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At least 1,171 records · Page 65

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DOE OSTI2026

A Structure-Preserving Decorated Particle Method for the Vlasov-Poisson System

We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-cell (PIC) algorithms approximate the distribution function by macro-particles with position and velocity. In contrast, Scovel-Weinstein decorated particles involve additional shape degrees of freedom, while maintaining a finite-dimensional reduction with Hamiltonian structure inherited from the continuum model. Although the original work established this structure three decades ago, its computational potential has remained largely unexplored. We present a practical implementation of the Scovel-Weinstein model and compare it with a standard PIC algorithm. Numerical experiments demonstrate that macro-particles in standard PIC can be replaced by far fewer decorated particles while retaining comparable accuracy. This decorated particle approach offers a new structure-preserving paradigm for kinetic plasma simulation.

65M75, 70H05, 70G65↗

NASA NTRS1984

Advanced numerics for multi-dimensional fluid flow calculations

In recent years, there has been a growing interest in the development and use of mathematical models for the simulation of fluid flow, heat transfer and combustion processes in engineering equipment. The equations representing the multi-dimensional transport of mass, momenta and species are numerically solved by finite-difference or finite-element techniques. However despite the multiude of differencing schemes and solution algorithms, and the advancement of computing power, the calculation of multi-dimensional flows, especially three-dimensional flows, remains a mammoth task. The following discussion is concerned with the author's recent work on the construction of accurate discretization schemes for the partial derivatives, and the efficient solution of the set of nonlinear algebraic equations resulting after discretization. The present work has been jointly supported by the Ramjet Engine Division of the Wright Patterson Air Force Base, Ohio, and the NASA Lewis Research Center.

Vanka, S. P.↗

NASA NTRS1984

Impact of new computing systems on computational mechanics and flight-vehicle structures technology

Advances in computer technology which may have an impact on computational mechanics and flight vehicle structures technology were reviewed. The characteristics of supersystems, highly parallel systems, and small systems are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario for future hardware/software environment and engineering analysis systems is presented. Research areas with potential for improving the effectiveness of analysis methods in the new environment are identified.

Noor, A. K.↗

NASA NTRS1985

Implicit flux-split schemes for the Euler equations

Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.

Thomas, J. L.↗

NASA NTRS1986

Numerical simulation of unsteady, viscous, high-angle-of-attack flows using a partially flux-split algorithm

Viscous separated flow surrounding a hemisphere-cylinder body at angles of attack ranging up to 19 deg in transonic flow has been computed using an implicit, approximately-factored, partially flux-split algorithm. The resulting flowfield structures, including the vortical flow on the leeward side of the body and the three-dimensional separation patterns, have been investigated. The computed results show good qualitative and quantitative agreement with experimental data. Furthermore, visualization of the flowfield patterns has yielded insight into the behavior of the three-dimensional separated flow.

Ying, S. X.↗

NASA NTRS1989

Recursive form of the eigensystem realization algorithm for system identification

An algorithm is developed for recursively calculating the minimum realization of a linear system from sampled impulse response data. The Gram-Schmidt orthonormalization technique is used to generate an orthonormal basis for factorization of the data matrix. The system matrix thus identified is in upper Hessenberg form, which has advantages for the identification of modal parameters including damping coefficients, frequencies, mode shapes, and modal participation factors. It also has the property that once an element of the system matrix is computed, it is never altered as the dimension of the model is increased in the recursive process. Numerical examples are presented for comparison of the recursive and nonrecursive forms of the eigensystem realization algorithm.

Longman, Richard W.↗

NASA NTRS1991

Leading-edge receptivity for blunt-nose bodies

This research program investigates boundary-layer receptivity in the leading-edge region for bodies with blunt leading edges. Receptivity theory provides the link between the unsteady distrubance environment in the free stream and the initial amplitudes of the instability waves in the boundary layer. This is a critical problem which must be addressed in order to develop more accurate prediction methods for boundary-layer transition. The first phase of this project examines the effects of leading-edge bluntness and aerodynamic loading for low Mach number flows. In the second phase of the project, the investigation is extended to supersonic Mach numbers. Singular perturbation techniques are utilized to develop an asymptotic theory for high Reynolds numbers. In the first year, the asymptotic theory was developed for leading-edge receptivity in low Mach number flows. The case of a parabolic nose is considered. Substantial progress was made on the Navier-Sotkes computations. Analytical solutions for the steady and unsteady potential flow fields were incorporated into the code, greatly expanding the types of free-stream disturbances that can be considered while also significantly reducing the the computational requirements. The time-stepping algorithm was modified so that the potential flow perturbations induced by the unsteady pressure field are directly introduced throughout the computational domain, avoiding an artificial 'numerical diffusion' of these from the outer boundary. In addition, the start-up process was modified by introducing the transient Stokes wave solution into the downstream boundary conditions.

