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NASA NTRS2016

On the Synergy Between Numerics and Subgrid Scale Modeling in LES of Stratified Flows: Grid Convergence of a Stratocumulus-Topped Boundary Layer

The effectiveness of a linear upwinding scalar advection scheme to suppress numerical dispersion errors near sharp inversions in large-eddy simulations of a nocturnal stratocumulus-topped boundary layer is assessed. Linear upwinding is a trade-off between non-dissipative and non-linear positive definite advection schemes. It is shown that linear upwinding does not negatively impact the model's grid convergence properties and a sharp inversion free of numerical artifacts is maintained. Even though mean profiles and turbulence fluxes show good grid convergence characteristics the liquid water amount varies significantly with grid resolution. The entrainment rate is identical for all resolutions and independent of the liquid water amount. For the present stratocumulus case, the impact of cloud-top radiative cooling is negligible and turbulence is largely driven by convection emanating from the surface.

Matheou, Georgios↗

NASA NTRS1999

A Non-Dissipative Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwell's Equations

We consider a divergence-free non-dissipative fourth-order explicit staggered finite difference scheme for the hyperbolic Maxwell's equations. Special one-sided difference operators are derived in order to implement the scheme near metal boundaries and dielectric interfaces. Numerical results show the scheme is long-time stable, and is fourth-order convergent over complex domains that include dielectric interfaces and perfectly conducting surfaces. We also examine the scheme's behavior near metal surfaces that are not aligned with the grid axes, and compare its accuracy to that obtained by the Yee scheme.

Yefet, Amir↗

NASA NTRS1995

Application of low dissipation and dispersion Runge-Kutta schemes to benchmark problems in computational aeroacoustics

We investigate accurate and efficient time advancing methods for computational aeroacoustics, where non-dissipative and non-dispersive properties are of critical importance. Our analysis pertains to the application of Runge-Kutta methods to high-order finite difference discretization. In many CFD applications, multi-stage Runge-Kutta schemes have often been favored for their low storage requirements and relatively large stability limits. For computing acoustic waves, however, the stability consideration alone is not sufficient, since the Runge-Kutta schemes entail both dissipation and dispersion errors. The time step is now limited by the tolerable dissipation and dispersion errors in the computation. In the present paper, it is shown that if the traditional Runge-Kutta schemes are used for time advancing in acoustic problems, time steps greatly smaller than that allowed by the stability limit are necessary. Low Dissipation and Dispersion Runge-Kutta (LDDRK) schemes are proposed, based on an optimization that minimizes the dissipation and dispersion errors for wave propagation. Optimizations of both single-step and two-step alternating schemes are considered. The proposed LDDRK schemes are remarkably more efficient than the classical Runge-Kutta schemes for acoustic computations. Numerical results of each Category of the Benchmark Problems are presented. Moreover, low storage implementations of the optimized schemes are discussed. Special issues of implementing numerical boundary conditions in the LDDRK schemes are also addressed.

Hu, F. Q.↗

DOE OSTI2020

First Principles Nonadiabatic Excited-State Molecular Dynamics in NWChem

Computational simulation of non-adiabatic molecular dynamics is an indispensable tool for understanding complex photoinduced processes such as internal conversion, energy transfer, charge separation, and spatial localization of excitons, to name a few. Here, we report an implementation of the fewest-switches surface hopping algorithm in the NWChem computational chemistry program. Here the surface hopping method is combined with linear-response time-dependent density functional theory calculations of adiabatic excited state potential energy surfaces. To treat quantum transitions between arbitrary electronic Born{Oppenheimer states, we have implemented both numerical and analytical differentiation schemes for derivative non-adiabatic couplings. A numerical approach for the time-derivative non-adiabatic couplings together with an analytical method for calculating non-adiabatic coupling vectors is an efficient combination for surface hopping approaches. Additionally, electronic decoherence schemes and a state reassigned unavoided crossings algorithm are also implemented to improve the accuracy of the simulated dynamics and to handle trivial unavoided crossings. We apply our code to study the ultrafast decay of photoexcited benzene, including a detailed analysis of the potential energy surface, population decay time scales, and vibrational coordinates coupled to the excitation dynamics. The development presented in this work is a baseline for future implementations of more sophisticated frameworks for simulating of non-adiabatic molecular dynamics in NWChem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1997

