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DOE OSTI2026

A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method that maintains high-order temporal accuracy in both velocity and pressure for steady and unsteady velocity boundary conditions. Fourth order spatial accuracy is achieved through a novel fifth order IIM discretization scheme for the advection term, as well as existing high-order interface-corrected finite difference schemes for the other differential operators. Using a set of manufactured flow problems with stationary and moving boundaries, we demonstrate fourth order convergence of velocity and pressure in the infinity norm, both inside the domain and on the immersed boundaries. The solver’s performance is further validated through a range of practical flow simulations, highlighting its efficiency over a second order scheme. Finally, we showcase the ability of our immersed discretization scheme to handle interface-coupled multiphysics problems by solving a conjugate heat transfer problem with multiple immersed solids. Overall, the proposed approach robustly combines the efficiency of high order discretization schemes with the flexibility of immersed discretizations for flow problems with complex, moving boundaries and interfaces.

42 ENGINEERING↗

DOE OSTI2026

Development of MOSCATO: A CFD-Level Electrochemistry and Corrosion Simulator for Molten Salt Systems

For both coolant and fueled variants of molten salt reactors (MSRs), the corrosion of structural materials is a significant challenge. The corrosion stems from chemical and electrochemical reactions initiated by fissile material, fission products, and impurities in the salt. Lower-fidelity models rely on empirical correlations for mass transfer, simplified lumped temperature profiles, and similar assumptions. They do not capture detailed spatial variations in complex geometries, creating the need for high-fidelity modeling to bridge this gap.As we approach the demonstration and possible deployment of MSRs in this decade, the development of a high-fidelity, high-performance simulator becomes imperative. To simulate the complex electrochemical environment and corrosion within molten salt systems, we have developed the Molten Salt Chemistry And TranspOrt (MOSCATO) code. This endeavor is comprised of three essential components. First, mass transfer equations are coupled with the Navier-Stokes equations in order to account for the transport of species in the salt. Second, the diffusion of alloy constituents, such as Cr, Fe, Ni, etc. is simulated within the structural metals. Third, the alloy and salt domains are coupled to account for the heterogeneous chemical and electrochemical reactions that occur at the salt-alloy interface.MOSCATO manages all three components within the framework of the highly scalable, open-source spectral element method computational fluid dynamics code Nek5000/NekRS. This integration enables MOSCATO to harness the immense computational power of modern high-performance computing resources, ensuring both high fidelity and computational speed.In addition to code development, we have initiated a comprehensive verification and validation campaign, utilizing data from diverse sources. First, MOSCATO's electrochemical solver was verified with reference numerical data. Then validation occurred against experiments: one of a thermal galvanic cell and the other for corrosion in flowing molten salt of FLiNaK (LiF-NaF-KF). This campaign verified and validated MOSCATO as a reliable tool for simulating electrochemical environments and corrosion in molten salt systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

Emergent viscous hydrodynamics from a single quantum particle

We investigate an explicit example of how spatial decoherence can lead to hydrodynamic behavior in the late-time, long-wavelength regime of open quantum systems. We focus on the case of a single nonrelativistic quantum particle linearly coupled to a thermal bath of noninteracting harmonic oscillators at temperature T , a la Caldeira and Leggett. Taking advantage of decoherence in the position representation, we expand the reduced density matrix in powers of the off-diagonal spatial components, so that high-order terms are suppressed at late times. Truncating the resulting power series at second order leads to a set of dissipative transient hydrodynamic equations similar to the nonrelativistic limit of equations widely used in simulations of the quark-gluon plasma formed in ultrarelativistic heavy-ion collisions. Transport coefficients are directly determined by the damping constant γ , which quantifies the influence of the environment. The asymptotic limit of our hydrodynamic equations reduces to the celebrated Navier-Stokes equations for a compressible fluid in the presence of a drag force. Furthermore, our results shed new light on the onset of hydrodynamic behavior in open quantum systems where a system with few degrees of freedom is coupled to a large thermal environment.

