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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

AthenaK: A Performance-portable Version of the Athena++ Adaptive Mesh Refinement Framework

We describe AthenaK: a new implementation of the Athena++ block-based adaptive mesh refinement framework using the Kokkos programming model. Finite volume methods for Newtonian, special relativistic, and general relativistic (GR) hydrodynamics and magnetohydrodynamics (MHD), and GR-radiation hydrodynamics and MHD, as well as a module for evolving Lagrangian tracer or charged test particles (e.g., cosmic rays) are implemented using the framework. In two companion papers, we describe (1) a new solver for the Einstein equations based on the Z4c formalism, and (2) a GRMHD solver in dynamical spacetimes also implemented using the framework, enabling new applications in numerical relativity. By adopting Kokkos, the code can be run on virtually any hardware, including CPUs, GPUs from multiple vendors, and emerging Advanced RISC Machine processors. AthenaK shows excellent performance and weak scaling, achieving over 1 billion cell updates per second for hydrodynamics in three dimensions on a single NVIDIA Grace Hopper processor. It does this with a typical parallel efficiency of 80% on 65,536 AMD GPUs on the OLCF Frontier system. Such performance portability enables AthenaK to leverage modern exascale computing systems for challenging applications in astrophysical fluid dynamics, numerical relativity, and multimessenger astrophysics.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Simulating coupled surface–subsurface flows with ParFlow v3.5.0: capabilities, applications, and ongoing development of an open-source, massively parallel, integrated hydrologic model

Surface flow and subsurface flow constitute a naturally linked hydrologic continuum that has not traditionally been simulated in an integrated fashion. Recognizing the interactions between these systems has encouraged the development of integrated hydrologic models (IHMs) capable of treating surface and subsurface systems as a single integrated resource. IHMs are dynamically evolving with improvements in technology, and the extent of their current capabilities are often only known to the developers and not general users. This article provides an overview of the core functionality, capability, applications, and ongoing development of one open-source IHM, ParFlow. ParFlow is a parallel, integrated, hydrologic model that simulates surface and subsurface flows. ParFlow solves the Richards equation for three-dimensional variably saturated groundwater flow and the two-dimensional kinematic wave approximation of the shallow water equations for overland flow. The model employs a conservative centered finite-difference scheme and a conservative finite-volume method for subsurface flow and transport, respectively. ParFlow uses multigrid-preconditioned Krylov and Newton–Krylov methods to solve the linear and nonlinear systems within each time step of the flow simulations. The code has demonstrated very efficient parallel solution capabilities. ParFlow has been coupled to geochemical reaction, land surface (e.g., the Common Land Model), and atmospheric models to study the interactions among the subsurface, land surface, and atmosphere systems across different spatial scales. This overview focuses on the current capabilities of the code, the core simulation engine, and the primary couplings of the subsurface model to other codes, taking a high-level perspective.

58 GEOSCIENCES↗

DOE OSTI2024

rSHUD v2.0: advancing the Simulator for Hydrologic Unstructured Domains and unstructured hydrological modeling in the R environment

Abstract. Hydrological modeling is a crucial component in hydrology research, particularly for projecting future scenarios. However, achieving reproducibility and automation in distributed hydrological modeling research for modeling, simulation, and analysis is challenging. This paper introduces rSHUD v2.0, an innovative, open-source toolkit developed in the R environment to enhance the deployment and analysis of the Simulator for Hydrologic Unstructured Domains (SHUD). The SHUD is an integrated surface–subsurface hydrological model that employs a finite-volume method to simulate hydrological processes at various scales. The rSHUD toolkit includes pre- and post-processing tools, facilitating reproducibility and automation in hydrological modeling. The utility of rSHUD is demonstrated through case studies of the Shale Hills Critical Zone Observatory in the USA and the Waerma watershed in China. The rSHUD toolkit's ability to quickly and automatically deploy models while ensuring reproducibility has facilitated the implementation of the Global Hydrological Data Cloud (https://ghdc.ac.cn, last access: 1 September 2023), a platform for automatic data processing and model deployment. This work represents a significant advancement in hydrological modeling, with implications for future scenario projections and spatial analysis.

Shu, Lele (ORCID:0000000269034466)↗

NASA NTRS1976

Finite-volume solution of the Euler equations for steady three-dimensional transonic flow

A numerical finite-volume method is proposed for solving the Euler equations of a steady three-dimensional flow. The subsonic regions embedded in steady supersonic flow about aircraft are computed by introducing a time-dependent coordinate system that maps the fuselage and wing into one coordinate surface. The suitability of the method to a delta-winged aircraft is demonstrated, and its applicability to rectangular-winged aircraft and problems in internal transonic flow is pointed out.

