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DOE OSTI2021

A High Resolution Simulation of a Single Shock-Accelerated Particle

We report particle drag models, which capture macroviscous and pressure effects, have been developed over the years for various flow regimes to enable cost effective simulations of particle-laden flows. The relatively recent derivation by Maxey and Riley has provided an exact equation of motion for spherical particles in a flow field based on the continuum assumption. Many models that have been simplified from these equations have provided reasonable approximations; however, the sensitivity of particle-laden flows to particle drag requires a very accurate model to simulate. To develop such a model, a two-dimensional axisymmetric Navier–Stokes direct numerical simulation of a single particle in a transient, shock-driven flow field was conducted using the hydrocode FLAG. FLAGs capability to run arbitrary Lagrangian-Eulerian hydrodynamics coupled with solid mechanic models makes it an ideal code to capture the physics of the flow field around and in the particle as it is shock-accelerated—a challenging regime to study. The goal of this work is twofold: to provide a validation for FLAGs Navier–Stokes and heat diffusion solutions and to provide a rationale for recent experimental particle drag measurements.

42 ENGINEERING↗

DOE OSTI2024

Supporting Greater Interactivity in the IPython Visualization Ecosystem

Interactive visualizations are invaluable tools for building intuition and supporting rapid exploration of datasets and models. Numerous libraries in Python support interactivity, and workflows that combine Jupyter and IPyWidgets in particular make it straightforward to build data analysis tools on the fly. However, the field is missing the ability to arbitrarily overlay widgets and plots on top of others to support more flexible details-on-demand techniques. This work discusses some limitations of the base IPyWidgets library, explains the benefits of IPyVuetify and how it addresses these limitations, and finally presents a new open-source solution that builds on IPyVuetify to provide easily integrated widget overlays in Jupyter.

Martindale, Nathan↗

DOE OSTI2019

Distributionally robust polynomial chance-constraints under mixture ambiguity sets

Given $\mathrm{X}\subset\mathbb{R}^n, ε \in (0,1)$, a parametrized family of probability distributions $(μ_a)_{a\in \mathrm{A}}$ on $\mathrm{Ω}\subset \mathbb{R}^p$, we consider the feasible set $\mathrm{X}^*_ε \subset\mathrm{X}$ associated with the distributionally robust chance-constraint $\mathrm{X}^*_ε = \mathrm{x \in X : Prob}_μ[f(\mathrm{x}, ω) >0] > 1 - ε, \forall μ \in \mathscr{M}_{\mathrm{a}}$}, where $\mathscr{M}_{\mathrm{a}}$ is the set of all possibles mixtures of distributions $μ_{\mathrm{a}}, \mathrm{a \in A}$. For instance and typically, the family $\mathscr{M}_{\mathrm{a}}$ is the set of all mixtures of Gaussian distributions on $\mathbb{R}$ with mean and standard deviation $\mathrm{a}=(a,σ)$ in some compact set $\mathrm{A}\subset \mathbb{R}^2$. We provide a sequence of inner approximations $\mathrm{X}^d_ε = {\mathrm{x \in X} : w_d(\mathrm{x}) < ε}, d \in \mathbb{N}$, where $w_d$ is a polynomial of degree d whose vector of coefficients is an optimal solution of a semidefinite program. The size of the latter increases with the degree d. We also obtain the strong and highly desirable asymptotic guarantee that $λ(\mathrm{X}^*_ε$\$\mathrm{X}^d_ε$) → 0 as d increases, where λ is the Lebesgue measure on X. Same results are also obtained for the more intricated case of distributionally robust “joint” chance-constraints. Finally, there is a price to pay for this strong asymptotic guarantee which is the scalability of such a numerical scheme, and so far this important drawback makes it limited to problems of modest dimension.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Chapter 7: Learning Stable Local Volt/Var Controllers in Distribution Grids

This chapter describes a framework to synthesize provably stable local Volt/Var controllers for distributed energy resources (DERs) in power distribution grids (DGs). The goal is to control the reactive power injections of DERs to improve the system performance as quantified by a generic optimal reactive power flow (ORPF) problem. To achieve this, we jointly design for each DER the control function, which prescribes the reactive power update rule, and the equilibrium function, which approximates the ORPF solutions from local measurements of voltages and powers. We provide conditions on the equilibrium functions and the control parameters ensuring the stability of the closed-loop system. In particular, we discuss the trade-offs between each set of conditions accounting for practical considerations, like fully exploiting the DERs' generation capabilities and reducing the optimality gap. These conditions are then translated into learning constraints on the neural networks' parameters that are enforced in the training phase. We validate our framework with numerical simulations on the IEEE 37-bus network and through a comparison with an optimized version of standard piece wise linear control rules.