Experimental Assessment and Enhancement of Planar Laser-Induced Fluorescence Measurements of Nitric Oxide in an Inverse Diffusion Flame

We have experimentally assessed the quantitative nature of planar laser-induced fluorescence (PLIF) measurements of NO concentration in a unique atmospheric pressure, laminar, axial inverse diffusion flame (IDF). The PLIF measurements were assessed relative to a two-dimensional array of separate laser saturated fluorescence (LSF) measurements. We demonstrated and evaluated several experimentally-based procedures for enhancing the quantitative nature of PLIF concentration images. Because these experimentally-based PLIF correction schemes require only the ability to make PLIF and LSF measurements, they produce a more broadly applicable PLIF diagnostic compared to numerically-based correction schemes. We experimentally assessed the influence of interferences on both narrow-band and broad-band fluorescence measurements at atmospheric and high pressures. Optimum excitation and detection schemes were determined for the LSF and PLIF measurements. Single-input and multiple-input, experimentally-based PLIF enhancement procedures were developed for application in test environments with both negligible and significant quench-dependent error gradients. Each experimentally-based procedure provides an enhancement of approximately 50% in the quantitative nature of the PLIF measurements, and results in concentration images nominally as quantitative as LSF point measurements. These correction procedures can be applied to other species, including radicals, for which no experimental data are available from which to implement numerically-based PLIF enhancement procedures.

Partridge, William P.↗

NASA NTRS2003

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows: Minimization of Delta * B Numerical Error - II

The generalization of a class of low-dissipative high order filter finite difference schemes for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been developed. The new scheme consists of a divergence free preserving high order spatial base scheme with a filter approach which can be divergence-free preserving depending on the type of filter operator being used, the method of applying the filter step, and the type of flow problem to be considered. Several variants of the filter approach that cater to different flow types are proposed. These filters provide a natural and efficient way for the minimization of the divergence of the magnetic field (Delta * B) numerical error in the sense that no standard divergence cleaning is required. Performance evaluation of these variants, and the key role that the proper treatment of their corresponding numerical boundary conditions can play will be illustrated. Many levels of grid refinement and detailed comparison with several commonly used compressible MHD shock-capturing schemes will be sought. For certain MHD 2-D test problems, divergence free preservation of the magnetic fields of these filter schemes has been achieved.

Sjoegreen, Bjoern↗

NASA NTRS1981

Application of variable structure system theory to aircraft flight control

The current status of research on the application of variable structure system (VSS) theory to design aircraft flight control systems is summarized. Two aircraft types are currently being investigated: the Augmentor Wing Jet STOL Research Aircraft (AWJSRA), and AV-8A Harrier. The AWJSRA design considers automatic control of longitudinal dynamics during the landing phase. The main task for the AWJSRA is to design an automatic landing system that captures and tracks a localizer beam. The control task for the AV-8A is to track velocity commands in a hovering flight configuration. Much effort was devoted to developing computer programs that are needed to carry out VSS design in a multivariable frame work, and in becoming familiar with the dynamics and control problems associated with the aircraft types under investigation. Numerous VSS design schemes were explored, particularly for the AWJSRA. The approaches that appear best suited for these aircraft types are presented. Examples are given of the numerical results currently being generated.