Rizzi, A.↗

NASA NTRS1979

Recent progress in finite-volume calculations for wing-fuselage combinations

Progress in the application of finite-volume methods to the calculation of transonic potential flows past general wing-body combinations is reviewed. Two different methods of generating boundary-conforming grids are investigated, and the results compared to provide an estimate of solution sensitivity to grid geometry. Both conservative and quasi-conservative difference schemes are used in one of the coordinate systems. Results show that the error introduced by the quasi-conservative formulation seems to be small, although a one-dimensional analysis suggests that schemes of this type do not necessarily produce mass-conserving shocks. Comparison of calculated results with experimental data for realistic fuselage geometries clearly shows the importance of modelling the effect of fuselage geometry upon the wing pressure distribution.

Caughey, D. A.↗

NASA NTRS1980

WIND: Computer program for calculation of three dimensional potential compressible flow about wind turbine rotor blades

A computer program is presented which numerically solves an exact, full potential equation (FPE) for three dimensional, steady, inviscid flow through an isolated wind turbine rotor. The program automatically generates a three dimensional, boundary conforming grid and iteratively solves the FPE while fully accounting for both the rotating cascade and Coriolis effects. The numerical techniques incorporated involve rotated, type dependent finite differencing, a finite volume method, artificial viscosity in conservative form, and a successive line overrelaxation combined with the sequential grid refinement procedure to accelerate the iterative convergence rate. Consequently, the WIND program is capable of accurately analyzing incompressible and compressible flows, including those that are locally transonic and terminated by weak shocks. The program can also be used to analyze the flow around isolated aircraft propellers and helicopter rotors in hover as long as the total relative Mach number of the oncoming flow is subsonic.

Dulikravich, D. S.↗

NASA NTRS1981

Calculations of transonic potential flow over cascades

Transonic flow through a cascade was studied by using the full potential equation and the finite volume method of Jameson and Caughey. The C-type computational grid is generated by an electrostatic analogy and simple shearing transformation. The solution algorithm includes an option of using either an artificial density or an artificial viscosity formulation of the dissipative term. Using the developed code, flows through a cascade of NACA 0012 airfoils and flows through a cascade of shockless blades were computed. It is found that the designed flow through the shockless blade is accurately predicted, the artificial density formulation shows more tolerance to the mesh irregularity, and the C-type mesh does not extend very far upstream for a small pitch-cord ratio.

Jou, W. H.↗

NASA NTRS1982

A vectorized, finite-volume, adaptive-grid algorithm for Navier-Stokes calculations

An adaptive grid, finite-volume method has been used to solve the Navier-Stokes equations for complete (forebody and afterbody) flowfields around blunt bodies. The code, which is applicable for axisymmetric or two-dimensional flows, allows the mesh to adjust during the computation to provide a closer spacing of mesh points in regions of high gradients, thus minimizing the number of required computational points. The solution technique is explicit, utilizing a maximum time-step advancement at each grid point to accelerate convergence to the steady state. The code has been fully vectorized for efficient solution on the CYBER 203 computer. A very flexible rezoning routine is used to concentrate mesh points anywhere in the field, either by a user-defined weighting function or by allowing high gradient regions to adjust the grid. The grid adjustment routine is implicit in nature and represents a very small portion of the total computational cost. Currently, the code runs in approximately 0.000016 seconds per grid point per iteration.

Gnoffo, P. A.↗

NASA NTRS1984

Error reduction program: A progress report

Five finite differences schemes were evaluated for minimum numerical diffusion in an effort to identify and incorporate the best error reduction scheme into a 3D combustor performance code. Based on this evaluated, two finite volume method schemes were selected for further study. Both the quadratic upstream differencing scheme (QUDS) and the bounded skew upstream differencing scheme two (BSUDS2) were coded into a two dimensional computer code and their accuracy and stability determined by running several test cases. It was found that BSUDS2 was more stable than QUDS. It was also found that the accuracy of both schemes is dependent on the angle that the streamline make with the mesh with QUDS being more accurate at smaller angles and BSUDS2 more accurate at larger angles. The BSUDS2 scheme was selected for extension into three dimensions.

Syed, S. A.↗

NASA NTRS1985

Unsteady Flow in Multistage Turbines

The development of an efficient model for the response of a multistage turbine to either a total pressure or total temperature distortion is discussed. Each turbine blade row is modeled as an actuator disk and is often used to describe the flow through turbine and compressor blade rows. The flow approaching the blade row is assumed to be subsonic and inviscid. The distortion occurs at upstream infinity and is in the form of total pressure or total temperature. A solution was found to unsteady Euler equations by using a finite volume method. With prescribed inlet and boundary conditions flow variables such as density, pressure, and velocities can be calculated at cell centers in the entire flow region. The inlet and exit of the blade row coincide with lines of constant.

Surampudi, S. P.↗

NASA NTRS1986

Finite volume solultion of the compressible boundary layer equations

A box-type finite volume discretization is applied to the integral form of the compressible boundary layer equations. Boundary layer scaling is introduced through the grid construction: streamwise grid lines follow eta = y/h = const., where y is the normal coordinate and h(x) is a scale factor proportional to the boundary layer thickness. With this grid, similarity can be applied explicitly to calculate initial conditions. The finite volume method preserves the physical transparency of the integral equations in the discrete approximation. The resulting scheme is accurate, efficient, and very simple. Computations for similar and non-similar flows show excellent agreement with tabulated results, solutions computed with Keller's Box scheme, and experimental data.