closed-loop asymptotic stability↗

DOE OSTI2021

A fast reduced model for a shell-and-tube based latent heat thermal energy storage heat exchanger and its application for cost optimal design by nonlinear programming

Numerical simulation of latent heat thermal energy storage (LHTES) systems plays a fundamental role in studying the physical process and guiding the engineering design. Discretization of the PDEs describing the nonlinear solidification/melting process of phase change materials (PCMs) leads to a large-scale complex dynamics system, where the system behavior depends on a set of parameters. In a design setting, repeated model evaluations are required over the set of parameters results in significant computational burden. In this paper, an explicit analytic solution was built for the propagation of the solidification front in a cylindrical coordinate. The analytic solution approach is further employed to develop a low computational reduced model (RM) as a module for a shell-and-tube based LHTES heat exchanger. The levelized Cost of Energy (LCOE) is used as a design metric and the RM model is used to apply system-level constraints in the nonlinear programming formulation that facilitates efficient global optimal design of the PCM properties, flow conditions and tube geometries. The use of LCOE as the design metric prevents over design of the heat transfer rate and also establishes a fair ground for evaluation of different thermal storage technologies and their integrated applications with other systems. Optimal results showed that a higher effectiveness results in a higher LCOE; the velocity of the HTF and the length of the channel are highly correlated with each other; both larger PCM latent energy and conductivity result in lower LCOE.

25 ENERGY STORAGE↗

DOE OSTI2024

Approximating accelerator impedances with resonator networks

It is common in the accelerator community to use the impedance of accelerator components to describe wake interactions in the frequency domain. However, it is often desirable to understand such wake interactions in the time domain in a general manner for excitations that are not necessarily Gaussian in nature. Here, the conventional method for doing this involves taking the inverse Fourier Transform of the component impedance, obtaining the Green's Function, and then convolving it with the desired excitation distribution. This method can prove numerically cumbersome, for a convolution integral must be evaluated for each individual point in time when the wake function is desired. An alternative to this method would be to compute the wake function analytically, which would sidestep the need for repetitive integration. Only a handful of cases, however, are simple enough for this method to be tenable. One of these cases is the case where the component in question is an RLC resonator, which has a closed-form analytical wake function solution. This means that a component which can be represented in terms of resonators can leverage this solution. As it happens, common network synthesis techniques may be used to map arbitrary impedance profiles to RLC resonator networks in a manner the accelerator community has yet to take advantage of. In this work, we will use Foster Canonical Resonator Networks and partial derivative descent optimization to develop a technique for synthesizing resonator networks that well approximate the impedances of real-world accelerator components. We will link this synthesis to the closed-form resonator wake function solution, giving rise to a powerful workflow that may be used to streamline beam dynamics simulations.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Mapping and probing Froggatt-Nielsen solutions to the quark flavor puzzle

The Froggatt-Nielsen (FN) mechanism is an elegant solution to the flavor problem. In its minimal application to the quark sector, the different quark types and generations have different charges under a 𝑈⁢(1)𝑋 flavor symmetry. The SM Yukawa couplings are generated below the flavor breaking scale with hierarchies dictated by the quark charge assignments. Only a handful of charge assignments are generally considered in the literature. We analyze the complete space of possible charge assignments with |𝑋 𝑞𝑖 | ≤ 4 and perform both a set of Bayesian-inspired numerical scans and an analytical spurion analysis to identify those charge assignments that reliably generate SM-like quark mass and mixing hierarchies. The resulting set of top-20 flavor charge assignments significantly enlarges the viable space of FN models but is still compact enough to enable focused phenomenological study. We then apply our numerical methodology to demonstrate that these distinct charge assignments result in the generation of correlated flavor-violating four-quark operators characterized by significantly varied strengths, potentially differing substantially from the possibilities previously explored in the literature. Future precision measurement of Δ⁢𝐹 = 2 observables, along with increasingly accurate SM predictions, may therefore enable us to distinguish among otherwise equally plausible FN charges, thus shedding light on the UV structure of the flavor sector.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Analytical Modeling of Metal Foam Composite Phase Change Materials (PCM) in Thermal Energy Storage Using Asymptotic Analysis

