRN is an efficient analysis tool for studying the effects of space radiation on humans, electronics, and shielding materials. In a previous work, numerical methods in the code were reviewed, and new methods were developed that further improved efficiency and reduced overall discretization error. It was also shown that the remaining discretization error could be attributed to low energy light ions (A < 4) with residual ranges smaller than the physical step-size taken by the code. Accurately resolving the spectrum of low energy light particles is important in assessing risk associated with astronaut radiation exposure. In this work, modifications to the light particle transport formalism are presented that accurately resolve the spectrum of low energy light ion target fragments. The modified formalism is shown to significantly reduce overall discretization error and allows a physical approximation to be removed. For typical step-sizes and energy grids used in HZETRN, discretization errors for the revised light particle transport algorithms are shown to be less than 4% for aluminum and water shielding thicknesses as large as 100 g/cm{sup 2} exposed to both solar particle event and galactic cosmic ray environments.

61 RADIATION PROTECTION AND DOSIMETRY↗

Asymptotic Preserving schemes for highly oscillatory Vlasov–Poisson equations

This work is devoted to the numerical simulation of a Vlasov–Poisson model describing a charged particle beam under the action of a rapidly oscillating external field. We construct an Asymptotic Preserving numerical scheme for this kinetic equation in the highly oscillatory limit. This scheme enables to simulate the problem without using any time step refinement technique. Moreover, since our numerical method is not based on the derivation of the simulation of asymptotic models, it works in the regime where the solution does not oscillate rapidly, and in the highly oscillatory regime as well. Our method is based on a “two scale” reformulation of the initial equation, with the introduction of an additional periodic variable.

97 MATHEMATICS AND COMPUTING↗

A discrete geometric approach for simulating the dynamics of thin viscous threads

We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematic constraints linking the centerline's tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistency of the discrete model with the classical, smooth equations for thin threads is established formally. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension.

42 ENGINEERING↗

Tempered fractional calculus

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A probabilistic graphical model based stochastic input model construction

Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A spectral unaveraged algorithm for free electron laser simulations

We propose and discuss a numerical method to model electromagnetic emission from the oscillating relativistic charged particles and its coherent amplification. The developed technique is well suited for free electron laser simulations, but it may also be useful for a wider range of physical problems involving resonant field–particles interactions. The algorithm integrates the unaveraged coupled equations for the particles and the electromagnetic fields in a discrete spectral domain. Using this algorithm, it is possible to perform full three-dimensional or axisymmetric simulations of short-wavelength amplification. In this paper we describe the method, its implementation, and we present examples of free electron laser simulations comparing the results with the ones provided by commonly known free electron laser codes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Certified dual-corrected radiation patterns of phased antenna arrays by offline–online order reduction of finite-element models

This paper presents a fast numerical method for computing certified far-field patterns of phased antenna arrays over broad frequency bands as well as wide ranges of steering and look angles. The proposed scheme combines finite-element analysis, dual-corrected model-order reduction, and empirical interpolation. To assure the reliability of the results, improved a posteriori error bounds for the radiated power and directive gain are derived. Both the reduced-order model and the error-bounds algorithm feature offline–online decomposition. A real-world example is provided to demonstrate the efficiency and accuracy of the suggested approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Accurate derivative evaluation for any Grad–Shafranov solver

We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad–Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of convergence as the solution itself. At the heart of our scheme is an efficient and accurate computation of the Dirichlet to Neumann map through the evaluation of a singular volume integral and the solution to a Fredholm integral equation of the second kind. Our numerical method is particularly useful for magnetic confinement fusion simulations, since it allows the evaluation of quantities such as the magnetic field, the parallel current density and the magnetic curvature with much higher accuracy than has been previously feasible on the affordable coarse grids that are usually implemented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A high-accuracy Eulerian gyrokinetic solver for collisional plasmas

We describe here 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.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