Fluid dynamics from the Boltzmann equation using a maximum entropy distribution
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73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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Results for “equation of fluid dynamics”
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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A mathematical model for simulating noise suppression of lined ejectors
A mathematical model containing the essential features embodied in the noise suppression of lined ejectors is presented. Although some simplification of the physics is necessary to render the model mathematically tractable, the current model is the most versatile and technologically advanced at the current time. A system of linearized equations and the boundary conditions governing the sound field are derived starting from the equations of fluid dynamics. A nonreflecting boundary condition is developed. In view of the complex nature of the equations, a parametric study requires the use of numerical techniques and modern computers. A finite element algorithm that solves the differential equations coupled with the boundary condition is then introduced. The numerical method results in a matrix equation with several hundred thousand degrees of freedom that is solved efficiently on a supercomputer. The model is validated by comparing results either with exact solutions or with approximate solutions from other works. In each case, excellent correlations are obtained. The usefulness of the model as an optimization tool and the importance of variable impedance liners as a mechanism for achieving broadband suppression within a lined ejector are demonstrated.
Watson, Willie R.↗
Fluid dynamics applications of the Illiac IV computer
The Illiac IV is a parallel-structure computer with computing power an order of magnitude greater than that of conventional computers. It can be used for experimental tasks in fluid dynamics which can be simulated more economically, for simulating flows that cannot be studied by experiment, and for combining computer and experimental simulations. The architecture of Illiac IV is described, and the use of its parallel operation is demonstrated on the example of its solution of the one-dimensional wave equation. For fluid dynamics problems, a special FORTRAN-like vector programming language was devised, called CFD language. Two applications are described in detail: (1) the determination of the flowfield around the space shuttle, and (2) the computation of transonic turbulent separated flow past a thick biconvex airfoil.
Maccormack, R. W.↗
Fully Threaded Tree for Adaptive Refinement Fluid Dynamics Simulations
A fully threaded tree (FTT) for adaptive refinement of regular meshes is described. By using a tree threaded at all levels, tree traversals for finding nearest neighbors are avoided. All operations on a tree including tree modifications are O(N), where N is a number of cells, and are performed in parallel. An efficient implementation of the tree is described that requires 2N words of memory. A filtering algorithm for removing high frequency noise during mesh refinement is described. A FTT can be used in various numerical applications. In this paper, it is applied to the integration of the Euler equations of fluid dynamics. An adaptive mesh time stepping algorithm is described in which different time steps are used at different l evels of the tree. Time stepping and mesh refinement are interleaved to avoid extensive buffer layers of fine mesh which were otherwise required ahead of moving shocks. Test examples are presented, and the FTT performance is evaluated. The three dimensional simulation of the interaction of a shock wave and a spherical bubble is carried out that shows the development of azimuthal perturbations on the bubble surface.
FINITE ELEMENT ANALYSIS↗
The development of flux-split algorithms for flows with non-equilibrium thermodynamics and chemical reactions
A finite-volume method for the numerical computation of flows with nonequilibrium thermodynamics and chemistry is presented. A thermodynamic model is described which simplifies the coupling between the chemistry and thermodynamics and also results in the retention of the homogeneity property of the Euler equations (including all the species continuity and vibrational energy conservation equations). Flux-splitting procedures are developed for the fully coupled equations involving fluid dynamics, chemical production and thermodynamic relaxation processes. New forms of flux-vector split and flux-difference split algorithms are embodied in a fully coupled, implicit, large-block structure, including all the species conservation and energy production equations. Several numerical examples are presented, including high-temperature shock tube and nozzle flows. The methodology is compared to other existing techniques, including spectral and central-differenced procedures, and favorable comparisons are shown regarding accuracy, shock-capturing and convergence rates.