Loyd, B.↗

NASA NTRS1986

Transonic potential flow in hyperbolic nozzles

The full potential equation for the classical problem of transonic flow through a hyperbolic nozzle (with or without a shock wave) is solved in conservation form using the finite volume method of Jameson and Caughey (1977). Either a firstor a second-order numerical viscosity is added in the direction of the flow, explicitly, in conservation form. A multigrid alternating direction implicit method is used to solve the difference equations, and the results obtained are compared with analytical and numerical results from previous researches.

Park, M.↗

NASA NTRS1986

Finite volume solution of the compressible boundary-layer equations

A box-type finite volume discretization is applied to the integral form of the compressible boundary layer equations. Boundary layer scaling is introduced through the grid construction: streamwise grid lines follow eta = y/h = const., where y is the normal coordinate and h(x) is a scale factor proportional to the boundary layer thickness. With this grid, similarity can be applied explicity to calculate initial conditions. The finite volume method preserves the physical transparency of the integral equations in the discrete approximation. The resulting scheme is accurate, efficient, and conceptually simple. Computations for similar and non-similar flows show excellent agreement with tabulated results, solutions computed with Keller's Box scheme, and experimental data.

Loyd, B.↗

NASA NTRS1986

Implicit time-marching solution of the Navier-Stokes equations for thrust reversing and thrust vectoring nozzle flows

An implicit finite volume method is investigated for the solution of the compressible Navier-Stokes equations for flows within thrust reversing and thrust vectoring nozzles. Thrust reversing nozzles typically have sharp corners, and the rapid expansion and large turning angles near these corners are shown to cause unacceptable time step restrictions when conventional approximate factorization methods are used. In this investigation these limitations are overcome by using second-order upwind differencing and line Gauss-Siedel relaxation. This method is implemented with a zonal mesh so that flows through complex nozzle geometries may be efficiently calculated. Results are presented for five nozzle configurations including two with time varying geometries. Three cases are compared with available experimental data and the results are generally acceptable.

Imlay, S. T.↗

NASA NTRS1987

Computational and experimental investigation of cavity flowfields

This paper presents a computational and experimental investigation of supersonic flow past a cavity in a flat plate. The source of the particular interest in this problem is the ongoing study of the aerodynamic interference effects between a separating store and its bay in the parent body. An upwind relaxation scheme, utilizing flux vector splitting and line-Gauss-Seidel iterations, is used to solve Reynolds-averaged Navier-Stokes equations. Spatial discretizations of this two-dimensional analysis are based on implicit and finite-volume methods. Turbulence is modeled and shocks are captured. The flowfield of the symmetry plane at the half-width is computationally visualized and all flow properties are computed. Experimental tests are conducted in the Langley Unitary Plan Wind Tunnel to measure wall pressures and to capture schlieren photographs. Qualitative as well as quantitative data of computations and experiments agree very well. These two vehicles of investigation are merged to show open, closed and transitional cavity flow behaviors.

Baysal, O.↗

NASA NTRS1988

Improved 3-D turbomachinery CFD algorithm

The building blocks of a computer algorithm developed for the time-accurate flow analysis of rotating machines are described. The flow model is a finite volume method utilizing a high resolution approximate Riemann solver for interface flux definitions. This block LU implicit numerical scheme possesses apparent unconditional stability. Multi-block composite gridding is used to orderly partition the field into a specified arrangement. Block interfaces, including dynamic interfaces, are treated such as to mimic interior block communication. Special attention is given to the reduction of in-core memory requirements by placing the burden on secondary storage media. Broad applicability is implied, although the results presented are restricted to that of an even blade count configuration. Several other configurations are presently under investigation, the results of which will appear in subsequent publications.

Janus, J. Mark↗

NASA NTRS1987

Calculation of wall and free turbulent-shear flows at supersonic speeds

Supersonic turbulent flows are simulated numerically by solving the Reynolds-averaged full Navier-Stokes equations by an implicit finite-volume method. This flux-vector-split upwind scheme uses approximate factorization followed by line-Gauss-Seidel relaxations. The effects of turbulence are modeled by two eddy viscosity models. High-Reynolds-number form of the k-epsilon model is coupled with a wall-function to avoid excessive refinement of the grid in the low-Reynolds number regions. The k-epsilon equations are solved by the explicit-implicit MacCormack method. The algebraic Baldwin-Lomax model is also being used as an inexpensive alternative for the cases which do not experience massive separation. Several examples of two-dimensional solutions are given to illustrate both wall and free turbulent shear flows which include fluid dynamic phenomena, such as shocks, boundary layers, shear layers, wakes, separations and recirculations. The results compared with experimental data show good agreeent.

Baysal, O.↗