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DOE OSTI2021

A continuum meshfree method for sandbox-style numerical modeling of accretionary and doubly vergent wedges

Here, in this study, we introduce and utilize GEOSPH, a Lagrangian particle-based continuum Smoothed Particle Hydrodynamics (SPH) code to simulate the deformation of geologic materials in sandbox-style experiments using an elastoplastic constitutive model. Due to the meshfree nature of SPH, our proposed framework is capable of handling the large deformations characteristic of sandbox-style experiments. SPH is also able to capture strain localization and discontinuities, allowing us to resolve faulting patterns emerging in the sandbox experiments. We successfully validate our SPH implementation against the benchmark experiments of Buiter and co-workers, and then apply SPH to understand the deformational processes occurring in doubly vergent orogens resultant from the S-point experimental setup and from finitely high wedge-like indenter backstops of different inclinations. We find that the topographic slope of the prowedge results from the competing processes of vertical uplift due to the indenter and forward thrusting, while the topographic slope of the retrowedge is a product of repeated shallow slope failure. Our findings show that SPH is a promising numerical method which should be added to the current palette of computational tools used by structural geologists for solving problems relating to tectonics and crustal deformation.

58 GEOSCIENCES↗

DOE OSTI2023

SPH modeling of biomass granular flow: Theoretical implementation and experimental validation

The commercialization of biomass-derived energy is impeded by flowability challenges arising from the feeding and handling of granular biomass materials in full-scale biorefineries. To overcome these obstacles, a robust and accurate model to simulate the flow of granular biomass is indispensable. However, conventional mesh-based numerical codes are limited by inherent mesh distortion in simulating large deformation that commonly occurs in granular biomass handling. Here, in this study, we propose a graphics processing unit (GPU)-accelerated meshless Smoothed Particle Hydrodynamics (SPH) code to model the flow of granular biomass materials. A modified void ratio-based mass conversation, a hybrid particle-to-particle/surface frictional boundary treatment, and a hypoplastic constitutive model are implemented. Four numerical examples, an elastic block sliding on inclined planes, sand column collapse, Angle of Repose, and axial compression tests for pine chips, were simulated using the developed SPH code. The results demonstrate good agreement between numerical predictions and analytical and experimental data for all four examples, validating the SPH code and increasing confidence that it can be applied to simulate more complex granular biomass handling processes, such as hopper feeding or auger conveyance.

09 BIOMASS FUELS↗

DOE OSTI2023

Simulating Hydrodynamics in Cosmology with CRK-HACC

Abstract We introduce CRK-HACC, an extension of the Hardware/Hybrid Accelerated Cosmology Code (HACC), to resolve gas hydrodynamics in large-scale structure formation simulations of the universe. The new framework couples the HACC gravitational N -body solver with a modern smoothed-particle hydrodynamics (SPH) approach called conservative reproducing kernel SPH (CRKSPH). CRKSPH utilizes smoothing functions that exactly interpolate linear fields while manifestly preserving conservation laws (momentum, mass, and energy). The CRKSPH method has been incorporated to accurately model baryonic effects in cosmology simulations—an important addition targeting the generation of precise synthetic sky predictions for upcoming observational surveys. CRK-HACC inherits the codesign strategies of the HACC solver and is built to run on modern GPU-accelerated supercomputers. In this work, we summarize the primary solver components and present a number of standard validation tests to demonstrate code accuracy, including idealized hydrodynamic and cosmological setups, as well as self-similarity measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Meshfree simulation and prediction of recrystallized grain size in friction stir processed 316L stainless steel

