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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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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Performance Portable, Fully Implicit Landau Collision Operator with Batched Linear Solvers

Modern accelerators use hierarchical parallel programming models that enable massive multithreading within a processing element (PE), with multiple PEs per device driven by traditional processes. Batching is a technique for exposing PE-level parallelism in algorithms that have traditionally run on MPI processes or multiple threads within a single process. Opportunities for batching arise in, for example, kinetic discretizations of magnetized plasmas where collisions are advanced in velocity space at each spatial point independently. This paper builds on previous work on a high-performance, fully nonlinear, Landau collision operator by batching the linear solver, as well as batching the spatial point problems and adding new support for multiple grids for multiscale, multispecies problems. An anisotropic relaxation verification test that agrees well with previously published results and analytical models is presented. The performance results from NVIDIA A100 and AMD MI250X nodes are presented with hardware utilization analysis for each architecture. Finally, the entire implicit Landau operator time advance is implemented in Kokkos for performance portability, running entirely on the device and is available in the PETSc numerical library.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Improving ADAM through an implicit-explicit (IMEX) time-stepping approach

The ADAM optimizer, often used in machine learning for neural network training, corresponds to an underlying ordinary differential equation (ODE) in the limit of very small learning rates. Here, this work shows that the classical ADAM algorithm is a first-order implicit-explicit (IMEX) Euler discretization of the underlying ODE. Employing the time discretization point of view, we propose new extensions of the ADAM scheme obtained by using higher-order IMEX methods to solve the ODE. Based on this approach, we derive a new optimization algorithm for neural network training that performs better than classical ADAM on several regression and classification problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

An Implicit Finite Difference Solution to the Viscous Radiating Shock Layer with Strong Blowing

An implicit finite difference scheme is developed for the fully coupled solution of the viscous radiating stagnation line equations, including strong blowing. Solutions are presented for both air injection and carbon phenolic ablation products injection into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized.

Garrett, L. B.↗
NASA NTRS1972

On implicit equations in nonlinear network analysis.

Derivation of conditions for existence of unique solutions to implicit equations of the form y = f(x, u) or x = h(x, u) which are frequently encountered in the analysis of nonlinear networks. The existence of such solutions is demonstrated by applying the principle of contraction mapping and by ascertaining the possibility of a functional inversion according to the Palais (1959) theorem.

Sathe, S. T.↗
NASA NTRS1972

Transient, compressible heat and mass transfer in porous media using the strongly implicit iteration procedure.

Coupled nonlinear partial differential equations describing heat and mass transfer in a porous matrix are solved in finite difference form with the aid of a new iterative technique (the strongly implicit procedure). Example numerical results demonstrate the characteristics of heat and mass transport in a porous matrix such as a charring ablator. It is emphasized that multidimensional flow must be considered when predicting the thermal response of a porous material subjected to nonuniform boundary conditions.

Curry, D. M.↗
NASA NTRS1972

On stiffly stable implicit linear multistep methods.

The motivation to increase the step size with no degradation of numerical accuracy and stability has led to the discovery of particular members of the class of stiffly stable implicit linear multistep algorithms. Sufficient conditions for a consistent linear multistep method to be stiffly stable are given. These conditions involve properties of the stability mapping from the extended complex plane onto itself.

Cooke, C. H.↗
NASA NTRS1972

An implicit finite-difference solution to the viscous shock layer, including the effects of radiation and strong blowing

An implicit finite-difference scheme is developed for the fully coupled solution of the viscous, radiating stagnation-streamline equations, including strong blowing. Solutions are presented for both air injection and injection of carbon-phenolic ablation products into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative-transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized in the study. With minimum number of assumptions for the initially unknown parameters and profile distributions, convergent solutions to the full stagnation-line equations are rapidly obtained by a method of successive approximations. Damping of selected profiles is required to aid convergence of the solutions for massive blowing. It is shown that certain finite-difference approximations to the governing differential equations stabilize and improve the solutions. Detailed comparisons are made with the numerical results of previous investigations. Results of the present study indicate lower radiative heat fluxes at the wall for carbonphenolic ablation than previously predicted.