Kerschen, Edward J.↗

NASA NTRS1991

An intrinsically n-dimensional generalized flux vector splitting implicit finite element Euler algorithm

A generalized flux-vector splitting implicit Galerkin finite-element algorithm for the Euler equations in curvilinear coordinates for ideal and reacting gases is derived. For an arbitrary equation of state, the curvilinear-coordinate flux vector is split in kinematic and kinetic components, and the associated jacobian matrix eigenvalues explicitly depend on the metric data. After directional semidiscretization, the terminal ordinary differential-equation system is solved via a nonlinearly stable implicit Runge-Kutta scheme in concert with an accurate tensor matrix product factorization. The results for selected two-dimensional supersonic and axisymmetric hypersonic flows validate the algorithm and verify its robustness for curvilinear-coordinate computations. The evolution towards a steady state is achieved for large Courant numbers without indication of numerical instabilities.

Iannelli, G. S.↗

NASA NTRS1991

Computation of incompressible viscous flows through artificial heart devices with moving boundaries

The extension of computational fluid dynamics techniques to artificial heart flow simulations is illustrated. Unsteady incompressible Navier-Stokes equations written in 3-D generalized curvilinear coordinates are solved iteratively at each physical time step until the incompressibility condition is satisfied. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. The efficiency and robustness of the time accurate formulation of the algorithm are tested by computing the flow through model geometries. A channel flow with a moving indentation is computed and validated with experimental measurements and other numerical solutions. In order to handle the geometric complexity and the moving boundary problems, a zonal method and an overlapping grid embedding scheme are used, respectively. Steady state solutions for the flow through a tilting disk heart valve was compared against experimental measurements. Good agreement was obtained. The flow computation during the valve opening and closing is carried out to illustrate the moving boundary capability.

Kiris, Cetin↗

NASA NTRS1992

Acceleration of FDNS flow simulations using initial flowfields generated with a parabolized Navier-Stokes method

The capability of computational fluid dynamics (CFD) analysis to predict complex flowfields has been greatly advanced by the widespread use of flow simulation programs based on the Navier-Stokes (NS) equations. The flow physics are theoretically well represented, and with proper care the numerical solution should not introduce appreciable uncertainties. However, the computational cost of a typical simulation in terms of both memory and execution time are large by current standards. Therefore, the efficiency of the numerical algorithm in solving the set of model equations is one factor determining the usefulness of CFD tools. The objective of the present study is to reduce the execution time of the FDNS flow simulation code by using the parabolized Navier-Stokes (PNS) equations to provide a 'good' starting condition. The technique is not universal, however the PNS model can be applied to convection dominated flows with moderate deflection in geometries that are free of large obstructions.

Tenpas, Peter W.↗

NASA NTRS2008

AutoBayes Program Synthesis System Users Manual

Program synthesis is the systematic, automatic construction of efficient executable code from high-level declarative specifications. AutoBayes is a fully automatic program synthesis system for the statistical data analysis domain; in particular, it solves parameter estimation problems. It has seen many successful applications at NASA and is currently being used, for example, to analyze simulation results for Orion. The input to AutoBayes is a concise description of a data analysis problem composed of a parameterized statistical model and a goal that is a probability term involving parameters and input data. The output is optimized and fully documented C/C++ code computing the values for those parameters that maximize the probability term. AutoBayes can solve many subproblems symbolically rather than having to rely on numeric approximation algorithms, thus yielding effective, efficient, and compact code. Statistical analysis is faster and more reliable, because effort can be focused on model development and validation rather than manual development of solution algorithms and code.

Schumann, Johann↗

NASA NTRS2020

A Numerical Investigation of Parachute Deployment in Supersonic Flow

A validated computational fluid-structure interaction method applied to supersonic parachute inflation is extended to consider a unique, parallel self-contact algorithm, porosity interface conditions on the canopy, improved flow field sampling procedures for obtaining quality loading on the parachute canopy, adaptive mesh refinement, and improved treatment of thin geometries in an immersed boundary framework. These extensions are discussed in detail and demonstrated individually on test problems. Finally, the developments are brought together for demonstration on a sub-scale MSL parachute geometry.

Boustani, Jonathan↗

DOE OSTI2012

Dense LU Factorization on Multicore Supercomputer Nodes

Dense LU factorization is a prominent benchmark used to rank the performance of supercomputers. Many implementations, including the reference code HPL, use block-cyclic distributions of matrix blocks onto a two-dimensional process grid. The process grid dimensions drive a trade-off between communication and computation and are architecture- and implementation-sensitive. We show how the critical panel factorization steps can be made less communication-bound by overlapping asynchronous collectives for pivot identification and exchange with the computation of rank-k updates. By shifting this trade-off, a modified block-cyclic distribution can beneficially exploit more available parallelism on the critical path, and reduce panel factorization's memory hierarchy contention on now-ubiquitous multi-core architectures. The missed parallelism in traditional block-cyclic distributions arises because active panel factorization, triangular solves, and subsequent broadcasts are spread over single process columns or rows (respectively) of the process grid. Increasing one dimension of the process grid decreases the number of distinct processes in the other dimension. To increase parallelism in both dimensions, periodic 'rotation' is applied to the process grid to recover the row-parallelism lost by a tall process grid. During active panel factorization, rank-1 updates stream through memory with minimal reuse. In a column-major process grid, the performance of this access pattern degrades as too many streaming processors contend for access to memory. A block-cyclic mapping in the more popular row-major order does not encounter this problem, but consequently sacrifices node and network locality in the critical pivoting steps. We introduce 'striding' to vary between the two extremes of row- and column-major process grids. As a test-bed for further mapping experiments, we describe a dense LU implementation that allows a block distribution to be defined as a general function of block to processor. Other mappings can be tested with only small, local changes to the code.

