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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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The curled wake model: a three-dimensional and extremely fast steady-state wake solver for wind plant flows

Abstract. Wind turbine wake models typically require approximations, such as wake superposition and deflection models, to accurately describe wake physics. However, capturing the phenomena of interest, such as the curled wake and interaction of multiple wakes, in wind power plant flows comes with an increased computational cost. To address this, we propose a new hybrid method that uses analytical solutions with an approximate form of the Reynolds-averaged Navier–Stokes equations to solve the time-averaged flow over a wind plant. We compare results from the solver to supervisory control and data acquisition data from the Lillgrund wind plant obtaining wake model predictions which are generally within 1 standard deviation of the mean power data. We perform simulations of flow over the Columbia River Gorge to demonstrate the capabilities of the model in complex terrain. We also apply the solver to a case with wake steering, which agreed well with large-eddy simulations. This new solver reduces the time – and therefore the related cost – it takes to simulate a steady-state wind plant flow (on the order of seconds using one core). Because the model is computationally efficient, it can also be used for different applications including wake steering for wind power plants and layout optimization.

17 WIND ENERGY↗

SANDWake3D

SAND2026-23958O SANDWake3D models atmospheric surface layers and turbine wakes using a 3D parabolic RANS solver. This Python-based tool uses an efficient method to simulate wakes, capturing complex wake behaviors such as wind shear, veer, and atmospheric stratification, naturally. It has been calibrated and validated against higher-fidelity large eddy simulations (LES), providing reliable results for wind energy and atmospheric research applications. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗

Impact of Numerical Hydrodynamics in Turbulent Mixing Transition Simulations

Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the Harten–Lax–van Leer (HLL) Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep—denoted split; the Harten–Lax–Van Leer-Contact (HLLC) Riemann solver using a directionally unsplit strategy and parabolic reconstruction—denoted unsplit; and the HLLC Riemann solver using unsplit and a low-Ma correction (LMC)—denoted unsplit*. Three case studies are considered: (1) a shock tube problem prototyping shock-driven turbulent mixing, (2) the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and, (3) an homogeneous isotropic turbulence (HIT) case, focusing on the impact of discretization on transition and decay from fixed well-characterized initial conditions. Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC. For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments. Relevant comparisons of ILES based on Euler and Navier–Stokes equations addressing potential occurrence of low-Re regimes in the applications are presented. Unsplit schemes are instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution. HIT analysis confirms higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.

74 ATOMIC AND MOLECULAR PHYSICS↗

Exponential Time Differencing Schemes for Fuel Depletion and Transport in Molten Salt Reactors: Theory and Implementation

A numerical framework for modeling depletion and mass transport in liquid-fueled molten salt reactions is presented based on exponential time differencing. The solution method involves using the finite volume method to transform the system of partial differential equations (PDEs) into a much larger system of ordinary differential equations. The key part of this method involves solving for the exponential of a matrix. We explore six different algorithms to compute the exponential in a series of progression problems that explore physical transport phenomena in molten salt reactors. This framework shows good results for solving linear parabolic PDEs with each of the six matrix exponential algorithms. For large problems, the series solvers such as Padé and Taylor have large run times, which can be mitigated by using the Krylov subspace.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A Study on Particle Trajectory Error in Finite-Element Particle-in-Cell Algorithms

Particle-in-cell (PIC) algorithms are widely used for the simulation of kinetic plasmas. PIC algorithms account for the interaction between charged particles in a plasma and the electromagnetic field in ambient space, including self-field interactions. The objective of this article is to study the error in charged particle trajectories present in finite-element (FE)-based PIC algorithms on unstructured meshes. We study how the trajectory error behaves according to the FE mesh resolution and the matrix solver employed in the FE algorithm. The study is performed by considering a trajectory established by a parabolic electric potential and an axial magnetic force acting on the charged particle. Under a proper choice combination of electric and magnetic field parameters, the 2-D particle trajectories comprise closed orbits. Numerical errors cause small perturbations on the trajectories, with cumulative effects. As a result, the resulting orbital trajectories exhibit distortions including spurious apsidal precession. These distortions provide a clear imprint of the numerical error. Here, we also study the numerical error in a quantitative fashion by computing the distance norm between the trajectories obtained by the exact fields and numerical fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Efficient Solution Methods for Large-scale Optimization Problems Constrained by Time-dependent Partial Differential Equations (Final Report)

The objectives of this project are to devise and analyze efficient solvers for several classes of PDE- constrained optimization problems. The project was initially focused on, but not restricted to time- dependent PDE-constraints such as parabolic equations, time-dependent fluid flows (Navier-Stokes equations), hyperbolic equations (Burgers equation, shallow water equations). Other constraints considered are PDEs with stochastic coefficients. Additional elements of interest are the handling of problems with control and/or state inequality constraints or non-differentiable regularization terms, and boundary controls. A direction of work not initially listed among the goals, which was triggered by conversations with DOE scientists from the Sandia National Labs, is to develop efficient solvers for optimization- based domain-decomposition PDE-solvers. Also targeted in the project are a number of technical issues necessary for facilitating the integration of the methods resulted from this project with existing high-performance packages developed at DOE national labs; this integration is expected to further enable the scientific community to use the novel methods. An example of such a task is the need to develop algebraic multigrid (AMG) versions of the algorithms. A list of accomplishments in several areas is detailed as well as a list of publications.