The use of phase change materials (PCMs) for thermal energy storage can release or absorb a significant amount of latent heat during the freezing or melting process, offering a higher energy storage density. One of the main drawbacks of PCMs is their low thermal conductivity, resulting in poor thermal performance. Recent research has attempted to enhance heat transfer and increase the thermal conductivity of PCMs, including the use of metal foams. However, modeling the metal foam composite PCM using conventional methods is computationally expensive. This paper proposes an asymptotic solution for a Stefan-like problem subject to a convective boundary for outward solidification in a hollow cylinder, capable of predicting the freeze-melt cycle of the metal foam composite PCM. Specifically, three temporal regimes and four spatial layers are considered in the asymptotic analysis for each phase change process. The thermal conductivity is calculated by a theoretical three-dimensional tetrakaidecahedron model, while other thermophysical properties are obtained using the method of volume averaging. The results are verified with numerical data and validated against experimental data in the literature. The presented analytical modeling framework could have the potential to be applied to other types of composite PCMs with considerably lower computational costs compared with conventional methods.

analytical model↗

DOE OSTI2024

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

Chowdhury, Agniva↗

DOE OSTI2024

Peer-to-peer communication control for resilient operations of networked cyberphysical systems

This report includes two main accomplishments of the peer-to-peer communication control for resilient operation of networked microgrids project in FY24, which include a scheme for cyberattack-aware coordination of networked microgrids for supporting voltages of bulk power systems and a scheme for price signal-based operations of EV-rich networked microgrids with mixed ownership. First, the cyberattack-aware scheme enables networked microgrids to distributedly determine the amount of reactive power injection to support the voltage of bulk power system (BPS) in a fair manner. In this scheme, a risk-informed algorithm is presented to generate the peer-to- peer (P2P) communication graph with minimal risk of attack on communication links. To deal with cyberattacks on MG controllers, the resilient consensus algorithm (CA) is utilized for MG controllers to robustly estimate the total reactive power headroom, from which the MGs can accurately provide the needed amount of reactive power injection for supporting the voltage of BPS. The CA implementation and performance within the P2P communication framework are demonstrated on the IEEE 39-bus system with 6 microgrids contained in the distribution feeder under different cyberattack scenarios. Second, the price-based scheme enables the usage of the real-time price signal for the operations of electric vehicle (EV)-rich networked-microgrids with mixed ownership, in which not all the microgrids can communicate with the distribution system operator (DSO). In this scheme, a max consensus is introduced to enable the real-time price signal to be propagated from the DSO to all the microgrids, from which each microgrid controller will manage the DERs to balance the load demand and the power injection from the EV charging stations within its microgrid. Numerical results over one day with 288 slots of 5-minute intervals on the modified 123-node test feeder including 3 microgrids with high penetration of EV are presented to evaluate how the price signal affects the operations of networked microgrids under different charging strategies of the EV charging stations. The result indicates that our proposed EVCS (dis)charging strategy, which leverages the flexibility of EVs to support the grid through discharging during peak demand, proves to be a cost-effective solution that reduces operational costs while improving the social welfare of EV charging.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Value of Nuclear Energy to the Reliability of the North American Power System: Results for Western and Eastern Interconnections