99 GENERAL AND MISCELLANEOUS↗

NASA NTRS2002

An Automated Method to Compute Orbital Re-entry Trajectories with Heating Constraints

Determining how to properly manipulate the controls of a re-entering re-usable launch vehicle (RLV) so that it is able to safely return to Earth and land involves the solution of a two-point boundary value problem (TPBVP). This problem, which can be quite difficult, is traditionally solved on the ground prior to flight. If necessary, a nearly unlimited amount of time is available to find the 'best' solution using a variety of trajectory design and optimization tools. The role of entry guidance during flight is to follow the pre- determined reference solution while correcting for any errors encountered along the way. This guidance method is both highly reliable and very efficient in terms of onboard computer resources. There is a growing interest in a style of entry guidance that places the responsibility of solving the TPBVP in the actual entry guidance flight software. Here there is very limited computer time. The powerful, but finicky, mathematical tools used by trajectory designers on the ground cannot in general be converted to do the job. Non-convergence or slow convergence can result in disaster. The challenges of designing such an algorithm are numerous and difficult. Yet the payoff (in the form of decreased operational costs and increased safety) can be substantiaL This paper presents an algorithm that incorporates features of both types of guidance strategies. It takes an initial RLV orbital re-entry state and finds a trajectory that will safely transport the vehicle to Earth. During actual flight, the computed trajectory is used as the reference to be flown by a more traditional guidance method.

Zimmerman, Curtis↗

NASA NTRS1987

The hypercluster: A parallel processing test-bed architecture for computational mechanics applications

The development of numerical methods and software tools for parallel processors can be aided through the use of a hardware test-bed. The test-bed architecture must be flexible enough to support investigations into architecture-algorithm interactions. One way to implement a test-bed is to use a commercial parallel processor. Unfortunately, most commercial parallel processors are fixed in their interconnection and/or processor architecture. In this paper, we describe a modified n cube architecture, called the hypercluster, which is a superset of many other processor and interconnection architectures. The hypercluster is intended to support research into parallel processing of computational fluid and structural mechanics problems which may require a number of different architectural configurations. An example of how a typical partial differential equation solution algorithm maps on to the hypercluster is given.

Blech, Richard A.↗

NASA NTRS2002

An Automated Method to Compute Orbital Re-Entry Trajectories with Heating Constraints

Determining how to properly manipulate the controls of a re-entering re-usable launch vehicle (RLV) so that it is able to safely return to Earth and land involves the solution of a two-point boundary value problem (TPBVP). This problem, which can be quite difficult, is traditionally solved on the ground prior to flight. If necessary, a nearly unlimited amount of time is available to find the "best" solution using a variety of trajectory design and optimization tools. The role of entry guidance during flight is to follow the pre-determined reference solution while correcting for any errors encountered along the way. This guidance method is both highly reliable and very efficient in terms of onboard computer resources. There is a growing interest in a style of entry guidance that places the responsibility of solving the TPBVP in the actual entry guidance flight software. Here there is very limited computer time. The powerful, but finicky, mathematical tools used by trajectory designers on the ground cannot in general be made to do the job. Nonconvergence or slow convergence can result in disaster. The challenges of designing such an algorithm are numerous and difficult. Yet the payoff (in the form of decreased operational costs and increased safety) can be substantial. This paper presents an algorithm that incorporates features of both types of guidance strategies. It takes an initial RLV orbital re-entry state and finds a trajectory that will safely transport the vehicle to a Terminal Area Energy Management (TAEM) region. During actual flight, the computed trajectory is used as the reference to be flown by a more traditional guidance method.

Zimmerman, Curtis↗

DOE OSTI2024

Tensor network representation of non-abelian gauge theory coupled to reduced staggered fermions

We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because reduced staggered fermions can be represented in terms of a minimal number of tensor indices while the gauge sector can be approximated using Gaussian quadrature with a truncation. Numerical results obtained using the Grassmann TRG algorithm are shown for the case of SU(2) lattice gauge theory and compared to Monte Carlo results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Efficient phase-factor evaluation in quantum signal processing

Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in principle be obtained for a range of tasks, such as Hamiltonian simulation and the quantum linear system problem. A further benefit of QSP is that it uses a minimal number of ancilla qubits, which facilitates its implementation on near-to-intermediate term quantum architectures. However, there is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits. Existing methods require the use of variable precision arithmetic and can only be applied to polynomials of a relatively low degree. We present here an optimization-based method that can accurately compute the phase factors using standard double precision arithmetic operations. We demonstrate the performance of this approach with applications to Hamiltonian simulation, eigenvalue filtering, and quantum linear system problems. Furthermore, our numerical results show that the optimization algorithm can find phase factors to accurately approximate polynomials of a degree larger than 10000 with errors below 10 -12 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