Grossman, B.↗
Online Machine Learning for Accelerating Molecular Dynamics Modeling of Cells
We developed a biomechanics-informed online learning framework to learn the dynamics with ground truth generated with multiscale modeling simulation. It was built on Summit-like supercomputers, which were also used to benchmark and validate our framework on one physiologically significant modeling of deformable biological cells. We generalized the century-old equation of Jeffery orbits to a new equation of motion with additional parameters to account for the flow conditions and the cell deformability. Using simulation data at particle-based resolutions for flowing cells and the learned parameters from our framework, we validated the new equation by the motions, mostly rotations, of a human platelet in shear blood flow at various shear stresses and platelet deformability. Our online framework, which surrogates redundant computations in the conventional multiscale modeling by solutions of our learned equation, accelerates the conventional modeling by three orders of magnitude without visible loss of accuracy.
multiscale modeling↗
Theory of the magnetothermal instability in coronal plasma flows
The theory of the magnetothermal instability (MTI) is revisited through the lens of the stability of uniform systems. The linear stability analysis includes flow advection and Nernst transport. The instability criteria derived distinguish between the convective and the absolute nature of the perturbation growth. It is proven that, in the region where the Nernst and plasma blowoff velocities cancel, the MTI can be absolute and wave-packet perturbations grow in situ. This instability is mediated by the internal feedback between the Biermann battery and Righi–Leduc terms. Here, the analysis is extended to derive the dispersion relation for short-wavelength perturbations developing in nonuniform profiles with the application to coronal plasmas. It is found that the condition for MTI requires the net B-field convection velocity to be small at the isothermal sonic section, and the plasma conditions in this section govern the dynamics of the instability. Analysis of hydro-equivalent implosions suggests that unstable perturbations undergo more e-foldings of growth in larger-size targets.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Direct imaging of shock wave splitting in diamond at Mbar pressure
Understanding the behavior of matter at extreme pressures of the order of a megabar (Mbar) is essential to gain insight into various physical phenomena at macroscales—the formation of planets, young stars, and the cores of super-Earths, and at microscales—damage to ceramic materials and high-pressure plastic transformation and phase transitions in solids. Under dynamic compression of solids up to Mbar pressures, even a solid with high strength exhibits plastic properties, causing the induced shock wave to split in two: an elastic precursor and a plastic shock wave. This phenomenon is described by theoretical models based on indirect measurements of material response. The advent of x-ray free-electron lasers (XFELs) has made it possible to use their ultrashort pulses for direct observations of the propagation of shock waves in solid materials by the method of phase-contrast radiography. However, there is still a lack of comprehensive data for verification of theoretical models of different solids. Here, we present the results of an experiment in which the evolution of the coupled elastic–plastic wave structure in diamond was directly observed and studied with submicrometer spatial resolution, using the unique capabilities of the x-ray free-electron laser (XFEL). The direct measurements allowed, for the first time, the fitting and validation of the 2D failure model for diamond in the range of several Mbar. Our experimental approach opens new possibilities for the direct verification and construction of equations of state of matter in the ultra-high-stress range, which are relevant to solving a variety of problems in high-energy-density physics.
36 MATERIALS SCIENCE↗
Adaptive computational methods for SSME internal flow analysis
Adaptive finite element methods for the analysis of classes of problems in compressible and incompressible flow of interest in SSME (space shuttle main engine) analysis and design are described. The general objective of the adaptive methods is to improve and to quantify the quality of numerical solutions to the governing partial differential equations of fluid dynamics in two-dimensional cases. There are several different families of adaptive schemes that can be used to improve the quality of solutions in complex flow simulations. Among these are: (1) r-methods (node-redistribution or moving mesh methods) in which a fixed number of nodal points is allowed to migrate to points in the mesh where high error is detected; (2) h-methods, in which the mesh size h is automatically refined to reduce local error; and (3) p-methods, in which the local degree p of the finite element approximation is increased to reduce local error. Two of the three basic techniques have been studied in this project: an r-method for steady Euler equations in two dimensions and a p-method for transient, laminar, viscous incompressible flow. Numerical results are presented. A brief introduction to residual methods of a-posterior error estimation is also given and some pertinent conclusions of the study are listed.