Friction stir processing (FSP) is a promising solid-phase microstructural modification technique that can repair and enhance damaged stainless steel surfaces exposed to harsh environments. The quality of the repaired material is closely correlated to the recrystallized grain size in the stir zone (SZ), which is influenced by the thermomechanical conditions dictated by FSP process parameters. Thus, establishing a reliable relationship between these parameters and recrystallized grain size in the SZ is crucial for optimizing repair quality. However, existing experimental approaches often rely on indirect temperatures measured far from the SZ, along with rough strain rate estimations, which are imprecise and time-consuming. Meanwhile, existing mesh-based modeling methods usually face numerical challenges when dealing with the large material deformations inherent in FSP. Here, to address these issues, this study introduces a meshfree process model for FSP based on the smoothed particle hydrodynamics (SPH) method, aimed at predicting process conditions under different parameters. The model is validated using experimental data from 11 combinations of tool traverse and rotation speeds on 316 L stainless steel. Correlations between process parameters, material flow, temperature, strain, strain rate, and recrystallized grain size are revealed through SPH simulations and electron backscatter diffraction (EBSD) imaging. The results show that in situ SZ temperatures range from 1071 to 1322°C, which exceed the tool temperature by over 300°C. Furthermore, SZ temperature, strain rate, and grain size increase monotonically with higher tool temperature and faster traverse speed. A relationship is then established between the model-predicted Zener-Hollomon parameter and the recrystallized grain size based on EBSD data, expressed as ln(d) = -0.364 ln(Z) + 14.673. Finally, this relationship exhibits satisfactory accuracy with errors of less than 26.9% in predicting grain sizes at various SZ locations, which offers valuable insights for optimizing FSP repair processes for 316 L stainless steel.

316L stainless steel↗

DOE OSTI2023

Gaussian process hydrodynamics

Abstract We present a Gaussian process (GP) approach, called Gaussian process hydrodynamics (GPH) for approximating the solution to the Euler and Navier-Stokes (NS) equations. Similar to smoothed particle hydrodynamics (SPH), GPH is a Lagrangian particle-based approach that involves the tracking of a finite number of particles transported by a flow. However, these particles do not represent mollified particles of matter but carry discrete/partial information about the continuous flow. Closure is achieved by placing a divergence-free GP prior ξ on the velocity field and conditioning it on the vorticity at the particle locations. Known physics (e.g., the Richardson cascade and velocity increment power laws) is incorporated into the GP prior by using physics-informed additive kernels. This is equivalent to expressing ξ as a sum of independent GPs ξ l , which we call modes, acting at different scales (each mode ξ l self-activates to represent the formation of eddies at the corresponding scales). This approach enables a quantitative analysis of the Richardson cascade through the analysis of the activation of these modes, and enables us to analyze coarse-grain turbulence statistically rather than deterministically. Because GPH is formulated by using the vorticity equations, it does not require solving a pressure equation. By enforcing incompressibility and fluid-structure boundary conditions through the selection of a kernel, GPH requires significantly fewer particles than SPH. Because GPH has a natural probabilistic interpretation, the numerical results come with uncertainty estimates, enabling their incorporation into an uncertainty quantification (UQ) pipeline and adding/removing particles (quanta of information) in an adapted manner. The proposed approach is suitable for analysis because it inherits the complexity of state-of-the-art solvers for dense kernel matrices and results in a natural definition of turbulence as information loss. Numerical experiments support the importance of selecting physics-informed kernels and illustrate the major impact of such kernels on the accuracy and stability. Because the proposed approach uses a Bayesian interpretation, it naturally enables data assimilation and predictions and estimations by mixing simulation data and experimental data.

Mathematics↗

DOE OSTI2020

Simulations of Tidal Disruption Events

Numerical simulations have historically played a major role in understanding the hydrodynamics of the tidal disruption process. Given the complexity of the geometry of the system, the challenges posed by the problem have indeed stimulated much work on the numerical side. Smoothed Particles Hydrodynamics methods, for example, have seen their very first applications in the context of tidal disruption and still play a major role to this day. Likewise, initial attempts at simulating the evolution of the disrupted star with the so-called affine method have been historically very useful. Here, we provide an overview of the numerical techniques used in the field and of their limitations, and summarize the work that has been done to simulate numerically the tidal disruption process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Bipolar planetary nebulae from outflow collimation by common envelope evolution