This report documents the fulfillment of a milestone for the United States (U.S.) Department of Energy Office of Nuclear Energy Light Water Reactor Sustainability Program: completing a baseline study of regional impact of nuclear power plants and hydrogen production in maintaining grid services and power quality. Models have been comprehensively demonstrated for the Western Interconnection, or Western Electric Coordinating Council area, and in the Eastern Interconnection for scenarios representative of past extreme events (e.g., drought and heat waves). Understanding the impact on the reliability of the bulk electric system of any reduction in generation capacity from nuclear power, for any reason, is the motivation of this work. Factors that might lead to the premature or unplanned closure of nuclear plants, extended outages, or repurposing of nuclear power include: • Aging infrastructure: Many nuclear power plants in the U.S. are nearing the end of their designed operating lives. Upgrading aging infrastructure can be expensive, and some utilities may choose to retire plants rather than invest in costly upgrades. • Low wholesale electricity prices: The deregulation of the electricity market in many states has led to increased competition and driven down wholesale electricity prices, causing nuclear power operators to seek other revenue sources for their heat and power such as clean hydrogen production. • Renewables growth: The rapid growth of renewable energy sources like solar and wind power is posing a challenge to traditional generation sources like nuclear. While many see renewables as a key part of the clean energy transition, their intermittent nature requires additional grid solutions for reliable power supply. • The potential for regulatory decisions to be in conflict: In its 2021 rulemaking, EPA rule (86 FR 880), the Environmental Protection Agency (EPA) set a compliance date for the ban on processing and distribution in commerce of Decabromodiphenyl Ether (DecaBDE). Since DecaBDE is in many components, particularly wiring, of nuclear power plants which are deemed safety-related or important to safety, three plants would not have been able to restart after their 2023 spring outages, and numerous others would have faced issues in the near future. Fortunately, in this case, the EPA provided relief to the nuclear energy industry. The report provides a summary of the significant role nuclear energy plays in the United States’ power generation mix, supplying around 20% of the nation’s electricity generation, spread across 28 U.S. states. Nuclear power is reliable, mostly unaffected by weather and seasonal changes, and provides a consistent source of baseload power. In terms of capacity, nuclear power plants account for as much as 26% of balancing area power generation capacity. Nuclear power also provides a substantial contribution (e.g., 10% of the inertia in the Eastern Interconnection) of the synchronous spinning mass/inertia that buffers the rate at which frequency changes when a load and generation imbalance occurs (e.g., a large plant trips or a load is suddenly shed due to a transmission outage). This contribution is critical for maintaining grid stability during sudden changes in load or generation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Image-Driven Hybrid Structural Analysis Based on Continuum Point Cloud Method with Boundary Capturing Technique

Conventional approaches for the structural health monitoring of infrastructures often rely on physical sensors or targets attached to structural members, which require considerable preparation, maintenance, and operational effort, including continuous on-site adjustments. This paper presents an image-driven hybrid structural analysis technique that combines digital image processing (DIP) and regression analysis with a continuum point cloud method (CPCM) built on a particle-based strong formulation. Polynomial regressions capture the boundary shape change due to the structural loading and precisely identify the edge and corner coordinates of the deformed structure. The captured edge profiles are transformed into essential boundary conditions. This allows the construction of a strongly formulated boundary value problem (BVP), classified as the Dirichlet problem. Capturing boundary conditions from the digital image is novel, although a similar approach was applied to the point cloud data. It was shown that the CPCM is more efficient in this hybrid simulation framework than the weak-form-based numerical schemes. Unlike the finite element method (FEM), it can avoid aligning boundary nodes with regression points. A three-point bending test of a rubber beam was simulated to validate the developed technique. The simulation results were benchmarked against numerical results by ANSYS and various relevant numerical schemes. The technique can effectively solve the Dirichlet-type BVP, yielding accurate deformation, stress, and strain values across the entire problem domain when employing a linear strain model and increasing the number of CPCM nodes. In addition, comparative analysis with conventional displacement tracking techniques verifies the developed technique’s robustness. The proposed technique effectively circumvents the inherent limitations of traditional monitoring methods resulting from the reliance on physical gauges or target markers so that a robust and non-contact solution for remote structural health monitoring in real-scale infrastructures can be provided, even in unfavorable experimental environments.

Chemistry↗

DOE OSTI2023

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Time-domain all-frequency stable formulation for low-frequency electromagnetic simulation with Newmark-β time integration

An implicitly Coulomb-gauged A-ϕ formulation has previously been proposed and validated for finite ele- ment simulations of low-frequency and multiscale electromag- netic problems in the frequency domain. This formulation has demonstrated numerical stability across all frequencies, with its accuracy, efficiency, and iterative convergence established in various frequency-domain scenarios. However, direct time- domain computation is often preferable for wideband electro- magnetic problems and is typically indispensable in nonlinear and multiphysics simulations. In this work, the A-ϕ formulation is extended to the time domain. By incorporating the well-known Newmark-β time integration scheme, the proposed formulation is validated through capacitive and inductive test cases. The results confirm the solution’s accuracy and demonstrate the formulation’s stability in the time domain.