Oden, J. T.↗
Efficient grid generation
Because the governing equations in fluid dynamics contain partial differentials and are too difficult in most cases to solve analytically, these differentials are generally replaced by finite difference terms. These terms contain terms in the solution at nearby states. This procedure discretizes the field into a finite number of states. These states, when plotted, form a grid, or mesh, of points. It is at these states, or field points, that the solution is found. The optimum choice of states, the x, y, z coordinate values, minimizes error and computational time. But the process of finding these states is made more difficult by complex boundaries, and by the need to control step size differences between the states, that is, the need to control the spacing of field points. One solution technique uses a different set of state variables, which define a different coordinate system, to generate the grid more easily. A new method, developed by Dr. Joseph Steger, combines elliptic and hyperbolic partial differential equations into a mapping function between the physical and computational coordinate systems. This system of equations offers more control than either equation provides alone. The Steger algorithm was modified in order to allow bodies with stronger concavities to be used, offering the possibility of generating a single grid about multiple bodies. Work was also done on identifying areas where grid breakdown occurs.
Seki, Rycichi↗
GPU-enabled extreme-scale turbulence simulations: Fourier pseudo-spectral algorithms at the exascale using OpenMP offloading
Fourier pseudo-spectral methods for nonlinear partial differential equations are of wide interest in many areas of advanced computational science, including direct numerical simulation of three-dimensional (3-D) turbulence governed by the Navier-Stokes equations in fluid dynamics. This paper presents a new capability for simulating turbulence at a new record resolution up to 35 trillion grid points, on the world's first exascale computer, Frontier, comprising AMD MI250x GPUs with HPE's Slingshot interconnect and operated by the US Department of Energy's Oak Ridge Leadership Computing Facility (OLCF). Key programming strategies designed to take maximum advantage of the machine architecture involve performing almost all computations on the GPU which has the same memory capacity as the CPU, performing all-to-all communication among sets of parallel processes directly on the GPU, and targeting GPUs efficiently using OpenMP offloading for intensive number-crunching including 1-D Fast Fourier Transforms (FFT) performed using AMD ROCm library calls. With 99% of computing power on Frontier being on the GPU, leaving the CPU idle leads to a net performance gain via avoiding the overhead of data movement between host and device except when needed for some I/O purposes. Memory footprint including the size of communication buffers for MPI_ALLTOALL is managed carefully to maximize the largest problem size possible for a given node count. Detailed performance data including separate contributions from different categories of operations to the elapsed wall time per step are reported for five grid resolutions, from 2048 3 on a single node to 32768 3 on 4096 or 8192 nodes out of 9408 on the system. Both 1D and 2D domain decompositions which divide a 3D periodic domain into slabs and pencils respectively are implemented. The present code suite (labeled by the acronym GESTS, GPUs for Extreme Scale Turbulence Simulations) achieves a figure of merit (in grid points per second) exceeding goals set in the Center for Accelerated Application Readiness (CAAR) program for Frontier. The performance attained is highly favorable in both weak scaling and strong scaling, with notable departures only for 2048 3 where communication is entirely intra-node, and for 32768 3 , where a challenge due to small message sizes does arise. Communication performance is addressed further using a lightweight test code that performs all-to-all communication in a manner matching the full turbulence simulation code. Performance at large problem sizes is affected by both small message size due to high node counts as well as dragonfly network topology features on the machine, but is consistent with official expectations of sustained performance on Frontier. Overall, although not perfect, the scalability achieved at the extreme problem size of 32768 3 (and up to 8192 nodes — which corresponds to hardware rated at just under 1 exaflop/sec of theoretical peak computational performance) is arguably better than the scalability observed using prior state-of-the-art algorithms on Frontier's predecessor machine (Summit) at OLCF. New science results for the study of intermittency in turbulence enabled by this code and its extensions are to be reported separately in the near future.
