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DOE OSTI2023

Bipolar Membranes with an Electrospun 3D Junction

Freestanding bipolar membranes (BPMs) with an entirely new and transformative morphology were fabricated and characterized. The key disruptive design element was a water-splitting/water-generation junction layer of finite thickness composed of interwoven and interlocking electrospun anion-exchange polymer (AEP) fibers and cation-exchange polymer (CEP) fibers. Methods were developed to sandwich the 3D junction layer between two pre-formed dense AEP and CEP films., with the closure of all interfiber voids, where the processing steps are easily incorporated into a commercial roll-to-roll membrane manufacturing scheme. A series of membranes were made using different polymers and junction layers to identify the optimum morphology and composition for water-splitting and water-generation applications. For water splitting, the 3D junction BPMs worked remarkably well with operating current densities at/above 1.0 A/cm2 (10X greater than commercial BPMs) at a transmembrane voltage drop of only 1.1 V. In water generation mode, the 3D junction BPMs operated at 0.5 A/cm2, a world-record current density. The membranes were found to exhibit outstanding durability and can be manufactured at scale for low cost. The high operating current densities and stable long-term operation are due to the 3D junction layer design, where there is a high interfacial area for water splitting or water generation reactions and where the interlocking fibers prevent delamination of the outer films. These new BPMs are ideal candidate materials for both existing water-splitting electrodialysis separations and new electrochemical processes, such as large-scale direct air capture of CO 2 , reactors for CO 2 reduction, self-hydrating fuel cells, and redox flow batteries.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2024

An unstructured body-of-revolution electromagnetic particle-in-cell algorithm with radial perfectly matched layers and dual polarizations

A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code, utilizes a set of field scalings and a coordinate mapping, reducing the Maxwell field problem in a cylindrical system to a Cartesian finite element Maxwell solver in the meridian plane. The latter obviates the cylindrical coordinate singularity in the symmetry axis. The choice of an unstructured finite element discretization enhances the geometrical flexibility of the BORPIC++ solver compared to the more traditional finite difference solvers. Symmetries in Maxwell’s equations are explored to decompose the problem into two dual polarization states with isomorphic representations that enable code reuse. The particle-in-cell scatter and gather steps preserve charge conservation at the discrete level. Our previous algorithm (BORPIC+) discretized the E and B field components of TE Φ and TM Φ polarizations on the finite element (primal) mesh. Here, we employ a new field-update scheme. Using the same finite element (primal) mesh, this scheme advances two sets of field components independently: (1) E and B of TE Φ polarized fields, (E z , E ρ , B Φ ) and (2) D and H of TM Φ polarized fields, (D Φ , H z , H ρ ). Since these field updates are not explicitly coupled, the new field solver obviates the coordinate singularity, which otherwise arises at the cylindrical symmetric axis, ρ = 0 when defining the discrete Hodge matrices (generalized finite element mass matrices). Here, a cylindrical perfectly matched layer is implemented as a boundary condition in the radial direction to simulate open space problems, with periodic boundary conditions in the axial direction. We investigate effects of charged particles moving next to the cylindrical perfectly matched layer. We model azimuthal currents arising from rotational motion of charged rings, which produce TMΦ polarized fields. Several numerical examples are provided to illustrate the first application of the algorithm.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Evolution of microstructures in radiation fields using a coupled binary-collision Monte Carlo phase field approach

The simulation of radiation effects in materials broadly falls into two categories. At short time and length scales lies the modeling of primary radiation damage, such as point defect creation, energy deposition, and ballistic mixing. This is followed by the modeling at longer time scales of thermally activated microstructure evolution and defect reactions, such as recombination, clustering, and coarsening. The binary collision Monte Carlo method is an established, numerically efficient method for the computation of primary radiation damage. Conversely, the phase field method is a state of the art method for microstructure evolution on longer time and length scales. Here we present a concurrent coupling of these two methods, overcoming the difference between the discrete object Monte Carlo paradigm for primary radiation damage and the continuum field variable approach for microstructure evolution. The coupling is bidirectional, in which the microstructure evolution in the MOOSE finite element frame- work provides the spatial scattering data set for the charged particle trans- port and receives point defect, mass transport, and heat source terms from the simulated collision cascades that contribute to the field variable evolution. The concurrent coupling scheme is implemented in the code Magpie and demonstrated by investigating patterning for a model irradiated immiscible binary alloy. The results from the coupled binary collision Monte Carlo/phase field simulations reproduce the results of analytical models for phase separation, phase mixing, and patterning, supporting the approach and indicating its utility for modeling real materials systems.