Mekonnen, Minyechil↗

DOE OSTI2022

A radioisotope - enabled reactive transport model for deep vadose zone carbon

In mountainous regions, which constitute the principle source of recharge to major rivers and regional aquifers, infiltration occurs through fractured, partially saturated, weathered bedrock that acts as a boundary layer between saturated aquifers and surface soil. Commonly this deep vadose zone (DVZ) is many meters thick, and yet its role in regulating the generation, retention and mobility of reactive solutes, including nutrients, contaminants and weathering products, is largely unknown. In particular, many of the key reactions that drive the formation of the weathered DVZ and the quality of water moving through it are redox processes, regulated by the availability of organic carbon and oxygen below the soil layer. The role of the DVZ is thus also poorly constrained in the context of carbon stocks and mobility, particularly in lithologies that are naturally high in organic carbon, such as shales. The overarching hypothesis of this study is that upland regions developed in geologic settings with abundant petrogenic carbon store and actively cycle carbon in the weathered DVZ below the soil and above the water table at rates that are significant and currently unconstrained. In order to quantify this cycling, the current study combines novel instrumentation techniques allowing new direct sampling of DVZ systems with advanced numerical reactive transport simulations of carbon transport and transformation. Critically, these simulations will explicitly treat the three isotopes of carbon (the abundant 12C, the stable rare 13C and the radioactive 14C) in a unified framework, thus clearly parsing between the contributions of modern surface derived carbon and lithologic carbon sources in integrated measurements of fluid and gas phase fluxes. This novel model capability will be applied to test the role of DVZ carbon cycling as a regulator of water quality and geological weathering in two complementary field sites both located in organic carbon rich shale lithologies. The first is the Eel River Critical Zone Observatory (ERCZO) in Mendocino County, California, and the second is the Lawrence Berkeley National Laboratory Watershed Function Scientific Focus Area (SFA) in the East River watershed, near Crested Butte, Colorado. At the ERCZO, a novel vadose zone monitoring system has been installed in a 20 m thick, partially saturated, weathered shale hillslope, and preliminary data already indicate substantial CO2 flux generated many meters below the soil surface. At the SFA field site, an instrumented hillslope transect indicates a more complex multi-dimensional fluid and solute transport regime, which will serve as a key test of the calibrated models. Collectively, this project will advance understanding of the cycling of carbon belowground and in relation to transport pathways across the poorly constrained DVZ characteristic of primary water recharge areas. The key product of this work will be enhanced isotope simulation capabilities that are robust and publicly available for application across a broad diversity of systems.

58 GEOSCIENCES↗

DOE OSTI2024

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗

DOE OSTI2026

An immersed interface method for microstructure-scale electrochemical battery models: numerical formulation and performance portable implementation

We present the numerical formulation, verification, and performance portable implementation of an immersed interface method for microstructure scale electrochemical modeling of batteries. The innovation in this approach is the resolution of chemical species and electrostatic potential discontinuities at active interfaces without the use of interface conforming unstructured grids. A unified formulation on Cartesian grids for all domains (electrodes and electrolyte) is used with interfacial flux conditions applied using volume fraction or “color” function gradients. We have developed one dimensional and two dimensional test cases with analytic solutions for electrochemical modeling using which we verified the consistency and accuracy of our scheme. Our solver is also validated against solutions from a macroscale model and an unstructured multi-subdomain solver for a full lithium ion cell. We then demonstrated the utility of our solver on an image-based complex battery electrode microstructure at high charging rate. Our technique also exhibits good scalability on distributed memory architectures using central processing units (CPU), with problem sizes up to 1.8 billion degrees of freedom and with 5400 ranks. Initial performance studies of our open-source performance portable solver showed about 70 times speed up using a graphics processing unit (GPU) compared to single compute core for a problem with 4 million cells.

25 ENERGY STORAGE↗

DOE OSTI2024

A high-order finite difference method for moving immersed domain boundaries and material interfaces

Here, we present a high-order sharp treatment of immersed moving domain boundaries and material interfaces, and apply it to the advection-diffusion equation in two and three dimensions. The spatial discretization combines dimension-split finite difference schemes with an immersed boundary treatment based on a weighted least-squares reconstruction of the solution, providing stable discretizations with up to sixth order accuracy for diffusion terms and third order accuracy for advection terms. The temporal discretization relies on a novel strategy for maintaining high-order temporal accuracy in problems with moving boundaries that minimizes implementation complexity and allows arbitrary explicit or diagonally-implicit Runge-Kutta schemes. The approach is broadly compatible with popular PDE-specialized Runge-Kutta time integrators, including low-storage, strong stability preserving, and diagonally implicit schemes. Through numerical experiments we demonstrate that the full discretization maintains high-order spatial and temporal accuracy in the presence of complex 3D geometries and for a range of boundary conditions, including Dirichlet, Neumann, and flux conditions with large jumps in coefficients.

97 MATHEMATICS AND COMPUTING↗