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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

An adaptive multigrid model for hurricane track prediction

This paper describes a simple numerical model for hurricane track prediction which uses a multigrid method to adapt the model resolution as the vortex moves. The model is based on the modified barotropic vorticity equation, discretized in space by conservative finite differences and in time by a Runge-Kutta scheme. A multigrid method is used to solve an elliptic problem for the streamfunction at each time step. Nonuniform resolution is obtained by superimposing uniform grids of different spatial extent; these grids move with the vortex as it moves. Preliminary numerical results indicate that the local mesh refinement allows accurate prediction of the hurricane track with substantially less computer time than required on a single uniform grid.

Fulton, Scott R.↗
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗
NASA NTRS1990

Direct simulation for the instability and breakup of laminar liquid jets

A direct numerical simulation method is described for predicting the deformation of laminar liquid jets. In the present nonlinear direct simulation, the convective term, which has been discarded in past linear analyses by Rayleigh and others, is included in the hydrodynamic equations. It is shown that only by maintaining full complexity of the nonlinear surface tension term accurate drop formation can be predicted. The continuity and momentum equations in the transient form are integrated on an adaptive grid, conforming the jet and surface wave shape. The equations, which are parabolic in time and elliptic in space, are solved by a TVD scheme with characteristic flux splitting. The results of the present work are discussed and compared with available measurements and other analyses. The comparison shows that among the predictions, the current 1-D direct simulation results agree best with the experimental data. Furthermore, the computer time requirements are much (an order of magnitude) smaller than those of previously reported multidimensional analyses.

Chuech, S. G.↗
NASA NTRS1995

The method of space-time conservation element and solution element-applications to one-dimensional and two-dimensional time-marching flow problems

A nontraditional numerical method for solving conservation laws is being developed. The new method is designed from a physicist's perspective, i.e., its development is based more on physics than numerics. Even though it uses only the simplest approximation techniques, a 2D time-marching Euler solver developed recently using the new method is capable of generating nearly perfect solutions for a 2D shock reflection problem used by Helen Yee and others. Moreover, a recent application of this solver to computational aeroacoustics (CAA) problems reveals that: (1) accuracy of its results is comparable to that of a 6th order compact difference scheme even though nominally the current solver is only of 2nd-order accuracy; (2) generally, the non-reflecting boundary condition can be implemented in a simple way without involving characteristic variables; and (3) most importantly, the current solver is capable of handling both continuous and discontinuous flows very well and thus provides a unique numerical tool for solving those flow problems where the interactions between sound waves and shocks are important, such as the noise field around a supersonic over- or under-expansion jet.

Chang, Sin-Chung↗
DOE OSTI2024

On the convergence of the fixed point method for solving neutron transport alpha eigenvalue problems

It was shown that the Fixed Point Method (also known as the Rayleigh Quotient Method) is several times faster than the Critical Search Method for solving neutron transport alpha eigenvalue problems. It was also shown that the Fixed Point Method is able to determine the alpha eigenvalues of sub-critical systems that are beyond the reach of the Critical Search Method. Despite these significant advances, the Fixed Point Method remains an unproven algorithm. Here, this report provides a proof.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Space-time dependent thermal conductivity in nonlocal thermal transport

Nonlocal thermal transport is generally described by the Peierls-Boltzmann transport equation (PBE). However, solving the PBE for a general space-time dependent problem remains a challenging task due to the high dimensionality of the integro-differential equation. In this work, we present a direct solution to the space-time dependent PBE with a linearized collision matrix using an eigendecomposition method. We show that there exists a generalized Fourier-type relation that links heat flux to the local temperature, and this constitutive relation defines a thermal conductivity that depends on both time and space. Combining this approach with ab initio calculations of phonon properties, we demonstrate that the space-time dependent thermal conductivity gives rise to an oscillatory response in temperature in a transient grating geometry in high thermal conductivity materials. The present solution method allows us to extend the reach of our computational capability for heat conduction to space-time dependent nondiffusive transport regimes. Here, this capability will not only enable a more accurate interpretation of thermal measurements that observe nonlocal thermal transport, but also enhance our physical understanding of nonlocal thermal transport in high thermal conductivity materials that are promising candidates for nanoscale thermal management applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1974

Time-fixed rendezvous by impulse factoring with an intermediate timing constraint