36 MATERIALS SCIENCE↗

DOE OSTI2022

A concurrent irradiation-mechanics multiscale coupling model

The vast majority of our current knowledge regarding the basic mechanisms controlling irradiation effect on mechanical properties is based almost entirely on the results of post-irradiation experiments or theoretical models. However, the concurrent effects of irradiation, mechanical stress, and thermal damage on the failure phenomena of materials and components remain largely unexplored due to its internal multiscale-multiphysics coupling nature. Here, we present here a concurrent irradiation-mechanics multiscale coupling model. The concurrent evolutions of nanoscale irradiation defect clusters, microscale dislocation configurations, and mechanical responses are well captured based on coupling cluster dynamics, discrete dislocation dynamics, and the finite element methods using an effective time marching scheme. Model predictions of defect densities and size are in general agreement with experimental observations. Irradiation hardening is shown to take place also in samples undergoing concurrent irradiation-mechanical loading, similar to samples tested post-irradiation. However, the occurrence of plastic flow localization and dislocation channel formation is not accompanied with apparent yield drop (softening) under concurrent irradiation-mechanical loading conditions, which is different from the post-irradiation case.

42 ENGINEERING↗

DOE OSTI2024

Modeling and design of a separate effects irradiation test targeting fission gas release from Cr-doped UO 2

Fission gas release (FGR) from nuclear fuel during operation can diminish heat transfer properties across the pellet-cladding gap and increase the fuel rod internal pressure, thereby posing a concern to fuel reliability and safety during an accident. Enlarging the fuel grain size, which has been shown to improve fission gas retention, can be achieved by doping the fuel feedstock prior to sintering. In this work, the BISON fuel performance code was used to predict FGR from undoped and chromia-doped UO 2 (referred to as Cr-doped UO 2 ) fuel specimens with different grain sizes and across various temperatures. The BISON models identified the irradiation conditions for which FGR is most significant, and a separate effects irradiation experiment in the High Flux Isotope Reactor (HFIR) was then developed targeting those conditions. Further, the experiment leveraged the MiniFuel irradiation capability at Oak Ridge National Laboratory and consisted of 12 fuel specimens of varying grain size and Cr content. A coupling scheme between BISON FGR results and the ANSYS finite element thermal model used for experiment design was formulated to predict cumulative FGR from each fuel specimen based on expected irradiation temperature histories. The fuel samples were fabricated and characterized as a part of this work, and the fuel compositions modeled in BISON were representative of the specimens used in the experiment. This combined modeling and experimental effort aims to study the effect of fuel grain size and Cr content on FGR and to provide simulated BISON FGR results that can be used for future model validation activities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Rupture Jumping and Seismic Complexity in Models of Earthquake Cycles for Fault Stepovers with Off-Fault Plasticity

ABSTRACT Fault stepovers are prime examples of geometric complexity in natural fault zones that may affect seismic hazard by determining whether an earthquake rupture continues propagating or abruptly stops. However, the long-term pattern of seismicity near-fault stepovers and underlying mechanisms of rupture jumping in the context of earthquake cycles are rarely studied. Leveraging a hybrid numerical scheme combining the finite element and the spectral boundary integral methods, FEBE, we carry out fully dynamic simulations of sequences of earthquakes and aseismic slip for both compressive and tensile stepovers with off-fault plasticity. We consider a rate-and-state friction law for the fault friction and pressure-sensitive Drucker–Prager plasticity for the off-fault bulk response. We observe that the accumulation of plastic deformation, an indication of off-fault damage, is significantly different in the two cases, with more plastic deformation projected in the overlapping region for the tensile stepover. The seismic pattern for a tensile stepover is more complex than for a compressive stepover, and incorporating plasticity also increases complexity, relative to the elastic case. A tensile stepover with off-fault plasticity shows rupture segmentation, temporal clustering, and frequent rupture jumping from one fault to another. These results shed light on possible mechanisms of rupture jumping in fault stepovers as well as the long-term evolution of the fault zone.