ABSTRACT The morphology of bipolar planetary nebulae (PNe) can be attributed to interactions between a fast wind from the central engine and the dense toroidal-shaped ejecta left over from common envelope (CE) evolution. Here we use the 3D hydrodynamic adaptive mesh refinement (AMR) code AstroBEAR to study the possibility that bipolar PN outflows can emerge collimated even from an uncollimated spherical wind in the aftermath of a CE event. The output of a single CE simulation via the smoothed particle hydrodynamics (SPH) code phantom serves as the initial conditions. Four cases of winds, all with high enough momenta to account for observed high momenta pre-PN outflows, are injected spherically from the region of the CE binary remnant into the ejecta. We compare cases with two different momenta and cases with no radiative cooling versus application of optically thin emission via a cooling curve to the outflow. Our simulations show that in all cases highly collimated bipolar outflows result from deflection of the spherical wind via the interaction with the CE ejecta. Significant asymmetries between the top and bottom lobes are seen in all cases. The asymmetry is strongest for the lower momentum case with radiative cooling. While real post-CE winds may be aspherical, our models show that collimation via ‘inertial confinement’ will be strong enough to create jet-like outflows even beginning with maximally uncollimated drivers. Our simulations reveal detailed shock structures in the shock-focused inertial confinement (SFIC) model and develop a lens-shaped inner shock that is a new feature of SFIC-driven bipolar lobes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Modelling the Lyman-α forest with Eulerian and SPH hydrodynamical methods

ABSTRACT We compare two state-of-the-art numerical codes to study the overall accuracy in modelling the intergalactic medium and reproducing Lyman-α forest observables for DESI and high-resolution data sets. The codes employ different approaches to solving both gravity and modelling the gas hydrodynamics. The first code, Nyx, solves the Poisson equation using the Particle-Mesh (PM) method and the Euler equations using a finite-volume method. The second code, CRK-HACC , uses a Tree-PM method to solve for gravity, and an improved Lagrangian smoothed particle hydrodynamics (SPH) technique, where fluid elements are modelled with particles, to treat the intergalactic gas. We compare the convergence behaviour of the codes in flux statistics as well as the degree to which the codes agree in the converged limit. We find good agreement overall with differences being less than observational uncertainties, and a particularly notable ≲1 per cent agreement in the 1D flux power spectrum. This agreement was achieved by applying a tessellation methodology for reconstructing the density in CRK-HACC instead of using an SPH kernel as is standard practice. We show that use of the SPH kernel can lead to significant and unnecessary biases in flux statistics; this is especially prominent at high redshifts, z ∼ 5, as the Lyman-α forest mostly comes from lower-density regions that are intrinsically poorly sampled by SPH particles.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Giant Planet Scatterings and Collisions: Hydrodynamics, Merger-Ejection Branching Ratio, and Properties of the Remnants

Planetary systems with sufficiently small orbital spacings can experience planetary mergers and ejections. The branching ratio of mergers vs ejections depends sensitively on the treatment of planetary close encounters. Previous works have adopted a simple “sticky-sphere” prescription, whose validity is questionable. We apply both smoothed particle hydrodynamics and N-body integrations to investigate the fluid effects in close encounters between gas giants and the long-term evolution of closely-packed planetary systems. Focusing on parabolic encounters between Jupiter-like planets with MJ and 2MJ, we find that quick mergers occur when the impact parameter rp (the pericenter separation between the planets) is less than 2RJ, and the merger conserved at least 97% of the initial mass. Strong tidal effects can affect the “binary-planet” orbit when rp is between 2RJ and 4RJ. We quantify these effects using a set of fitting formulae that can be implemented in N-body codes. We run a suite of N-body simulations with and without the formulae for systems of two giant planets initially in unstable, nearly circular and nearly coplanar orbits. The fluid (tidal) effects significantly increase the branching ratio of planetary mergers relative to ejections by doubling the effective collision radius. While the fluid effects do not change the distributions of semi-major axis and eccentricity of each type of remnant planets (mergers vs surviving planets in ejections), the overall orbital properties of planet scattering remnants are strongly affected due to the branching ratio change. We also find that the merger products have broad distributions of spin magnitudes and obliquities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Hydrodynamic simulations of white dwarf–white dwarf mergers and the origin of R Coronae Borealis stars