A method is presented for factoring a two-impulse orbital transfer into a three- or four-impulse transfer which solves the rendezvous problem and satisfies an intermediate timing constraint. Both the time of rendezvous and the intermediate time of a alinement are formulated as any element of a finite sequence of times. These times are integer multiples of a constant plus an additive constant. The rendezvous condition is an equality constraint, whereas the intermediate alinement is an inequality constraint. The two timing constraints are satisfied by factoring the impulses into collinear parts that vectorially sum to the original impulse and by varying the resultant period differences and the number of revolutions in each orbit. Five different types of solutions arise by considering factoring either or both of the two impulses into two or three parts with a limit for four total impulses. The impulse-factoring technique may be applied to any two-impulse transfer which has distinct orbital periods.

Green, R. N.↗
NASA NTRS1993

Numerical investigations in three-dimensional internal flows

In the present reporting period, the 3D STUFF code was used to solve the underbody flow for the waverider configuration vehicle. In order to start the space-marched version of the code, the time-marched version (TUFF) was used to solve the forward portion of the underside of the forebody flowfield. A grid was generated which went from the tip of the nose to the location of the cowl lip. This includes all of the inlet ramp system. Previous indications were that three-dimensional effects could be expected on the ramps of such an aircraft. For purposes of the present study, no sidewalls were assumed. The sidewalls were eliminated to simplify the calculations and to show the potential effects of three-dimensional flow in the absence of a full sidewall. Further, this flow was also analyzed using the newly released OVERFLOW code and comparisons between the two codes were made. In addition to these 3D calculations, 2D calculations using the OVERFLOW code were also obtained for the Mach 5 inlet model in this reporting period. Comparisons between the experimental data, previous computational fluid dynamics (CFD) results and those from OVERFLOW were made.

Rose, William C.↗
NASA NTRS1987

Anticipation of the landing shock phenomenon in flight simulation

An aircraft landing may be described as a controlled crash because a runway surface is intercepted. In a simulation model the transition from aerodynamic flight to weight on wheels involves a single computational cycle during which stiff differential equations are activated; with a significant probability these initial conditions are unrealistic. This occurs because of the finite cycle time, during which large restorative forces will accompany unrealistic initial oleo compressions. This problem was recognized a few years ago at Ames Research Center during simulation studies of a supersonic transport. The mathematical model of this vehicle severely taxed computational resources, and required a large cycle time. The ground strike problem was solved by a described technique called anticipation equations. This extensively used technique has not been previously reported. The technique of anticipating a significant event is a useful tool in the general field of discrete flight simulation. For the differential equations representing a landing gear model stiffness, rate of interception and cycle time may combine to produce an unrealistic simulation of the continuum.

Mcfarland, Richard E.↗
NASA NTRS1989

Full potential unsteady computations including aeroelastic effects

A unified formulation is presented based on the full potential framework coupled with an appropriate structural model to compute steady and unsteady flows over rigid and flexible configurations across the Mach number range. The unsteady form of the full potential equation in conservation form is solved using an implicit scheme maintaining time accuracy through internal Newton iterations. A flux biasing procedure based on the unsteady sonic reference conditions is implemented to compute hyperbolic regions with moving sonic and shock surfaces. The wake behind a trailing edge is modeled using a mathematical cut across which the pressure is satisfied to be continuous by solving an appropriate vorticity convection equation. An aeroelastic model based on the generalized modal deflection approach interacts with the nonlinear aerodynamics and includes both static as well as dynamic structural analyses capability. Results are presented for rigid and flexible configurations at different Mach numbers ranging from subsonic to supersonic conditions. The dynamic response of a flexible wing below and above its flutter point is demonstrated.

Shankar, Vijaya↗
NASA NTRSDate not supplied

Crew Performance Support System to Aid in Anomaly Resolution: Concept of Operations

