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All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Smoothed particle hydrodynamics non-Newtonian model for ice-sheet and ice-shelf dynamics

Mathematical modeling of ice sheets is complicated by the non-linearity of the governing equations and boundary conditions. Standard grid-based methods require complex front tracking techniques and have limited capability to handle large material deformations and abrupt changes in bottom topography. As a consequence, numerical methods are usually restricted to shallow ice sheet and ice shelf approximations. We propose a new smoothed particle hydrodynamics (SPH) non-Newtonian model for coupled ice sheet and ice shelf dynamics. SPH, a fully Lagrangian particle method, is highly scalable and its Lagrangian nature and meshless discretization are well suited to the simulation of free surface flows, large material deformation, and material fragmentation. In this paper, SPH is used to study 3D ice sheet/ice shelf behavior, and the dynamics of the grounding line. The steady state position of the grounding line obtained from SPH simulations is in good agreement with laboratory observations for a wide range of simulated bedrock slopes, and density ratios, similar to those of ice and sea water. The numerical accuracy of the SPH algorithm is verif;ed by simulating Poiseuille flow, plane shear flow with free surface and the propagation of a blob of ice along a horizontal surface. In the laboratory experiment, the ice was represented with a viscous Newtonian fluid. In the present work, however, the ice is modeled as both viscous Newtonian fluid and non-Newtonian fluid, such that the effect of non-Newtonian rheology on the dynamics of grounding line was examined. The non-Newtonian constitutive relation is prescribed to be Glen’s law for the creep of polycrystalline ice. A V-shaped bedrock ramp is further introduced to model the real geometry of bedrock slope.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

A DENSITY-INDEPENDENT FORMULATION OF SMOOTHED PARTICLE HYDRODYNAMICS

The standard formulation of the smoothed particle hydrodynamics (SPH) assumes that the local density distribution is differentiable. This assumption is used to derive the spatial derivatives of other quantities. However, this assumption breaks down at the contact discontinuity. At the contact discontinuity, the density of the low-density side is overestimated while that of the high-density side is underestimated. As a result, the pressure of the low-density (high-density) side is overestimated (underestimated). Thus, unphysical repulsive force appears at the contact discontinuity, resulting in the effective surface tension. This tension suppresses fluid instabilities. In this paper, we present a new formulation of SPH, which does not require the differentiability of density. Instead of the mass density, we adopt the internal energy density (pressure) and its arbitrary function, which are smoothed quantities at the contact discontinuity, as the volume element used for the kernel integration. We call this new formulation density-independent SPH (DISPH). It handles the contact discontinuity without numerical problems. The results of standard tests such as the shock tube, Kelvin-Helmholtz and Rayleigh-Taylor instabilities, point-like explosion, and blob tests are all very favorable to DISPH. We conclude that DISPH solved most of the known difficulties of the standard SPH, without introducing additional numerical diffusion or breaking the exact force symmetry or energy conservation. Our new SPH includes the formulation proposed by Ritchie and Thomas as a special case. Our formulation can be extended to handle a non-ideal gas easily.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Does Explosive Nuclear Burning Occur in Tidal Disruption Events of White Dwarfs by Intermediate-mass Black Holes?

We investigate nucleosynthesis in tidal disruption events (TDEs) of white dwarfs (WDs) by intermediate-mass black holes. We consider various types of WDs with different masses and compositions by means of three-dimensional (3D) smoothed particle hydrodynamics (SPH) simulations. We model these WDs with different numbers of SPH particles, N , from a few 10{sup 4} to a few 10{sup 7} in order to check mass resolution convergence, where SPH simulations with N > 10{sup 7} (or a space resolution of several 10{sup 6} cm) have unprecedentedly high resolution in this kind of simulation. We find that nuclear reactions become less active with increasing N and that these nuclear reactions are excited by spurious heating due to low resolution. Moreover, we find no shock wave generation. In order to investigate the reason for the absence of a shock wave, we additionally perform one-dimensional (1D) SPH and mesh-based simulations with a space resolution ranging from 10{sup 4} to 10{sup 7} cm, using a characteristic flow structure extracted from the 3D SPH simulations. We find shock waves in these 1D high-resolution simulations, one of which triggers a detonation wave. However, we must be careful of the fact that, if the shock wave emerged in an outer region, it could not trigger the detonation wave due to low density. Note that the 1D initial conditions lack accuracy to precisely determine where a shock wave emerges. We need to perform 3D simulations with ≲10{sup 6} cm space resolution in order to conclude that WD TDEs become optical transients powered by radioactive nuclei.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Halted-pendulum Relaxation: Application to White Dwarf Binary Initial Data