97 MATHEMATICS AND COMPUTING↗

Optimizing multigrid reduction-in-time and Parareal coarse-grid operators for linear advection

Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent partial differential equations (PDEs) in modern high-performance computing environments. While these techniques have been very successful for parabolic equations, it has often been observed that their performance suffers dramatically when applied to advection-dominated problems or purely hyperbolic PDEs using standard rediscretization approaches on coarse grids. In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically nonscalable or even divergent behavior of these solvers for this problem. To overcome these failings, we replace rediscretization on coarse grids with improved coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory. Therefore, one of our main findings is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behavior of the hyperbolic problem by tracking the characteristic curves. Our approach is tested for schemes of various orders using explicit or implicit Runge–Kutta methods combined with upwind-finite-difference spatial discretizations. In all cases, we obtain scalable convergence in just a handful of iterations, with parallel tests also showing significant speed-ups over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗

High-order dimensionally-split Cartesian embedded boundary method for non-dissipative schemes

Centered finite-difference schemes are commonly used for high-fidelity turbulent flow simulations in canonical configurations because of their non-dissipative property and computational efficiency. However, their use in flow simulations over complex geometries is limited by the requirements of a structured grid and a stable boundary treatment in the absence of artificial (numerical) dissipation. Cartesian embedded boundary (EB) approaches provide an efficient structured-grid framework to apply difference schemes over complex domains. However, they are often restricted to low orders of accuracy because of numerical instabilities at the embedded boundaries and the issues of small-cell problem that are difficult to address with high-order accuracy. The present work discusses a systematic approach to obtain high-order EB methods with non-dissipative centered schemes in the interior. This approach, based on satisfying the primary and secondary conservation conditions, is employed to derive EB schemes that are up to sixth-order accurate in the interior and fourth-order accurate globally for hyperbolic, parabolic as well as incompletely parabolic problems. The proposed finite-difference discretization is, by construction, dimensionally split and addresses the small-cell problem without any cell/geometry transformations, thus, highly simplifying implementation in a flow solver. Various linear and non-linear numerical tests are performed to evaluate the stability and the accuracy of the proposed EB schemes.

97 MATHEMATICS AND COMPUTING↗

Formulation of 8-moment plasma transport with application to the Nernst effect

8-moment plasma models using two different distribution functions are used to study the Nernst effect and heat transport in dense plasma. These models are presented in hyperbolic form in contrast to traditional parabolic systems derived from perturbing the distribution function, as in Braginskii [Rev. Plasma Phys. 1, 205 (1965)]. The hyperbolic moment formulation can be solved implicitly in time with straightforward and fast local solvers. The numerical implementation of 8-moment models with the relaxation method in the PERSEUS code is also presented. To test 8-moment PERSEUS compared to Braginskii’s transport equations, a verification test for the Nernst thermomagnetic wave by Velikovich et al. [Phys. Plasmas 26, 112702 (2019)] is performed that confirms the presence of the same physics, but with slight differences in the transport coefficients, which are tabulated in the limits of high and low magnetization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Integral Kernel Methods for Nonlinear Parabolic-Elliptic Systems

Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic and parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.

PDE systems↗

Modeling of the effects of non-equilibrium excitation and electrode geometry on H 2 /air ignition in a nanosecond plasma discharge

In this work, we present the results of two-dimensional modeling of the effects of non-equilibrium excitation and electrode geometry on H 2 /air ignition in a nanosecond plasma discharge. A multiscale adaptive reduced chemistry solver for plasma assisted combustion (MARCS-PAC) based on PASSKEy discharge modeling package and compressible multi-component reactive flow solver ASURF+ is developed and validated. This model is applied to simulate the impact of non-equilibrium plasma excitation and electrode geometry and heat loss on the dynamics of the discharge from streamer to spark and ignition kernel development in a H 2 /air mixture with a pair of cylindrical electrodes. The results show that the plasmagenerated species (N 2 (A), N 2 (B), N 2 (a'), N 2 (C), O( 1 D), O and H) in the spark and afterglow significantly accelerate the ignition kernel development. The increase of discharge voltage at the same total discharge energy promotes the non-equilibrium active species production. It is found that the production of electronically excited species at higher reduced electric field strength is more efficient in enhancing ignition in comparison to the vibrational excitation and heating. Moreover, the 2D simulation clearly reveals that the electric field and active species distribution are highly non-uniform. The streamers are initiated at the sharp outer edges of the negative and positive electrodes by a strong electric field while the electric field is much weaker at the centerline of the electrodes. Furthermore, the simulations reveal that the ignition enhancement is sensitive to the variation of electrode shape, diameter, and gap size due to the changes of electric field distribution and location of streamer formation. A cylindrical electrode produces a larger discharge volume and ignition kernel than the parabolic and spherical electrodes, when the discharge is localized near the axis of the gap. It is found that there is a non-monotonic dependence of ignition kernel size on the electrode diameter and inter-electrode distance. The increase of electrode diameter and gap size above the optimal conditions leads to the reduction of ignition kernel volume, due to the decrease of active species concentration and gas temperature. At a larger electrode surface area and electrode diameter as well as smaller electrode gap size, the heat loss to electrode plays a greater role in reducing the ignition kernel size and slowing ignition kernel development. This work provides insights and guidance to understand the kinetic enhancement of non-equilibrium plasma and the effects of electrode geometries on ignition for the optimization ignitors in advanced engines.

42 ENGINEERING↗