As missions progress into deep space, communication delays and disruptions will disenable the crew’s reliance on Earth experts. There are also limitations in the amount of data that can be downlinked to the ground. It is prudent to assume that critical, complex vehicle or habitat sub-systems will malfunction at a time when a lunar or Mars’ crew cannot rely on the Earth-Support team to detect, diagnose and resolve the problem and it is impractical to expect a small crew to step-in with the same level of expertise as 50+ authorities. The crew will need novel processes and advanced technological support to independently identify and resolve safety- and time-critical anomalies. That a self-reliant crew is unable to respond appropriately to time-critical anomalies is a significant risk to crew safety and mission success. This risk is driven by several factors; novel and unanticipated anomalies would not have been trained pre-flight, the crew could forget their pre-flight training or spaceflight stressors could impair the crew’s problem-solving ability. At last year’s IWS, Beard reported that a single spaceflight stressor (elevated CO2) could undermine the crew’s ability to independently respond to emergencies. Concept of Operations (ConOps) provide a common view of future system functions to all stakeholders. For the current project, a ConOps was developed that describes the operational processes, practices and capabilities needed by a crew of astronauts on deep space missions to autonomously respond to anticipated and unanticipated anomalies. It is crucial to recognize that, as of August 2018 existing technologies are unable to effectively support crew anomaly response to unanticipated events. “Intelligent technology” has not reached a maturity level that permits generalizing a solution to novel situations. For example, to train intelligent technology requires volumes of data that do not exist. The complexities involved in a manned mission to Mars cannot be compared to sending rovers to Mars using scripted software. This ConOps proposes a Crew Performance Support System (CPSS) that will push NASA and its industry partners toward what will be required for a safe and successful manned mission to Mars. Anomaly resolution during a deep space mission will take place within a dynamic, or changing, context. The figure to the left shows five broad contextual variables: the organizational culture, mission context, system characteristics, team characteristics and individual characteristics. The yellow arrow indicates that spaceflight and task-related stressors can affect system, team and individual crewmember characteristics and therefore anomaly response potential. The figure depicts a protective umbrella of Human-System Integration (HSI) principles that should be instituted during CPSS development including a balanced workload, shared situation awareness and building an appropriate level of trust in the automation. The figure also depicts two interrelated and cooperative components, an HSI Data System and other Enabling Capabilities will be required to support crew anomaly response and Earth-Support situation awareness. As we journey from ISS to Gateway to Mars, multiple, simultaneous and integrated research and development efforts (i.e., support systems co-evolution) must be implemented to meet the problem-solving challenges a self-reliant crew will face on a Mars’ mission. The crossovers between the capabilities are just as important as the discrete capabilities themselves. As the capabilities mature, the lines between the support subdomains will blur and an integrated system will emerge. The ConOps summarizes current knowledge about how highly trained people solve anomalies in safety- and time-critical situations, describes a group of capabilities that could help to reduce the extant risk and documents requirements levied on additional systems that provides critical inputs to the CPSS. Scenarios are used to promote a shared understanding of processes, practices and technological goals needed for safe and productive manned missions beyond LEO.

HSIA risk↗
NASA NTRS1979

Explicit large time-step schemes for the shallow water equations

Modifications to explicit finite difference schemes for solving the shallow water equations for meteorological applications by increasing the time step for the fast gravity waves are analyzed. Terms associated with the gravity waves in the shallow water equations are treated on a coarser grid than those associated with the slow Rossby waves, which contain much more of the available energy and must be treated with higher accuracy, enabling a several-fold increase in time step without degrading the accuracy of the solution. The method is presented in Cartesian and spherical coordinates for a rotating earth, using generalized leapfrog, frozen coefficient, and Fourier filtering finite difference schemes. Computational results verify the numerical stability of the approach.

Turkel, E.↗
DOE OSTI2023

Floating Block Method for Quantum Monte Carlo Simulations

Quantum Monte Carlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum Monte Carlo simulations can in principle be used to build fast and accurate many-body emulators using eigenvector continuation or design time-dependent Hamiltonians for adiabatic quantum computing. Furthermore, these new applications require something that is missing from the published literature, an efficient quantum Monte Carlo scheme for computing the inner product of ground state eigenvectors corresponding to different Hamiltonians. In this work, we introduce an algorithm called the floating block method, which solves the problem by performing Euclidean time evolution with two different Hamiltonians and interleaving the corresponding time blocks. We use the floating block method and nuclear lattice simulations to build eigenvector continuation emulators for energies of 4 He, 8 Be, 12 C, and 16 O nuclei over a range of local and nonlocal interaction couplings. From the emulator data, we identify the quantum phase transition line from a Bose gas of alpha particles to a nuclear liquid.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Extension of OpenMC for Fixed Source Transmutation Calculations