3D fast Fourier transform↗
Derivation of physical equations for high-speed laser welding using large language models
It is challenging to formulate complex physical phenomena that occur in a manufacturing process, particularly when the available data are limited, rendering conventional data-driven approaches ineffective. This study aims to predict humping onset in high-speed laser welding by introducing a novel framework, namely text-to-equations generative pre-trained transformer (T2EGPT). This method leverages the capabilities of large language models (LLMs), in combination with sparse experimental data and enriched literature data, to derive an interpretable and generalizable equation for predicting humping initiation. By capturing key correlations among physical parameters, T2EGPT generates a compact and dimensionless expression that accurately predicts hump formation. The equation reveals that humping arises from the interplay between inertia-driven backward melt flow and capillary-driven surface stabilization, where inertial forces drive molten metal backward and capillary forces resist surface deformation. Furthermore, compared to traditional data-driven models, T2EGPT demonstrates enhanced predictive accuracy and cross-material transferability. More broadly, this study highlights the potential of LLMs to integrate textual information with data-driven discovery, enabling the extraction of physical laws in data-scarce scientific domains.
36 MATERIALS SCIENCE↗
Harmony code
Harmony is a finite element ALE code for solving the equations of fluid dynamics for single-material flows with arbitrary mesh motion in three dimensional geometry.
Chiravalle, Vincent↗
Computation of space shuttle flow fields using noncentered finite-difference schemes.
Second- and third-order, noncentered finite-difference schemes are described for the numerical solution of the hyperbolic equations of fluid dynamics. The advantages of noncentered methods over the more conventional centered schemes are: simpler programming logic, nonhomogeneous terms are easily included, and generalization to multidimensional problems is direct. Second- and third-order methods are compared with regard to dissipative and dispersive errors and shock-capturing ability. These schemes are then used in a shock-capturing technique to determine the inviscid, supersonic flow field surrounding space shuttle vehicles (SSV). Resulting flow fields about typical pointed and blunted, delta-winged SSVs at angle of attack are presented and compared with experiment.
Kutler, P.↗
Application of multigrid methods for integral equations to two problems from fluid dynamics
Multigrid methods were applied to fluid dynamic problems. The problems include calculation of potential flow around airfoils and oscillating disk flow. It is shown that in both cases the multigrid methods are sufficient to obtain an approximate solution while reducing the computational work.
Schippers, H.↗
A general method to determine the stability of compressible flows
Several problems were studied using two completely different approaches. The initial method was to use the standard linearized perturbation theory by finding the value of the individual small disturbance quantities based on the equations of motion. These were serially eliminated from the equations of motion to derive a single equation that governs the stability of fluid dynamic system. These equations could not be reduced unless the steady state variable depends only on one coordinate. The stability equation based on one dependent variable was found and was examined to determine the stability of a compressible swirling jet. The second method applied a Lagrangian approach to the problem. Since the equations developed were based on different assumptions, the condition of stability was compared only for the Rayleigh problem of a swirling flow, both examples reduce to the Rayleigh criterion. This technique allows including the viscous shear terms which is not possible in the first method. The same problem was then examined to see what effect shear has on stability.
Guenther, R. A.↗
Numerical methods for systems of conservation laws of mixed type using flux splitting
The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.
Shu, Chi-Wang↗
Flux-split algorithms for flows with non-equilibrium chemistry and vibrational relaxation
The present consideration of numerical computation methods for gas flows with nonequilibrium chemistry thermodynamics gives attention to an equilibrium model, a general nonequilibrium model, and a simplified model based on vibrational relaxation. Flux-splitting procedures are developed for the fully-coupled inviscid equations encompassing fluid dynamics and both chemical and internal energy-relaxation processes. A fully coupled and implicit large-block structure is presented which embodies novel forms of flux-vector split and flux-difference split algorithms valid for nonequilibrium flow; illustrative high-temperature shock tube and nozzle flow examples are given.
Grossman, B.↗