Geochemistry & Geophysics↗

DOE OSTI2021

Supersaturation, buoyancy, and deep convection dynamics

Motivated by recent discussions concerning differences of convective dynamics in polluted and pristine environments, the so-called convective invigoration in particular, this paper provides an analysis of factors affecting convective updraft buoyancy, such as the in-cloud supersaturation, condensate and precipitation loading, and entrainment. We use the deep convective period from simulations of daytime convection development over land discussed in our previous publications. An entraining parcel framework is used in the theoretical analysis. We show that for the specific case considered here, finite (positive) supersaturation noticeably reduces pseudo-adiabatic parcel buoyancy and cumulative convective available potential energy (cCAPE) in the lower troposphere. This comes from keeping a small fraction of the water vapor in a supersaturated state and thus reducing the latent heating. Such a lower-tropospheric impact is comparable to the effects of condensate loading and entrainment in the idealized parcel framework. For the entire tropospheric depth, loading and entrainment have a much more significant impact on the total CAPE. For the cloud model results, we compare ensemble simulations applying either a bulk microphysics scheme with saturation adjustment or a more comprehensive double-moment scheme with supersaturation prediction. We compare deep convective updraft velocities, buoyancies, and supersaturations from all ensembles. In agreement with the parcel analysis, the saturation-adjustment scheme provides noticeably stronger updrafts in the lower troposphere. For the simulations predicting supersaturation, there are small differences between pristine and polluted conditions below the freezing level that are difficult to explain by standard analysis of the in-cloud buoyancy components. By applying the piggybacking technique, we show that the lower-tropospheric buoyancy differences between pristine and polluted simulations come from a combination of temperature (i.e., latent heating) and condensate loading differences that work together to make polluted buoyancies and updraft velocities slightly larger when compared to their pristine analogues. Overall, the effects are rather small and contradict previous claims of a significant invigoration of deep convection in polluted environments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Constitutive Model of Radiation Aging Effects in Filled Silicone Elastomers under Strain

Filled silicone elastomers, an essential component in many technological applications, are often subjected to controlled or unintended radiation for a variety of reasons. Radiation exposure can lead to permanent mechanical and structural changes in the material, which is manifested as altered mechanical response, and in some cases, a permanent set. For unfilled elastomers, network theories developed and refined over decades can explain these effects in terms of chain-scission and cross-link formation and a hypothesis involving independent networks formed at different strain levels of the material. In this work, we expose a filled silicone rubber to gamma radiation while being under finite elongational strain and show that the observed mechanical and structural changes can be quantitatively modeled within the same theoretical framework developed for unfilled elastomers as long as nuances associated with the Mullins effect are accounted for in a consistent manner. In this work, we employ Ogden’s incompressible hyperelastic model within the framework of Tobolsky’s two-network scheme to describe the observed permanent set and mechanical modulus changes as a function of radiation dosage. In the process, we conclude that gamma radiation induces both direct cross-linking at chain crossings (H-links) and main-chain-scission followed by cross-linking (Y-links). We provide an estimate of the ratio of chain-scission to cross-linking rates, which is in reasonable agreement with previous experimental estimate from Charlesby–Pinner analysis. We use density functional theory (DFT)-based quantum mechanical calculations to explore the stability of –Si and –SiO radicals that form upon a radiation-induced chain-scission event, which sheds light on the relative rates of Y-linking and H-linking processes.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