Studying compact-star binaries and their mergers is integral to determining progenitors for observable transients. Today, compact-star mergers are typically studied via state-of-the-art computational fluid dynamics codes. One such numerical technique, smoothed particle hydrodynamics (SPH), is frequently chosen for its excellent mass, energy, and momentum conservation. The natural treatment of vacuum and the ability to represent highly irregular morphologies make SPH an excellent tool for the study of compact-star binaries and mergers. For many scenarios, including binary systems, the outcome of simulations is only as accurate as the initial conditions. For SPH, it is essential to ensure that the particles are distributed regularly, representing the initial density profile but without long-range correlations. Particle noise in the form of high-frequency local motion and low-frequency global dynamics must be damped out. Damping the latter can be as computationally intensive as the actual simulation. We discuss a new and straightforward relaxation method, halted-pendulum relaxation (HPR), to remove global oscillation modes of SPH particle configurations. In combination with effective external potentials representing gravitational and orbital forces, we show that HPR has an excellent performance in efficiently relaxing SPH particles to the desired density distribution and removing global oscillation modes. We compare the method to frequently used relaxation approaches and test it on a white dwarf binary model at its Roche-lobe overflow limit. We highlight the importance of our method in achieving accurate initial conditions and its effect on achieving circular orbits and realistic accretion rates when compared with other general relaxation methods.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Hybrid super homogenization and discontinuity factor method for continuous finite element diffusion

This paper presents a novel homogenization equivalence technique aiming to simultaneously leveragethe simplicity of the Super Homogenization (SPH) method to reproduce reference reaction rates andthe ability to preserve reference leakage rates at desired surfaces through Discontinuity Factors (DF).The need for this new class of methods arises from the inability of the current state-of-the-art SPH technology to properly reproduce the reactor multiplication factor for problems with significant leakage. This work shows that this defect lies in the use of normalization factors in the SPH algorithm: while they are necessary with purely reflecting problems to ensure uniqueness of the solution, they introduce homogenization inconsistencies if at least one vacuum boundary condition is present. Two solutions to this problem are presented in this work: (i) to simply remove the normalization factor or (ii) to introduce additional degrees of freedom in the form of DFs in such a way that the normalization factors can still constrain the problem. While the former clearly offers unrivaled simplicity and can lead to very satisfactory results for leakage-dominated cores or if spatial restriction of the SPH regions is applied – as demonstrated for the High Temperature Test Reactor, the latter is more robust and does not require to scale the fission terms with the reference eigenvalue.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

Multiscale Universal Interface: A concurrent framework for coupling heterogeneous solvers

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

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Smoothed Particle Hydrodynamics and its applications for multiphase flow and reactive transport in porous media

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and Advection-Diffusion-Reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.