Calise, A. J.↗

NASA NTRS1992

Numerical simulation of conservation laws

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

Chang, Sin-Chung↗

NASA NTRS2005

Turbulent Vortex-Flow Simulation Over a 65 deg Sharp and Blunt Leading-Edge Delta Wing at Subsonic Speeds

Turbulent thin-layer, Reynolds-Averaged Navier-Stokes solutions, based on a multi-block structured grid, are presented for a 65 deg delta wing having either a sharp leading edge (SLE) or blunt leading edge (BLE) geometry. The primary objective of the study is to assess the prediction capability of the method for simulating the leading-edge flow separation and the ensuing vortex flow characteristics. Computational results are obtained for two angles of attack of approximately 13 and 20 deg, at free-stream Mach number of 0.40 and Reynolds number of 6 million based on the wing mean aerodynamic chord. The effects of two turbulence models of Baldwin-Lomax with Degani-Schiff (BL/DS) and the Spalart-Allmaras (SA) on the numerical results are also discussed. The computations also explore the effects of two numerical flux-splitting schemes, i.e., flux difference splitting (fds) and flux vector splitting (fvs), on the solution development and convergence characteristics. The resulting trends in solution sensitivity to grid resolution for the selected leading-edge geometries, angles of attack, turbulence models and flux splitting schemes are also presented. The validity of the numerical results is evaluated against a unique set of experimental wind-tunnel data that was obtained in the National Transonic Facility at the NASA Langley Research Center.

Ghaffari, Farhad↗

NASA NTRS1995

The construction of high-accuracy schemes for acoustic equations

An accuracy analysis of various high order schemes is performed from an interpolation point of view. The analysis indicates that classical high order finite difference schemes, which use polynomial interpolation, hold high accuracy only at nodes and are therefore not suitable for time-dependent problems. Thus, some schemes improve their numerical accuracy within grid cells by the near-minimax approximation method, but their practical significance is degraded by maintaining the same stencil as classical schemes. One-step methods in space discretization, which use piecewise polynomial interpolation and involve data at only two points, can generate a uniform accuracy over the whole grid cell and avoid spurious roots. As a result, they are more accurate and efficient than multistep methods. In particular, the Cubic-Interpolated Psuedoparticle (CIP) scheme is recommended for computational acoustics.

Tang, Lei↗

NASA NTRS2011

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.

Solakiewicz, Richard↗

NASA NTRS2011

Tests of the Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

Satellite lightning imagers such as the NASA Tropical Rainfall Measuring Mission Lightning Imaging Sensor (TRMM/LIS) and the future GOES-R Geostationary Lightning Mapper (GLM) are designed to detect total lightning (ground flashes + cloud flashes). However, there is a desire to discriminate ground flashes from cloud flashes from the vantage point of space since this would enhance the overall information content of the satellite lightning data and likely improve its operational and scientific applications (e.g., in severe weather warning, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters (one of which is the ground flash fraction), a scalar function was minimized by a numerical method. In order to improve this optimization, a Grobner basis solution was introduced to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. In this study, we test the efficacy of the Grobner basis initialization using actual lightning imager measurements and ground flash truth derived from the national lightning network.

Koshak, William↗

NASA NTRS1983

Stresses in a quasi-isotropic pin loaded connector using photoelasticity

Birefringent glass-epoxy and a numerical stress separation scheme are used to compute the stresses in the vicinity of a pin-loaded hole. The radial and circumferential stresses at the hole edge, and the net section and shear-out stresses are computed. The numerical and experimental results are compared with the computed stresses. The fixture used to load the connector is discussed and typical isochromatic and isoclinic fringe patterns are presented. The stress-separation scheme is briefly discussed.

Hyer, M. W.↗

NASA NTRS1984

Stresses in a quasi-isotropic pin-loaded connector using photoelasticity

Hyer, M. W.↗

DOE OSTI2024

Dynamic flux surrogate-based partitioned methods for interface problems

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix–vector multiplication. In conclusion, we provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.