We study the properties of double white dwarf (DWD) mergers by performing hydrodynamic simulations using the new and improved adaptive mesh refinement code OCTO-TIGER. We follow the orbital evolution of DWD systems of mass ratio $q=0.7$ for tens of orbits until and after the merger to investigate them as a possible origin for R Coronae Borealis (RCB) type stars. We reproduce previous results, finding that during the merger, the helium WD donor star is tidally disrupted within 20–80 min since the beginning of the simulation onto the accretor carbon–oxygen WD, creating a high temperature shell around the accretor. We investigate the possible helium burning in this shell and the merged object’s general structure. Specifically, we are interested in the amount of oxygen-16 dredged-up from the accretor to the hot shell and the amount of oxygen-18 produced. This is critical as the discovery of very low oxygen-16 to oxygen-18 ratios in RCB stars pointed out the merger scenario as a favourable explanation for their origin. A small amount of hydrogen in the donor may help keep the oxygen-16 to oxygen-18 ratios within observational bounds, even if moderate dredge-up from the accretor occurs. In addition, we perform a resolution study to reconcile the difference found in the amount of oxygen-16 dredge-up between smoothed-particle hydrodynamics and grid-based simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Cladding and Butt-Joining Dissimilar Aluminum Alloys Simultaneously via Shear Assisted Processing and Extrusion

Shear assisted processing and extrusion has been used to fabricate multi-metallic tubing that incorporates regions with clad and butt-joined structures. In this work, aluminum alloys 6061, 7075, and 1100 are combined to create a monolithic extruded tubing with weldable ends (6061), a high strength center (7075), and a corrosion-resistant cladding (1100). Optical microscopy shows a gradual, defect-free, transition between alloys at the butt-joint interfaces and a sharp transition between alloys at the clad interface. Tensile testing proved the mechanical coherency of the joint, with failure occurring outside the tri-metallic structure. In conclusion, smoothed particle hydrodynamic simulations identified a spiral pattern of the cladding alloy that leads to inconsistent cladding thickness, and identified a simplified 2-alloy combination of aluminum alloys 6082 and 2014 that accomplished the design objectives of the tri-metallic structure.

Coatings↗

DOE OSTI2025

Modeling of melting and erosion in high velocity microparticle impacts

High velocity collisions can cause melting, a situation involving elasticity, plasticity, and phase transformations in tandem, which is very challenging for mechanical modeling. Here, this paper advances the use of smoothed particle hydrodynamics (SPH) simulations for this complex situation, investigating stainless steel microspheres impacting a tin substrate. After extensive validation against a range of mechanical and geometrical measurements of experimental impacts, the model provides a detailed, quantitative view of melt volume production over a broad range of impact velocities. It also enables direct decomposition of the impact energy partitioning, including analysis of the energy absorbed by plasticity in the impactor, the system kinetic energy, and the adiabatic heating of the substrate in addition to the melting itself. Since these quantities are not available experimentally, SPH modeling substantially enhances the quantitative understanding of such impacts. Finally, the model speaks to the phase characteristics of the ejecta formed during impact, confirming the experimental inference that the ejected material likely contains a significant fraction of solid material.