Tartakovsky, Alexandre M.↗
DOE OSTI2016

Intercomparison of 3D pore-scale flow and solute transport simulation methods

Multiple numerical approaches have been developed to simulate porous media fluid flow and solute transport at the pore scale. These include methods that 1) explicitly model the three-dimensional geometry of pore spaces and 2) those that conceptualize the pore space as a topologically consistent set of stylized pore bodies and pore throats. In previous work we validated a model of class 1, based on direct numerical simulation using computational fluid dynamics (CFD) codes, against magnetic resonance velocimetry (MRV) measurements of pore-scale velocities. Here we expand that validation to include additional models of class 1 based on the immersed-boundary method (IMB), lattice Boltzmann method (LBM), smoothed particle hydrodynamics (SPH), as well as a model of class 2 (a pore-network model or PNM). The PNM approach used in the current study was recently improved and demonstrated to accurately simulate solute transport in a two-dimensional experiment. While the PNM approach is computationally much less demanding than direct numerical simulation methods, the effect of conceptualizing complex three-dimensional pore geometries on solute transport in the manner of PNMs has not been fully determined. We apply all four approaches (CFD, LBM, SPH and PNM) to simulate pore-scale velocity distributions and nonreactive solute transport, and intercompare the model results with previously reported experimental observations. Experimental observations are limited to measured pore-scale velocities, so solute transport comparisons are made only among the various models. Comparisons are drawn both in terms of macroscopic variables (e.g., permeability, solute breakthrough curves) and microscopic variables (e.g., local velocities and concentrations).

computational fluid dynamics↗
DOE OSTI2024

A GPU accelerated mixed-precision Smoothed Particle Hydrodynamics framework with cell-based relative coordinates

Smoothed Particle Hydrodynamics (SPH) is essential for modeling complex large-deformation problems across various applications, requiring significant computational power. A major portion of SPH computation time is dedicated to the Nearest Neighboring Particle Search (NNPS) process. While advanced NNPS algorithms have been developed to enhance SPH efficiency, the potential efficiency gains from modern computation hardware remain underexplored. Here, this study investigates the impact of GPU parallel architecture, low-precision computing on GPUs, and GPU memory management on NNPS efficiency. Our approach employs a GPU-accelerated mixed-precision SPH framework, utilizing low precision float-point 16 (FP16) for NNPS while maintaining high precision for other components. To ensure FP16 accuracy in NNPS, we introduce a Relative Coordinated-based Link List (RCLL) algorithm, storing FP16 relative coordinates of particles within background cells. Our testing results show three significant speedup rounds for CPU-based NNPS algorithms. The first comes from parallel GPU computations, with up to a 1000x efficiency gain. The second is achieved through low-precision GPU computing, where the proposed FP16-based RCLL algorithm offers a 1.5x efficiency improvement over the FP64-based approach on GPUs. By optimizing GPU memory bandwidth utilization, the efficiency of the FP16 RCLL algorithm can be further boosted by 2.7x, as demonstrated in an example with 1 million particles. Our code is released at https://github.com/pnnl/lpNNPS4SPH.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

We present an efficient implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The I2SPH's accuracy and convergence are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Pan, Wenxiao↗
DOE OSTI2022

Reticular chemistry for the rational design of mechanically robust mesoporous merged-net metal-organic frameworks

Access to metal-organic frameworks (MOFs) with enhanced mechanical stability is key to their successful deployment in practical applications. However, the high porosity of the material often affects mechanical stability. In this article, to achieve highly porous MOFs with enhanced mechanical stability, we explored the merged-net approach where two relatively fragile frameworks were merged into a robust MOF structure. We demonstrate the effectiveness of this approach by computationally evaluating mechanical properties of sph-MOFs with varying lengths of linkers. Prominently, we pinpoint the significance of triangular rigidity on the robustness of large-pore MOFs and, subsequently, designed and synthesized a rare earth (RE)-based RE-sph-MOF-5 by the reticulation of hexanuclear RE clusters, tritopic linkers, and unprecedentedly large planar hexatopic linkers containing 19 phenyl rings. The mechanical properties of sph-MOFs were characterized and quantified using amplitude-frequency modulation (AM-FM) bimodal atomic force microscopy (AFM) analyses. Markedly, the mesoporous RE-sph-MOF-5 expresses high mechanical stability despite its large mesoporous cavities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Electronic Structure, Optical Properties, and Photoelectrochemical Activity of Sn-Doped Fe 2 O 3 Thin Films