This report documents work performed under a Strategic Partnership Project between Argonne National Laboratory (ANL) and the United Kingdom Atomic Energy Authority (UKAEA). The overall goal of this project is to extend OpenMC [1], a community-developed Monte Carlo particle transport code, to be able to perform fixed-source transmutation calculations. In fission and fusion reactors, the high flux of energetic neutrons causes materials within the reactor to “transmute,” or undergo a nuclear reaction that results in the addition/removal of neutrons and protons from the nucleus of an atom. If subjected to these reactions for long enough, the overall composition and physical properties of the material itself begin to change as a result of transmutation. Such a feature is vital for predicting the decrease in tritium production rate within a breeder blanket during the lifetime of a fusion reactor. OpenMC is capable of simulating neutron transport in fission/fusion systems, thereby allowing it to estimate the flux that causes transmutation. It is also capable of solving the transmutation equations, which determine how the composition of a material changes over time due to neutron irradiation and radioactive decay. However, solving the transmutation equations was previously only possible when the source of neutrons came from a fission system. In a fusion system, the source of neutrons is typically determined by a separate code and then given as an input to the particle transport simulation. This is known as a fixed source calculation. Through this project, we have extended OpenMC to solve the transmutation equations for a fixed source calculation. Evaluating the change in material compositions due to transmutation and its effect on physical properties is of key importance to a range of engineering analyses for fission and fusion systems. For example, in a fusion reactor, estimating the dose rate at different physical locations resulting from irradiated materials in the reactor allows designers to ensure that workers are not exposed to doses beyond applicable regulations. In order to properly dispose of irradiated materials, designers also need to estimate the radiotoxicity, which again relies on knowledge of the material composition at some future time. The specific tasks for this project that were agreed to between ANL and UKAEA were as follows: 1. Make changes and additions in the openmc.deplete and related modules in OpenMC to support transmutation calculations following a fixed source transport simulation. 2. Make necessary changes to OpenMC to model transmutation due to an arbitrary set of reactions needed for fusion applications. Use this new capability to generate a depletion chain file based on the TENDL nuclear data library. 3. Improve the openmc.deplete module in OpenMC to keep track of gases produced as a by-product of nuclear reactions during transmutation calculations. 4. Validate the new capabilities by carrying out fixed-source transmutation calculations on a suitable benchmark problem using OpenMC and a comparable Monte Carlo neutron transport code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Introduction of the Adding and Doubling Method for Solving Bateman Equations for Nuclear Fuel Depletion

This paper introduces and evaluates the Adding and Doubling Method (ADM) for solving the Bateman equations for depletion systems with varying numbers of nuclides and compares it to the Chebyshev Rational Approximation Method (CRAM), both implemented in the reactor physics analysis application Griffin. ADM, when applied to the Crank-Nicolson Finite Difference method, can produce results comparable in accuracy and precision to CRAM with comparable run times for systems with 35 or 297 nuclides. For systems with more than 300 nuclides, the matrix-matrix operations required by ADM are significantly more costly than the matrix-vector operations required by CRAM, making CRAM the more efficient method for systems with large numbers of nuclides. ADM is an accurate method that maintains other advantages over CRAM in that it does not depend on pre-generated coefficients or require complex number operations. ADM also manages to outperform CRAM by a factor of more than 250 in terms of run time for depletion systems that require multiple Bateman solves while the depletion matrix and time step size remain constant over all depletion intervals.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1991

Leading-edge receptivity to a vortical freestream disturbance: A numerical analysis

The receptivity to freestream vorticity of the boundary layer over a flat plate with an elliptic leading edge is investigated numerically. The flow is simulated by solving the incompressible Navier-Stokes system in general curvilinear coordinates with the vorticity and stream function as dependent variables. A finite-difference scheme which is second-order accurate in both space and time is used. As a first step, the steady basic-state solution is computed. Then a small amplitude vortical disturbance is introduced at the upstream boundary and the governing equations are solved time-accurately to evaluate the spatial and temporal growth of the perturbations leading to instability waves (Tollmien-Schlichting waves) inside the boundary layer. Preliminary results for a symmetric, 2-D disturbance reveal the presence of Tollmien-Schlichting waves aft of the flat-plate/ellipse juncture.

Buter, Thomas A.↗
NASA NTRS1971

An efficient parallel algorithm for the solution of a tridiagonal linear system of equations

Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.

Stone, H. S.↗
NASA NTRS1973

An efficient parallel algorithm for the solution of a tridiagonal linear system of equations.

Tridiagonal linear systems of equations can be solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computation on computers of the Illiac IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log(sub-2) N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.

Stone, H. S.↗