Hydrodynamics↗

DOE OSTI2025

Dominant balance-based adaptive mesh refinement for incompressible fluid flows

This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a Gaussian mixture model (GMM) to classify grid cells into active and passive regions based on the dominant physical interactions within the equation space. By modeling truncation error probabilistically from discretized terms, the method identifies regions of high interaction where numerical accuracy is most sensitive to resolution. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined thresholds, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for steady and unsteady flow past a cylinder, the DBA-based AMR method achieves comparable accuracy to high-resolution grids while reducing computational costs by up to 70 %. The validation highlights the method’s effectiveness in capturing complex flow features while minimizing grid cells, directing computational resources toward regions with the most critical dynamics. This modular and scalable strategy is adaptable to a wide range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

A Geometric Volume of Fluid-Based Multiphase Flow Solver Extension to the Reacting Flow Solver, PeleLM

A new algorithm is presented to simulate multiphase flows with surface tension in a pathway for spray combustion simulation. The algorithm combines capabilities from two open-source packages, including the interface reconstruction library (IRL), a library of computational geometry routines to enable the volume of fluid (VOF) method, and PeleLM, a solver for the reacting Navier-Stokes equations. Additionally, surface tension is implemented using the continuum surface force (CSF) model with an improved height function technique in the volume fraction field. Spurious errors in volume fraction arising from our combined strategy are corrected through a topology-based method that improves both numerical stability and accuracy. Multiple validation simulations are conducted, including (i) translations and rotations of Zalesak's disk, (ii) a stationary circular droplet with surface tension, (iii) an oscillating elliptical droplet, and (iv) three-dimensional deformation of a spherical droplet. Results indicate that the combined scheme retains the favorable properties of each of the component algorithms.

42 ENGINEERING↗

DOE OSTI2025

Analysis of the weighted shifted boundary method for the Poisson and Stokes problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L2-error estimates can also be derived.

Approximate domain boundaries↗

DOE OSTI2025

Porous Flow Modeling of Axial Gas Redistribution in Fragmented LWR Fuel Rods using MOOSE

Understanding how gas axially redistributes within fragmented fuel pellets is crucial for predicting the behavior of Light Water Reactor (LWR) fuel rods, particularly during transient and accidental scenarios. The time scale of this phenomenon plays a fundamental role in determining the progression and hazard of a Loss Of Coolant Accident (LOCA), especially when high burn-up fuel in a severe state of fragmentation is involved. Here, this study presents a Computational Fluid Dynamics (CFD) model developed within the Multiphysics Object-Oriented Simulation Environment (MOOSE) to predict the time-scale of plenum depressurization in Light-Water Reactor (LWR) fuel rods driven by axial gas transport through fragmented pellets. The model examines the effects of incorporating non-linearities in the friction term by comparing the results with experimental data. The experiment employed surrogate fuel rods containing pellets subjected to mechanical and/or thermal loadings to simulate various severity of cracking, and aimed at studying the influence of fuel conditions on axial gas redistribution. The results of this analysis indicate that under certain flow regime conditions - determined by the value of an equivalent Reynolds number - accounting for the non-linear friction term in Navier-Stokes equations guarantees better predictions for the time-scale of plenum depressurization. Also, the model enabled the simulation of the pressure decay by assigning distinct permeability values to each pellet instead of a single uniform value. Multiple simulations were run across all possible pellet position combinations, having each pellet assigned with values of permeability extracted from the experimental data. This allows to quantify the impact of the considering various non-uniform distributions of permeability on the dynamics of axial gas redistribution. The present work findings enhance the understanding of axial gas transport, and provide valuable insights for the integration of a model for predicting the axial gas redistribution during a LOCA scenario into the BISON fuel performance code.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Openpronghorn

OpenPronghorn is a simulation tool specifically tailored for modeling thermal-hydraulic phenomena in advanced nuclear reactors. It is built on the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source platform that facilitates the development of high-performance scientific computing applications. OpenPronghorn solves the Navier-Stokes equations, which describe the conservation of mass, momentum, and energy in fluid flows, using the finite volume numerical method. The code supports a wide range of fluid flow conditions that are applicable to nuclear reactors, including incompressible and weakly compressible flows, as well as single-phase and multiphase flows. It is capable of modeling diverse flow regimes, including laminar and turbulent flows, using various turbulence models such as the standard k-epsilon models, the v2f model, and the mixing length model. For multiphase flows, OpenPronghorn employs a mixture a Eulerian modeling approach with mixture, drift-flux, and full Eulerian models, and includes open-sourced interfacial transfer correlations for drag, exchange, and heat transfer coming from the scientific literature. OpenPronghorn's modular design allows it to handle multiscale simulations, ranging from detailed Reynolds-Averaged Navier Stokes (RANS) simulations to coarse-mesh and lumped parameter models. This flexibility enables users to perform high-fidelity simulations of specific reactor components as well as system-level analyses of entire reactor circuits. The code can be coupled with other MOOSE-based tools using the MultiApp system, allowing for the transfer of coupling quantities such as mass flow rates, heat fluxes, and boundary conditions between different simulation scales. One of the main features of OpenPronghorn is the it includes built-in validation cases from the open-source scientific literature and supports the implementation of user-defined models and correlations through MOOSE's FunctorMaterial system. OpenPronghorn is designed to be computationally efficient, leveraging the SIMPLE projection method for large-scale problems, and can be run on high-performance computing systems to handle the extensive computational demands of detailed reactor simulations. Overall, OpenPronghorn is a versatile and robust tool that provides critical insights into the thermal-hydraulic behavior of advanced nuclear reactors, supporting the design, safety, and optimization of next-generation nuclear energy systems.