Hematite (Fe 2 O 3 ) is a well-known oxide semiconductor suitable for photoelectrochemical (PEC) water splitting and industry gas sensing. It is widely known that Sn doping of Fe 2 O 3 can enhance the device performance, yet the underlying mechanism remains elusive. In this work, we determine the relationship between electronic structure, optical properties and PEC activity of Sn doped Fe 2 O 3 by studying highly crystalline, well-controlled thin films prepared by pulsed laser deposition (PLD). We show that Sn doping substantially increases the n-type conductivity of Fe 2 O 3 , and the conduction mechanism is better described by small-polaron hoping (SPH) model. Only 0.2% Sn doping significantly reduce the activation energy barrier for SPH conduction from at least 0.5 eV for undoped Fe 2 O 3 to 0.14 eV for doped ones. A combination of X-ray photoemission, X-ray absorption spectroscopy and DFT calculations reveals the Fermi level gradually shifts toward the conduction band minimum with Sn doping. A localized Fe 2+ like gap state is observed at the top of valence band, accounting for the SPH conduction. Interestingly, in contrast to the literature, we find that only 0.2% Sn doping in Fe 2 O 3 significantly improves the PEC activity, while more Sn decreases it. The improved PEC activity is partially attributed to an increased band bending potential which facilitates the charge separation at space charge region. The reduced activation energy barrier for SPH will facilitate the transport of photo-excited carriers for the enhanced PEC, which is of interest for further carrier dynamics study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

NUMERICAL CONVERGENCE IN SMOOTHED PARTICLE HYDRODYNAMICS

We study the convergence properties of smoothed particle hydrodynamics (SPH) using numerical tests and simple analytic considerations. Our analysis shows that formal numerical convergence is possible in SPH only in the joint limit N → ∞, h → 0, and N{sub nb} → ∞, where N is the total number of particles, h is the smoothing length, and N{sub nb} is the number of neighbor particles within the smoothing volume used to compute smoothed estimates. Previous work has generally assumed that the conditions N → ∞ and h → 0 are sufficient to achieve convergence, while holding N{sub nb} fixed. We demonstrate that if N{sub nb} is held fixed as the resolution is increased, there will be a residual source of error that does not vanish as N → ∞ and h → 0. Formal numerical convergence in SPH is possible only if N{sub nb} is increased systematically as the resolution is improved. Using analytic arguments, we derive an optimal compromise scaling for N{sub nb} by requiring that this source of error balance that present in the smoothing procedure. For typical choices of the smoothing kernel, we find N{sub nb} ∝N {sup 0.5}. This means that if SPH is to be used as a numerically convergent method, the required computational cost does not scale with particle number as O(N), but rather as O(N {sup 1} {sup +} {sup δ}), where δ ≈ 0.5, with a weak dependence on the form of the smoothing kernel.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smooth particle hydrodynamics

We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.

Pan, Wenxiao↗
DOE OSTI2016

Comparing simulations of AGN feedback

We perform adaptive mesh refinement (AMR) and smoothed particle hydrodynamics (SPH) cosmological zoom simulations of a region around a forming galaxy cluster, comparing the ability of the methods to handle successively more complex baryonic physics. In the simplest, non-radiative case, the two methods are in good agreement with each other, but the SPH simulations generate central cores with slightly lower entropies and virial shocks at slightly larger radii, consistent with what has been seen in previous studies. The inclusion of radiative cooling, star formation, and stellar feedback leads to much larger differences between the two methods. Most dramatically, at z=5, rapid cooling in the AMR case moves the accretion shock to well within the virial radius, while this shock remains near the virial radius in the SPH case, due to excess heating, coupled with poorer capturing of the shock width. On the other hand, the addition of feedback from active galactic nuclei (AGNs) to the simulations results in much better agreement between the methods. For our AGN model, both simulations display halo gas entropies of 100 keV cm{sup 2}, similar decrements in the star formation rate, and a drop in the halo baryon content of roughly 30%. This is consistent with the AGN growth being self-regulated, regardless of the numerical method. However, the simulations with AGN feedback continue to differ in aspects that are not self-regulated, such that in SPH a larger volume of gas is impacted by feedback, and the cluster still has a lower entropy central core.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1993