Garrett, L. B.↗
NASA NTRS1974

Two-demensional analysis of heat and mass transfer in porous media using the strongly implicit procedure

Numerical results of the heat and mass transfer in a porous matrix are presented. The coupled, nonlinear partial differential equations describing this physical phenomenon are solved in finite difference form for two dimensions, using a new iterative technique (the strongly implicit procedure). The influence of the external environment conditions (heating and pressure) is shown to produce two-dimensional flow in the porous matrix. Typical fluid and solid temperature distributions in the porous matrix and internal pressure distributions are presented.

Curry, D. M.↗
NASA NTRS1974

An implicit sampling theorem for bounded bandlimited functions

A rigorous proof of the 'strong bias tone' scheme is embodied in the implicit sampling theorem. The representation of signals that are sample functions of possible nonstationary random processes being of principal interest, the proof could not directly invoke results from classical analysis, which depend on the existence of the Fourier transform of the function under consideration; rather, it is based on Zakai's (1965) theorem on the series expansion of functions, band-limited under a suitably extended definition. A practical circuit that restores an approximate version of the signal from its sine-wave-crossings is presented and possible improvements to it are discussed.

Bar-David, I.↗
NASA NTRS1973

Partial implicitization

The steady-state solution to the full Navier-Stokes equations for complicated flows is generally difficult to obtain. The Burgers (1948) equation is used as a model of the Navier-Stokes equations. The steady-state solution is obtained by a one-step explicit technique resulting from a partial implicitization of the difference equation. Stability analysis shows that the technique is unconditionally stable, and numerical tests show the technique to be accurate.

Graves, R. A., Jr.↗
NASA NTRS1975

Calculation of three-dimensional compressible laminar and turbulent boundary layers. An implicit finite-difference procedure for solving the three-dimensional compressible laminar, transitional, and turbulent boundary-layer equations

An implicit finite-difference procedure is presented for solving the compressible three-dimensional boundary-layer equations. The method is second-order accurate, unconditionally stable (conditional stability for reverse cross flow), and efficient from the viewpoint of computer storage and processing time. The Reynolds stress terms are modeled by (1) a single-layer mixing length model and (2) a two-layer eddy viscosity model. These models, although simple in concept, accurately predicted the equilibrium turbulent flow for the conditions considered. Numerical results are compared with experimental wall and profile data for a cone at an angle of attack larger than the cone semiapex angle. These comparisons clearly indicate that the numerical procedure and turbulence models accurately predict the experimental data with as few as 21 nodal points in the plane normal to the wall boundary.

Harris, J. E.↗
NASA NTRS1975

Implicit approximate-factorization schemes for the low-frequency transonic equation

Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

Ballhaus, W. F.↗
NASA NTRS1976

Time-asymptotic solutions of the Navier-Stokes equation for free shear flows using an alternating-direction implicit method

An uncoupled time asymptotic alternating direction implicit method for solving the Navier-Stokes equations was tested on two laminar parallel mixing flows. A constant total temperature was assumed in order to eliminate the need to solve the full energy equation; consequently, static temperature was evaluated by using algebraic relationship. For the mixing of two supersonic streams at a Reynolds number of 1,000, convergent solutions were obtained for a time step 5 times the maximum allowable size for an explicit method. The solution diverged for a time step 10 times the explicit limit. Improved convergence was obtained when upwind differencing was used for convective terms. Larger time steps were not possible with either upwind differencing or the diagonally dominant scheme. Artificial viscosity was added to the continuity equation in order to eliminate divergence for the mixing of a subsonic stream with a supersonic stream at a Reynolds number of 1,000.

Rudy, D. H.↗
NASA NTRS1976

An implicit finite-difference algorithm for hyperbolic systems in conservation-law form

An implicit finite-difference scheme is developed for the efficient numerical solution of nonlinear hyperbolic systems in conservation-law form. The algorithm is second-order time-accurate, noniterative, and in a spatially factored form. Second- or fourth-order central and second-order one-sided spatial differencing are accommodated within the solution of a block tridiagonal system of equations. Significant conceptual and computational simplifications are made for systems whose flux vectors are homogeneous functions (of degree one), e.g., the Eulerian gasdynamic equations. Conservative hybrid schemes, which switch from central to one-sided spatial differencing whenever the local characteristic speeds are of the same sign, are constructed to improve the resolution of weak solutions. Numerical solutions are presented for a nonlinear scalar model equation and the two-dimensional Eulerian gasdynamic equations.

Beam, R. M.↗