Retamales, Mauricio Eduardo Tano [Idaho National L↗

DOE OSTI2025

Photochemically Induced Acousto-optics Fluid Simulations

PIAFS is a finite-difference code to solve the compressible Navier-Stokes equations with chemical heating on Cartesian grids. It models chemical reactions of air (oxygen and carbon dioxide) with ozone subject to radiation. It uses a high-order WENO spatial discretization and explicit Runge-Kutta time integration. It is capable of parallel simulations using MPI. The code is written in C/C++.

Oudin, AlbertineN [Lawrence Livermore National Lab↗

DOE OSTI2025

A spline-based method to obtain spatially dependent viscosity in confined flows

Coupling chemical physics to continuum theories is a critical step to understanding multi-scale phenomena. This paper will connect non-equilibrium molecular dynamics simulations to a continuum-based Navier-Stokes equation that has relaxed the assumption of spatial uniformity in viscosity. Using a form for viscosity based on spline interpolation, viscosity as a function of position is obtained from the least squares fit of the velocity profile measured from molecular simulations of flow in a nanochannel. Viscosity can vary widely, particularly near the channel boundaries, indicating that uniform viscosity is no longer appropriate. Variations of the viscosity near the channel surfaces imply that considering solution and surface chemistry could be necessary to rigorously understand molecular-scale flows in nanochannels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Hydrogen Dispersion Modeling for Development of Smart Distributed Monitoring

Studying hydrogen dispersion is crucial for ensuring the safe and effective deployment of hydrogen as an energy carrier. This study presents a comprehensive CFD modeling framework for simulating hydrogen dispersion at a real-world hydrogen production, storage, and utilization facility. Utilizing the Hydrogen Research Facility under the Advanced Research on Integrated Energy Systems (ARIES) at the National Renewable Energy Laboratory's (NREL) Flatirons campus, controlled hydrogen releases at 27 kg-H2/hr were simulated. The model incorporated site-specific atmospheric conditions, including hourly wind speeds and temperatures recorded between 8 AM and 8 PM from October to December 2023. To reduce computational demands, a statistical reduction technique was applied to condense the dataset to 100 representative scenarios, validated by statistical tests for wind speeds and power law coefficients. Simulations were conducted using the Reynolds-Averaged Navier-Stokes equations. Results demonstrated that wind speed substantially influences hydrogen dispersion, with low wind conditions forming concentrated clouds and higher wind speeds stretching the plume. Additionally, clustering analysis informed optimal sensor placement at various elevations with up to 10 sensor locations on each elevation. This framework offers a robust approach for understanding hydrogen behavior in ambient conditions and informing detection strategies.

08 HYDROGEN↗

NASA NTRS1995

Analysis of developing laminar flows in circular pipes using a higher-order finite-difference technique

A higher-order finite-difference technique is developed to calculate the developing-flow field of steady incompressible laminar flows in the entrance regions of circular pipes. Navier-Stokes equations governing the motion of such a flow field are solved by using this new finite-difference scheme. This new technique can increase the accuracy of the finite-difference approximation, while also providing the option of using unevenly spaced clustered nodes for computation such that relatively fine grids can be adopted for regions with large velocity gradients. The velocity profile at the entrance of the pipe is assumed to be uniform for the computation. The velocity distribution and the surface pressure drop of the developing flow then are calculated and compared to existing experimental measurements reported in the literature. Computational results obtained are found to be in good agreement with existing experimental correlations and therefore, the reliability of the new technique has been successfully tested.