A detailed analysis of the systematic uncertainties in the calculation of the isovector momentum fraction, ( x ) u - d , helicity moment, ( x ) Δ u - Δ d , and the transversity moment, ( x ) δu - δd , of the nucleon is presented using high-statistics data on seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using 2 + 1-flavors of dynamical Wilson-clover quarks. The much higher statistics have facilitated better control over all systematics compared to previous lattice calculations. The least understood systematic — excited-state contamination — is quantified by studying the variation of the results as a function of different estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions, and as a function of the pion mass M π . The final results are obtained using a simultaneous fit in the lattice spacing a , pion mass M π and the finite volume parameter M π L keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. Our final results, in the $ \overline{\mathrm{MS}} $ scheme at 2 GeV, are ( x ) u - d = 0 . 155(17)(20), ( x ) Δ u - Δ d = 0 . 183(14)(20) and ( x ) δu - δd = 0 . 220(18)(20), where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with phenomenological global fit values.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Abstract Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [ Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

Silva, Goncalo↗

DOE OSTI2020

Image charge interaction correction in charged-defect calculations

Charged-defect calculation using a periodic supercell is a significant class of problems in solid state physics. However, the finite supercell size induces an undesirable long-range image charge Coulomb interaction. Although a variety of methods have been proposed to eliminate such image Coulomb interaction, most of the previous schemes are based on a rough approximation of the defect charge screening. In this work, we present a rigorous derivation of the image charge interaction with a defect screening model where the use of a bulk macroscopic dielectric constant can be avoided. Here, we have verified this approach in comparison with a widely used approach for 12 different defects. Our correction scheme offers a much faster convergence concerning the supercell size for cases with considerable image charge interactions. In those cases, we also found that the nonlinear dielectric screening might play an important role. Our proposed defect screening model will also shed new light on understanding the defect screening properties and can be applied to other defect systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Finite-range pairing in nuclear density functional theory

Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic pair densities and pairing fields are introduced. Many pairing functionals currently used can be traced back to zero-range nucleon-nucleon interactions. Unfortunately, such functionals are plagued by deficiencies that become apparent in large model spaces that contain unbound single-particle (continuum) states. In particular, the underlying computational schemes diverge as the single-particle space increases, and the results depend on how marginally occupied states are incorporated. These problems become more pronounced for pairing functionals that contain gradient-density dependence, such as in the Fayans functional. To remedy this, finite-range pairing functionals are introduced. In this study, this is done by folding the pair density with Gaussians. Here, we show that a folding radius of about 1 fm offers the best compromise between quality and stability, and substantially reduces the pathological behavior in different numerical applications.

Nuclear density functional theory↗

DOE OSTI2022

r -process nucleosynthesis and kilonovae from hypermassive neutron star post-merger remnants

ABSTRACT We investigate r-process nucleosynthesis and kilonova emission resulting from binary neutron star (BNS) mergers based on a three-dimensional (3D) general-relativistic magnetohydrodynamic (GRMHD) simulation of a hypermassive neutron star (HMNS) remnant. The simulation includes a microphysical finite-temperature equation of state (EOS) and neutrino emission and absorption effects via a leakage scheme. We track the thermodynamic properties of the ejecta using Lagrangian tracer particles and determine its composition using the nuclear reaction network SkyNet. We investigate the impact of neutrinos on the nucleosynthetic yields by varying the neutrino luminosities during post-processing. The ejecta show a broad distribution with respect to their electron fraction Ye, peaking between ∼0.25–0.4 depending on the neutrino luminosity employed. We find that the resulting r-process abundance patterns differ from solar, with no significant production of material beyond the second r-process peak when using luminosities recorded by the tracer particles. We also map the HMNS outflows to the radiation hydrodynamics code SNEC and predict the evolution of the bolometric luminosity as well as broadband light curves of the kilonova. The bolometric light curve peaks on the timescale of a day and the brightest emission is seen in the infrared bands. This is the first direct calculation of the r-process yields and kilonova signal expected from HMNS winds based on 3D GRMHD simulations. For longer-lived remnants, these winds may be the dominant ejecta component producing the kilonova emission.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Adaptive clipping‐and‐redistribution algorithms for bounded and conservative high‐order interpolations applied to discontinuous and reactive flows