Constitutive modeling↗

DOE OSTI2026

Validation of SPH code Spheral to model interacting solid bodies in a supersonic flow

Contemporary discussions of planetary defense involve analyzing the risks posed by smaller sized, 20 to 200 m diameter, asteroids which are capable of breaking up in the atmosphere and generating a blast wave. Consequence assessments for this size class of asteroids are performed through fast-running analytic or semi-analytic models which are informed by high-fidelity hydrocode simulations of asteroid entry and breakup. However, insufficient historical data necessitates validating the independent physical processes which dominate airburst events. Here, the Fluid Solid Interface Smoothed Particle Hydrodynamics solver was previously used by Pearl et al. in 2023 to model the Chelyabinsk airburst and is used here to perform a series of validation simulations. The first effort involves modeling a cylinder in a hypersonic flow and comparing the bow shock geometry to that predicted by analytic theory. The second effort involves modeling the separation of two spherical bodies in supersonic flow and validating against experimental footage. Combined, these exercises demonstrate the ability of the code to model the flight-path of interacting solid bodies in a hypersonic flow.

Airburst↗

DOE OSTI2026

X-ray observation of individual Ti-6Al-4V spherical powder particle impact in an in-situ operando laser directed energy deposition system

Understanding the particle capture mechanism in the laser directed energy deposition additive manufacturing process provides a foundation for improving productivity and reducing material loss. Capturing this phenomenon is challenging due to its highly transient time interval. To analyze the impact behavior of spherical Ti-6Al-4V powder, a custom laser directed energy deposition system was designed to control the deposition of individual particles. Synchrotron X-ray imaging at 24 kHz monitored the impact dynamics of individual powder particles. A multi-physics model based on the Smoothed-Particle Hydrodynamics scheme supported the analysis by providing the temperature and velocity fields of the molten pool. Results revealed that in laser directed energy deposition, surface tension forces dominated the powder–molten pool interaction. Hydrophobic Ti-6Al-4V powder particles had an equilibrium contact angle of 121 degrees with their molten state. Furthermore, Ti-6Al-4V powder particles required a high impact velocity (6 to 12 m/s) to transition from oscillation to submergence behavior. Lastly, oscillating powder particles that impacted near the location of the laser beam exhibited faster melting, highlighting the contribution of the laser beam to the melting mechanism. This work lays the foundation for investigations of powder particle impact in laser directed deposition and supports the validation of numerical models of powder–molten pool interactions.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Structural uniformity and compositional homogeneity of solid-phase alloyed rod

Solid-phase processes have emerged as an alternative to fusion-based alloying to avoid coarse microstructures, undesirable phase formation, and high energy consumption. However, achieving uniform distribution of alloying elements during friction-based processing remains challenging due to highly heterogeneous thermomechanical conditions. This work evaluates the structural uniformity and compositional homogeneity of Al–Cu–Zn alloyed rods produced by friction extrusion (FE) and establishes the role of the rotational speed to feed rate ratio (N/V) on alloying effectiveness. A systematic matrix of FE experiments was conducted at constant extrusion ratio with N/V values ranging from 3.7 to 300. Compositional uniformity was assessed along the rod length (ICP-OES), in three dimensions (X-ray computed tomography), and at the microscale (SEM–EDS), supported by a gray-level co-occurrence matrix (GLCM)–based homogeneity metric. Smoothed particle hydrodynamics (SPH) simulations were used to reveal material flow and thermomechanical fields. Results show that N/V = 100 produces a high-shear mixing zone that eliminates the unmixed core and enables near-full dissolution and dispersion of Cu and Zn. At lower N/V, a laminar flow region persists at the rod center, causing segregation and large composition gradients. The combined experimental–computational analysis provides mechanistic insight into the transition from fragmented particle dispersion to thermomechanically assisted metallurgical mixing. This study establishes processing–structure relationships for solid-phase alloying and provides guidance for achieving homogenized compositions comparable to wrought alloys via rapid, scalable FE processing.