Gladden, Herbert J.↗

NASA NTRS1995

Effect of turbulence models on criticality conditions in swirling flows

The critical state of vortex cores downstream of vortex breakdown has been studied. Base vortical flows were computed using the Reynolds-averaged, axisymmetric Navier-Stokes equations. Standard K - epsilon, RNG and second-order Reynolds stress models were employed. Results indicate that the return to supercriticality is highly dependent on the turbulence model. The K - epsilon model predicted a rapid return of the vortex to supercritical conditions, the location of which showed little sensitivity to changes in the swirl ratio. The Reynolds stress model predicted that the vortex remains subcritical to the end of the domain for each of the swirl ratios employed, and provided results in qualitative agreement with experimental work. The RNG model produced intermediate results, with a downstream movement in the critical location with increasing swirl. Calculations for which area reductions were introduced at the exit in a subcritical flow were also performed using the Reynolds stress model. The structure of the resulting recirculation zone was altered significantly. However, when area reductions were employed within supercritical flows as predicted using the two-equation models, no significant influence on the recirculation zone was noted.

Gatski, Thomas B.↗

DOE OSTI2026

HygroThermFEM v1.0

HygroThermFEM is a Finite Element Method-based numerical calculation engine for solving 2-D heat and moisture transfer problems. This numerical engine is used in the THERM software tool, and its primary purpose is for the analysis of building envelopes (e.g., windows, walls, roofs, foundations, etc.). However, the engine can also be used for any heat and moisture transfer problems that require solving fundamental 2-D energy and mass transfer equations. Fluid flow solutions (Navier-Stokes momentum equations) are not included, but the correlations for various convection heat transfer situations are provided, including the translation of complex cavity geometries into those for which correlations are applicable. The calculation engine is written in C++ and includes an API for connecting to third-party tools.

Vidanovic, Dragan [Lawrence Berkeley National Labo↗

DOE OSTI2025

Thermal relaxation and the complete set of second-order transport coefficients for the unitary Fermi gas from kinetic theory

We compute the complete set of second-order transport coefficients of the unitary Fermi gas, a dilute gas of spin-1/2 particles interacting via an 𝑠 -wave interaction tuned to infinite scattering length. The calculation is based on kinetic theory and the Chapman-Enskog method at second order in the Knudsen expansion. We take into account the exact two-body collision integral. We extend previous results on second-order coefficients related to shear stress by including terms related to heat flow and gradients of the fugacity. We confirm that the thermal relaxation time is given by the simple estimate 𝜏 𝜅 = 𝜅⁢𝑚/(𝑐 𝑃 ⁢𝑇) even if the full collision kernel is taken into account. Furthermore, 𝜅 is the thermal conductivity, 𝑚 is the mass of the particles, 𝑐𝑃 is the specific heat at constant pressure, and 𝑇 is the temperature.

Kinetic theory↗

NASA NTRSDate not supplied

Improvements to RANS Modeling for Aeroheating Predictions on Blunt Bodies

Accurate predictions of aeroheating are critical for designing thermal protection systems for planetary entry vehicles. For larger vehicles, turbulence in the boundary layer can substantially increase convective heating. This turbulence must be accurately modeled to ensure the thermal protection system is sufficient. The majority of hypersonic turbulence model development and validation focuses on boundary layers developing over flat-plates or sharp cones; these cases are substantially different than the boundary layer that develops over the heatshield of a blunt body traveling at hypersonic speeds. Planetary missions often use blunt body geometries, such as the 70-degree sphere-cone favored by Mars missions or the 45-degree sphere-cone planned for the upcoming DAVINCI mission. Due to smaller vehicle size and the lower velocities in the stagnation region, planetary entry vehicles have relatively low Reynolds numbers. Surface curvature and high enthalpy gradients create additional challenges. These difficulties must be addressed to obtain high accuracy needed for the ambitious planetary missions in the upcoming decade. This work focuses on both assessing and improving Reynolds-averaged Navier-Stokes (RANS) turbulence models for blunt-body geometries typical of planetary entry vehicles, with a focus on one-equation and two-equation formulations.

Mars2020↗

NASA NTRS1995

A Navier-Stokes boundary element solver

Using global interpolation functions (GIF's) boundary element solutions are obtained for two-dimensional laminar flows. Two schemes are proposed for handling the convective terms. The first treats convection as a forcing function, and converts the flow equations to pseudo-Poisson equations. In the second scheme, some convective effect is incorporated into the fundamental solution used in constructing the pertinent integral equations. The lid-driven cavity flow is selected as the benchmark problem.

Reddy, D. R.↗

DOE OSTI2025

Modeling and Simulation of Fuel Dispersal During the Loss-of-Coolant Accident

This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