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DOE OSTI2026

SIERRA Multimechanics Module: Aria Verification Manual - Version 5.30

Presented in this document is a portion of the tests that exist in the Sierra Thermal/Fluids verification test suite. Each of these tests is run nightly with the Sierra/TF code suite and the results of the test checked under mesh refinement against the correct analytic result. For each of the tests presented in this document the test setup, derivation of the analytic solution, and comparison of the code results to the analytic solution is provided. This document can be used to confirm that a given code capability is verified or referenced as a compilation of example problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Comparison of Full-Field and Integrated CFD Convergence Based on Richardson Extrapolation

This work investigated the usefulness of Richardson extrapolation--based discretization error estimates across all points in a solution field to produce a spatial convergence field for a computational fluid dynamics (CFD) simulation. The presented work used previously developed methods for Richardson extrapolation to compute the convergence orders of a CFD simulation at all points of the base (coarsest) mesh solution. Three test cases of increasing complexity were considered: Poiseuille flow, incompressible flow around a sharp corner, and transonic flow over an RAE 2822 airfoil. These test cases highlighted the potential of the proposed method to identify error sources and their relation to the model system-response-quantity convergence orders. However, these test cases also revealed the immaturity of the proposed method stemming from the unreliability of computing observed convergence orders at single points. Nonetheless, the test cases highlighted that the observed convergence orders allow for a more accurate diagnosis of constructive and destructive error transport than mesh pair error estimates. In the long run, the proposed method can be a tool for developing efficient and advanced error management strategies like adaptive mesh refinement.

Weinmeister, Justin↗

DOE OSTI2026

High-Fidelity, Low-Dissipation/Symmetry-Preserving Numerical Scheme for Solving the Euler Equations with Unstructured, Metric-Based Mesh Adaptation

This work presents an overview of a high-fidelity compressible Euler solver that utilizes the continuous Galerkin (CG) method with added artificial numerical diffusion for stabilization to solve a variety of unsteady and steady benchmark inviscid flow problems. This work shows that discretizing the Euler equations with this CG approach and first order basis functions produces a cost-effective stencil as well as simple well-posed boundary conditions. We show through convergence testing with manufactured solutions that the reduced stencil of CG, combined with the low amount of artificial diffusion required when using the stabilization method outlined in this work, leads to stable and highly accurate results for a variety of unsteady and steady applications. When combined with the adaptive mesh refinement approach used for many of the cases in this work, our results show that the flow solver achieves even more accurate results. A variety of inviscid flow cases are presented in this work, including transient 2D cases with complex shock structures and several steady 3D airfoils sections with a constant span.

Doetsch, Kevin [ORNL] (ORCID:0000000267051705)↗

DOE OSTI2025

Performance-portable Binary Neutron Star Mergers with AthenaK

We introduce an extension to the AthenaK code for general-relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes using a 3+1 conservative Eulerian formulation. Like the fixed-spacetime GRMHD solver, we use standard finite-volume methods to evolve the fluid and a constrained-transport scheme to preserve the divergence-free constraint for the magnetic field. We also utilize a first-order flux correction (FOFC) scheme to reduce the need for an artificial atmosphere and optionally enforce a maximum principle to improve robustness. We demonstrate the accuracy of AthenaK using a set of standard tests in flat and curved spacetimes. Using a SANE accretion disk around a Kerr black hole, we compare the new solver to the existing solver for stationary spacetimes using the so-called "HARM-like" formulation. We find that both formulations converge to similar results. We also include the first published binary neutron star (BNS) mergers performed on graphical processing units (GPUs). Thanks to the FOFC scheme, our BNS mergers maintain a relative error of $\mathcal{O}$(10 –11 ) or better in baryon mass conservation up to collapse. Finally, we perform scaling tests of AthenaK on OLCF Frontier, where we show excellent weak scaling of ≥80% efficiency up to 32,768 GPUs and 74% up to 65,536 GPUs for a GRMHD problem in dynamical spacetimes with six levels of mesh refinement. AthenaK achieves an order-of-magnitude speedup using GPUs compared to CPUs, demonstrating that it is suitable for performing numerical relativity problems on modern exascale resources.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

thornado+FLASH-X: A Hybrid Discontinuous Galerkin–Implicit-explicit and Finite-volume Framework for Neutrino-radiation Hydrodynamics in Core-collapse Supernovae