Abstract A new adaptive clipping‐and‐redistribution method is presented which provides bounds‐preservation for multidimensional interpolation in the context of high‐order finite‐volume discretizations with adaptive mesh refinement (AMR). The underlying finite‐volume method (FVM) for the computational fluid dynamics applications is fourth‐order accurate for smooth solutions and utilizes AMR for computational efficiency in solving multiscale problems involving turbulence and combustion. High‐order interpolation between different AMR levels is required. However, this operation often leads to numerical issues because combustion species must have physical bounds preserved. The present study overcomes two major challenges in the development of the high‐order interpolation method. First, the method needs to be bound‐preserving near extrema or discontinuities to prevent the emergence of unphysical oscillations while maintaining fourth‐order accuracy in smooth flows. Second, the method needs to satisfy the conservation requirement in multiple dimensions, particularly in the context of curvilinear coordinate transformations. Additionally, the method is designed to be localized and computationally inexpensive. The new interpolation scheme is demonstrated by solving reacting flows, which are extremely sensitive to unphysical overshoots in conserved quantities. The test problems are shock‐induced ‐ combustion and a ‐air flame in a practical bluff‐body combustor. Results show the method prevents new extrema near discontinuities while maintaining high‐order accuracy in smooth regions. In particular, the method is extremely beneficial for combustion with stiff chemistry. With the proposed new method, even if flame fronts cross AMR interfaces or new grids are created in the vicinity of the flame, solution stability is retained.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Real-time estimators for scattering observables: A full account of finite-volume errors for quantum simulation

The real-time correlators of quantum field theories can be directly probed through new approaches to simulation, such as quantum computing and tensor networks. This provides a new framework for computing scattering observables in lattice formulations of strongly interacting theories, such as lattice quantum chromodynamics. In this paper, we prove that the proposal of real-time estimators of scattering observables is universally applicable to all scattering observables of gapped quantum field theories. All finite-volume errors are exponentially suppressed, and the rate of this suppression is controlled by the regulator considered, namely, a displacement of the spectrum of the theory into the complex plane. A partial restoration of Lorentz symmetry by averaging over different boosts gives an additional suppression of finite volume errors. Our results also apply to the simulation of wave packet scattering, where a similar averaging is performed to construct the wave packets that regulate the finite volume effects. This result represents a necessary key step toward determining a broad class of scattering observables via quantum computing that are currently inaccessible via classical computing. Such observables are relevant for various applications, including hadron spectroscopy, hadron structure, and precision tests of the Standard Model. We also comment on potential applications of our results to traditional computational schemes.

Burbano, Ivan M. [University of California, Berkel↗

DOE OSTI2020

Investigation of finite-volume methods to capture shocks and turbulence spectra in compressible flows

The aim of the present paper is to provide a comparison between several finite-volume methods of different numerical accuracy: the second-order Godunov method with PPM interpolation and the high-order finite-volume WENO method. In this work, the results show that while on a smooth problem the high-order method performs better than the second-order one, when the solution contains a shock all the methods collapse to first-order accuracy. In the context of the decay of compressible homogeneous isotropic turbulence with shocklets, the actual overall order of accuracy of the methods reduces to second-order, despite the use of fifth-order reconstruction schemes at cell interfaces. Most important, results in terms of turbulent spectra are similar regardless of the numerical methods employed, except that the PPM method fails to provide an accurate representation in the high-frequency range of the spectra. It is found that this specific issue comes from the slope-limiting procedure and a novel hybrid PPM/WENO method is developed that has the ability to capture the turbulent spectra with the accuracy of a high-order method, but at the cost of the second-order Godunov method. Overall, it is shown that virtually the same physical solution can be obtained much faster by refining a simulation with the second-order method and carefully chosen numerical procedures, rather than running a coarse high-order simulation. Our results demonstrate the importance of evaluating the accuracy of a numerical method in terms of its actual spectral dissipation and dispersion properties on mixed smooth/shock cases, rather than by the theoretical formal order of convergence rate.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