Aluminum↗

DOE OSTI2024

Bifurcation of equilibrium positions for ellipsoidal particles in inertial shear flows between two walls

We conducted a systematic numerical investigation of spherical, prolate and oblate particles in an inertial shear flow between two parallel walls, using smoothed particle hydrodynamics (SPH). It was previously shown that above a critical Reynolds number, spherical particles experience a supercritical pitchfork bifurcation of the equilibrium position in shear flow between two parallel walls, namely that the central equilibrium position becomes unstable, leading to the emergence of two new off-centre stable positions (Foxet al.,J. Fluid Mech., vol. 915, 2021). This phenomenon was unexpected given the symmetry of the system. In addition to confirming this finding, we found, surprisingly, that ellipsoidal particles can also return to the centre position from the off-centre positions when the particle Reynolds number is further increased, while spherical particles become unstable under this increased Reynolds number. By utilizing both SPH and the finite element method for flow visualization, we explained the underlining mechanism of this reverse of bifurcation by altered streamwise vorticity and symmetry breaking of pressure. Furthermore, we expanded our investigation to include asymmetric particles, a novel aspect that had not been previously modelled, and we observed similar trends in particle dynamics for both symmetric and asymmetric ellipsoidal particles. While further validation through laboratory experiments is necessary, our research paves the road for development of new focusing and separation methods for shaped particles.

Mechanics↗

DOE OSTI2024

SPH Modeling of Biomass Granular Flow: Engineering Application in Hoppers and Augers

Numerical modeling of granular biomass material flow in handling operations is indispensable to decipher flow upsets, commonly manifested as clogging and jamming in hoppers and augers. With a computational tool developed based on smoothed particle hydrodynamics (SPH), we simulated the hopper flow and auger feeding of six granular biomass materials. The good agreement between the experimental and numerical flow rates demonstrated the capability of the developed SPH solver in modeling the complicated flow of granular biomass materials. Further, the impact of physical and numerical parameters is investigated, and the major results show that the hopper flow pattern is controlled by shear band evolution; hopper clogging is collectively influenced by the opening size, wall friction, and material packing, and the impact of material compressibility on the auger feed rate is minimal. These parametric studies validate the solver’s robustness in simulating biomass flow in handling equipment and demonstrate that the SPH computational tool can provide insights about granular flow mechanics to facilitate handling equipment design and optimize handling operations.

09 BIOMASS FUELS↗

DOE OSTI2021

Numerical and Analytical Modeling of Flow Partitioning in Partially Saturated Fracture Networks

Infiltration processes in fractured-porous media remain a crucial, yet not very well understood component of recharge and vulnerability assessment. Under partially-saturated conditions flows in fractures, percolating fracture networks, and fault zones contribute to the fastest spectrum of infiltration velocities via preferential pathways. Specifically, the partitioning dynamics at fracture intersections determine the magnitude of flow fragmentation into vertical and horizontal components and hence the bulk flow velocity and dispersion of fracture networks. In this work, we derive an approximate analytical solution for the partitioning process and validate it using smoothed particle hydrodynamics simulations. The developed transfer function is conceptually based on simulation results and laboratory experiments carried out in previous works. It allows to efficiently simulate flow through fracture networks with simple cubic structure and arbitrary number of fractures and aperture sizes via linear response theory and convolution of a given input signal. We derive a non-dimensional bulk flow velocity ($\widetilde{v}$) and dispersion coefficient ($\widetilde{D}$) to characterize fracture networks in terms of dimensionless horizontal and vertical time scales $\tau_m$ and $\tau_0$. The dispersion coefficient is shown to strongly depend on the horizontal time scale and converges towards a constant value of $0.08$ within reasonable fluid and geometrical parameter ranges, while the non-dimensional velocity exhibits a characteristic $\widetilde{v} \sim \tau_m^{-1/2}$ scaling. Given that hydraulic information is often only available at limited places within (fractured-porous) aquifer system, such as boreholes or springs, our study intends to provide a rudimentary analytical concept to potentially reconstruct internal fracture network geometries from external boundary information, e.g., the dispersive properties of discharge (groundwater level fluctuations).

42 ENGINEERING↗