We present neutrino-transport algorithms implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado) and their coupling to self-gravitating hydrodynamics within the adaptive mesh refinement–based multiphysics simulation framework FLASH-X. thornado, developed primarily for simulations of core-collapse supernovae (CCSNe), employs a spectral, six-species two-moment formulation with algebraic closure and special-relativistic observer corrections accurate to $\mathcal{O}(v/c)$, and uses discontinuous Galerkin (DG) methods for phase-space discretization combined with implicit-explicit time stepping. A key development is a nonlinear neutrino–matter coupling algorithm based on nested fixed-point iteration with Anderson acceleration, enabling fully implicit treatment of collisional processes, including energy-coupling interactions such as neutrino–electron scattering and pair production. Coupling to finite-volume (FV) hydrodynamics is achieved through a hybrid DG-FV representation of the fluid variables and operator-split evolution within FLASH-X. The implementation is verified using basic transport tests with idealized opacities and relaxation and deleptonization problems with tabulated microphysics. Spherically symmetric CCSN simulations demonstrate accuracy and robustness of the coupled scheme, including close agreement with the CCSN simulation code Chimera. An axisymmetric CCSN simulation further demonstrates the viability of DG-based neutrino transport for multidimensional supernova modeling within FLASH-X. thornado’s neutrino-transport solver is GPU-enabled using OpenMP offloading or OpenACC, and all CCSN applications included in this work use the GPU implementation. Together, these results establish a foundation for future enhancements in physics fidelity, numerical algorithms, and computational performance, for increasingly realistic large-scale CCSN simulations.

Endeve, Eirik [Oak Ridge National Laboratory (ORNL↗

DOE OSTI2026

Zooming in: SCREAM at 100 m using regional refinement over the San Francisco Bay Area

Pushing global climate models to large-eddy simulation (LES) scales over complex terrain has remained a major challenge. This study presents the first known implementation of a global model – SCREAM (Simple Cloud-Resolving E3SM Atmosphere Model) – at 100 m horizontal resolution using a regionally refined mesh (RRM) over the San Francisco Bay Area. Two hindcast simulations were conducted to test performance under both strong synoptic forcing and weak, boundary-layer-driven conditions. We demonstrate that SCREAM can stably run at LES scales while realistically capturing topography, surface heterogeneity, and coastal processes. The 100 m SCREAM-RRM substantially improves near-surface wind speed, temperature, humidity, and pressure biases compared to the baseline 3.25 km simulation, and better reproduces fine-scale wind oscillations and boundary-layer structures. These advances leverage SCREAM's scale-aware SHOC turbulence parameterization, which transitions smoothly across scales without tuning. Performance tests show that while CPU-only simulations remain costly, GPU acceleration with SCREAMv1 on NERSC's Perlmutter system enables two-day hindcasts to complete in under two wall-clock days. Our results open the door to LES-scale studies of orographic flows, boundary-layer turbulence, and coastal clouds within a fully comprehensive global modeling framework.

Geosciences↗

NASA NTRS1973

Mixed finite-difference scheme for analysis of simply supported thick plates.

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Noor, A. K.↗

NASA NTRS1978

Numerical solution of the Navier-Stokes equations for blunt nosed bodies in supersonic flows

A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.

Warsi, Z. U. A.↗

NASA NTRS1978

Finite element mesh configurations using isoenergetics and equalized energy levels

The concept of equalizing energy levels was shown to be a viable additional criterion in laying out finite element grids according to the isoenergetic discretization technique. Similar problems specifically with respect to mesh refinement in piecewise approximation theory are being researched. Common criteria in both areas are developed in an effort to cope with the question of discretization for improved piecewise approximations.

Turcke, D. J.↗

NASA NTRS1980

CAS2D: FORTRAN program for nonrotating blade-to-blade, steady, potential transonic cascade flows

An exact, full-potential-equation (FPE) model for the steady, irrotational, homentropic and homoenergetic flow of a compressible, homocompositional, inviscid fluid through two dimensional planar cascades of airfoils was derived, together with its appropriate boundary conditions. A computer program, CAS2D, was developed that numerically solves an artificially time-dependent form of the actual FPE. The governing equation was discretized by using type-dependent, rotated finite differencing and the finite area technique. The flow field was discretized by providing a boundary-fitted, nonuniform computational mesh. The mesh was generated by using a sequence of conforming mapping, nonorthogonal coordinate stretching, and local, isoparametric, bilinear mapping functions. The discretized form of the FPE was solved iteratively by using successive line overrelaxation. The possible isentropic shocks were correctly captured by adding explicitly an artificial viscosity in a conservative form. In addition, a three-level consecutive, mesh refinement feature makes CAS2D a reliable and fast algorithm for the analysis of transonic, two dimensional cascade flows.