Dynamic mode decomposition (DMD)↗

NASA NTRS1985

On a class of TVD schemes for gas dynamic calculations

The purpose of this paper is to review a class of explicit and implicit second-order accurate Total Variation Diminishing (TVD) schemes and to show by numerical experiments, the performance of these schemes to the Euler equations of gas dynamics. The method of constructing these second-order accurate TVD schemes is sometimes known as the modified flux approach.

Yee, H. C.↗

NASA NTRS2009

Simulating the Effects of Irrigation over the U.S. in a Land Surface Model Based on Satellite Derived Agricultural Data

A novel method is introduced for integrating satellite derived irrigation data and high-resolution crop type information into a land surface model (LSM). The objective is to improve the simulation of land surface states and fluxes through better representation of agricultural land use. Ultimately, this scheme could enable numerical weather prediction (NWP) models to capture land-atmosphere feedbacks in managed lands more accurately and thus improve forecast skill. Here we show that application of the new irrigation scheme over the continental US significantly influences the surface water and energy balances by modulating the partitioning of water between the surface and the atmosphere. In our experiment, irrigation caused a 12% increase in evapotranspiration (QLE) and an equivalent reduction in the sensible heat flux (QH) averaged over all irrigated areas in the continental US during the 2003 growing season. Local effects were more extreme: irrigation shifted more than 100 W/m from QH to QLE in many locations in California, eastern Idaho, southern Washington, and southern Colorado during peak crop growth. In these cases, the changes in ground heat flux (QG), net radiation (RNET), evapotranspiration (ET), runoff (R), and soil moisture (SM) were more than 3 W/m(sup 2), 20 W/m(sup 2), 5 mm/day, 0.3 mm/day, and 100 mm, respectively. These results are highly relevant to continental- to global-scale water and energy cycle studies that, to date, have struggled to quantify the effects of agricultural management practices such as irrigation. Based on the results presented here, we expect that better representation of managed lands will lead to improved weather and climate forecasting skill when the new irrigation scheme is incorporated into NWP models such as NOAA's Global Forecast System (GFS).

Ozdogan, Mutlu↗

DOE OSTI2023

Efficient Bayesian inference with latent Hamiltonian neural networks in No-U-Turn Sampling

When sampling for Bayesian inference, one popular approach in the computational field is to use Hamiltonian Monte Carlo (HMC) and specifically the No-U-Turn Sampler (NUTS), which automatically decides the end time of the Hamiltonian trajectory. However, HMC and NUTS can require numerous numerical gradients of the target density and can prove slow in practice when relying on computationally expensive forward models. We propose Latent Hamiltonian neural networks (L-HNNs) with HMC and NUTS for solving Bayesian inference problems. Once trained, L-HNNs do not require numerical gradients of the target density during sampling, and hence numerous evaluations of the forward computational model. Moreover, L-HNNs satisfy important properties such as perfect time reversibility and Hamiltonian conservation, making them well-suited for use within HMC and NUTS because stationarity can be shown. We also propose the integration of L-HNNs in an online error monitoring scheme, in which numerical gradients of the target density are used for a few samples whenever the L-HNNs prediction errors are large. This online error monitor scheme prevents sample degeneracy in regions of low probability density and ensures robust uncertainty quantification. We demonstrate L-HNNs in NUTS with online error monitoring on several analytical examples involving complex, heavy-tailed, and high-local-curvature probability densities. We then demonstrate the applicability of L-HNNs in NUTS to two computational case studies, namely the Allen-Cahn stochastic partial differential equation and an elliptic partial differential equation with 25 and 50 inference parameters, respectively. Overall, the L-HNNs in NUTS with online error monitoring satisfactorily inferred these probability densities. In conclusion, compared to traditional NUTS, L-HNNs in NUTS with online error monitoring required 1–2 orders of magnitude fewer numerical gradients of the target density and improved the effective sample size (ESS) per gradient (which is a measure of both the sampling quality and the computational expense) by an order of magnitude.

97 MATHEMATICS AND COMPUTING↗