Smoothed particle hydrodynamics with GRAPE-1A

We describe the implementation of a smoothed particle hydrodynamics (SPH) scheme using GRAPE-1A, a special-purpose processor used for gravitational N-body simulations. The GRAPE-1A calculates the gravitational force exerted on a particle from all other particles in a system, while simultaneously making a list of the nearest neighbors of the particle. It is found that GRAPE-1A accelerates SPH calculations by direct summation by about two orders of magnitudes for a ten thousand-particle simulation. The effective speed is 80 Mflops, which is about 30 percent of the peak speed of GRAPE-1A. Also, in order to investigate the accuracy of GRAPE-SPH, some test simulations were executed. We found that the force and position errors are smaller than those due to representing a fluid by a finite number of particles. The total energy and momentum were conserved within 0.2-0.4 percent and 2-5 x 10 exp -5, respectively, in simulations with several thousand particles. We conclude that GRAPE-SPH is quite effective and sufficiently accurate for self-gravitating hydrodynamics.

Umemura, Masayuki↗
NASA NTRS1994

A comparison of cosmological hydrodynamic codes

We present a detailed comparison of the simulation results of various hydrodynamic codes. Starting with identical initial conditions based on the cold dark matter scenario for the growth of structure, with parameters h = 0.5 Omega = Omega(sub b) = 1, and sigma(sub 8) = 1, we integrate from redshift z = 20 to z = O to determine the physical state within a representative volume of size L(exp 3) where L = 64 h(exp -1) Mpc. Five indenpendent codes are compared: three of them Eulerian mesh-based and two variants of the smooth particle hydrodynamics 'SPH' Lagrangian approach. The Eulerian codes were run at N(exp 3) = (32(exp 3), 64(exp 3), 128(exp 3), and 256(exp 3)) cells, the SPH codes at N(exp 3) = 32(exp 3) and 64(exp 3) particles. Results were then rebinned to a 16(exp 3) grid with the exception that the rebinned data should converge, by all techniques, to a common and correct result as N approaches infinity. We find that global averages of various physical quantities do, as expected, tend to converge in the rebinned model, but that uncertainites in even primitive quantities such as (T), (rho(exp 2))(exp 1/2) persists at the 3%-17% level achieve comparable and satisfactory accuracy for comparable computer time in their treatment of the high-density, high-temeprature regions as measured in the rebinned data; the variance among the five codes (at highest resolution) for the mean temperature (as weighted by rho(exp 2) is only 4.5%. Examined at high resolution we suspect that the density resolution is better in the SPH codes and the thermal accuracy in low-density regions better in the Eulerian codes. In the low-density, low-temperature regions the SPH codes have poor accuracy due to statiscal effects, and the Jameson code gives the temperatures which are too high, due to overuse of artificial viscosity in these high Mach number regions. Overall the comparison allows us to better estimate errors; it points to ways of improving this current generation ofhydrodynamic codes and of suiting their use to problems which exploit their best individual features.

Kang, Hyesung↗
DOE OSTI2021

Latent variable Gaussian process models: A rank‐based analysis and an alternative approach

Abstract Gaussian process (GP) models have been extended to emulate expensive computer simulations with both qualitative/categorical and quantitative/continuous variables. Latent variable (LV) GP models, which have been recently developed to map each qualitative variable to some underlying numerical LVs, have strong physics‐based justification and have achieved promising performance. Two versions use LVs in Cartesian (LV‐Car) space and hyperspherical (LV‐sph) space, respectively. Despite their success, the effects of these different LV structures are still poorly understood. This article illuminates this issue with two contributions. First, we develop a theorem on the effect of the ranks of the qualitative factor correlation matrices of mixed‐variable GP models, from which we conclude that the LV‐sph model restricts the interactions between the input variables and thus restricts the types of response surface data with which the model can be consistent. Second, following a rank‐based perspective like in the theorem, we propose a new alternative model named LV‐mix that combines the LV‐based correlation structures from both LV‐Car and LV‐sph models to achieve better model flexibility than them. Through extensive case studies, we show that LV‐mix achieves higher average accuracy compared with the existing two.

Tao, Siyu↗