Dulikravich, D. S.↗

NASA NTRS1980

A new coordinate transformation for turbulent boundary layer flows

The transformation permits a uniform mesh to be used in the computational coordinate which extends across the layer. This coordinate transformation uses the local value of the skin friction coefficient to scale the thickness of the wall layer region, and the local maximum value of turbulent viscosity to scale the boundary-layer thickness. Results are presented for two dimensional boundary layers in both positive and negative pressure gradients and comparisons are made with experimental data and conventional variable-grid results for low speed turbulent boundary-layers. The cases chosen illustrate the capability of this new transformation to capture the boundary layer growth over the full extent of laminar, transitional, and turbulent flow with no grid adjustment as well as its ability to consistently enlarge the wall layer region for accurate shear stress representation. Results of mesh refinement studies using the new coordinate transformation are presented.

Carter, J. E.↗

NASA NTRS1984

High speed inviscid compressible flow by the finite element method

The finite element method and an explicit time stepping algorithm which is based on Taylor-Galerkin schemes with an appropriate artificial viscosity is combined with an automatic mesh refinement process which is designed to produce accurate steady state solutions to problems of inviscid compressible flow in two dimensions. The results of two test problems are included which demonstrate the excellent performance characteristics of the proposed procedures.

Zienkiewicz, O. C.↗

NASA NTRS1984

Accuracy of Three Dimensional Solid Finite Elements

The results of a study to determine the accuracy of the three dimensional solid elements available in NASTRAN for predicting displacements is presented. Of particular interest in the study is determining how to effectively use solid elements in analyzing thick optical mirrors, as might exist in a large telescope. Surface deformations due to thermal and gravity loading can be significant contributors to the determination of the overall optical quality of a telescope. The study investigates most of the solid elements currently available in either COSMIC or MSC NASTRAN. Error bounds as a function of mesh refinement and element aspect ratios are addressed. It is shown that the MSC solid elements are, in general, more accurate than their COSMIC NASTRAN counterparts due to the specialized numerical integration used. In addition, the MSC elements appear to be more economical to use on the DEC VAX 11/780 computer.

Case, W. R.↗

NASA NTRS1984

A study of interply layer effects on the free-edge stress field of angleplied laminates

The general-purpose finite-element program MSC/NASTRAN is used to study the interply layer effects on the free-edge stress field of symmetric angleplied laminates subjected to uniform tensile stress. The free-edge region is modeled as a separate substructure (superelement) which enables easy mesh refinement and provides the flexibility to move the superelement along the edge. The results indicate that the interply layer reduces the stress intensity significantly at the free edge. Another important observation of the study is that the failures observed near free edges of these types of laminates could have been caused by the interlaminar shear stresses.

Murthy, P. L. N.↗

NASA NTRS1985

On the accuracy of least squares methods in the presence of corner singularities

Elliptic problems with corner singularities are discussed. Finite element approximations based on variational principles of the least squares type tend to display poor convergence properties in such contexts. Moreover, mesh refinement or the use of special singular elements do not appreciably improve matters. It is shown that if the least squares formulation is done in appropriately weighted space, then optimal convergence results in unweighted spaces like L(2).

Cox, C. L.↗

NASA NTRS1985

Study of second order upwind differencing in a recirculating flow

The accuracy and stability of the second order upwind differencing scheme was investigated. The solution algorithm employed is based on a coupled solution of the nonlinear finite difference equations by the multigrid technique. Calculations have been made of the driven cavity flow for several Reynolds numbers and finite difference grids. In comparison with the hybrid differencing, the second order upwind differencing is somewhat more accurate but it is not monotonically accurate with mesh refinement. Also, the convergence of the solution algorithm deteriorates with the use of the second order upwind differencing.

Vanka, S. P.↗

NASA NTRS1985

Recent improvements in efficiency, accuracy, and convergence for implicit approximate factorization algorithms

In 1977 and 1978, general purpose centrally space differenced implicit finite difference codes in two and three dimensions have been introduced. These codes, now called ARC2D and ARC3D, can run either in inviscid or viscous mode for steady or unsteady flow. Since the introduction of the ARC2D and ARC3D codes, overall computational efficiency could be improved by making use of a number of algorithmic changes. These changes are related to the use of a spatially varying time step, the use of a sequence of mesh refinements to establish approximate solutions, implementation of various ways to reduce inversion work, improved numerical dissipation terms, and more implicit treatment of terms. The present investigation has the objective to describe the considered improvements and to quantify advantages and disadvantages. It is found that using established and simple procedures, a computer code can be maintained which is competitive with specialized codes.

Pulliam, T. H.↗

NASA NTRS1985

A study of interply layer effects on the free edge stress field of angleplied laminates

Murthy, P. L. N.↗