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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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Planetary Spectrum Generator: An Accurate Online Radiative Transfer Suite for Atmospheres, Comets, Small Bodies and Exoplanets

We have developed an online radiative-transfer suite (https://psg.gsfc.nasa.gov) applicable to a broad range of planetary objects (e.g., planets, moons, comets, asteroids, TNOs, KBOs, exoplanets). The Planetary Spectrum Generator (PSG) can synthesize planetary spectra (atmospheres and surfaces) for a broad range of wavelengths (UV/Vis/near-IR/IR/far-IR/THz/sub-mm/Radio) from any observatory (e.g., JWST, ALMA, Keck, SOFIA), any orbiter (e.g., ExoMars, Juno), or any lander (e.g., MSL). This is achieved by combining several state-of-the-art radiative transfer models, spectroscopic databases and planetary databases (i.e., climatological and orbital). PSG has a 3D (three-dimensional) orbital calculator for most bodies in the solar system, and all confirmed exoplanets, while the radiative-transfer models can ingest billions of spectral signatures for hundreds of species from several spectroscopic repositories. It integrates the latest radiative-transfer and scattering methods in order to compute high resolution spectra via line-by-line calculations, and utilizes the efficient correlated-k method at moderate resolutions, while for computing cometary spectra, PSG handles non-LTE and LTE excitation processes. PSG includes a realistic noise calculator that integrates several telescope/instrument configurations (e.g., interferometry, coronagraphs) and detector technologies (e.g., CCD, heterodyne detectors, bolometers). Such an integration of advanced spectroscopic methods into an online tool can greatly serve the planetary community, ultimately enabling the retrieval of planetary parameters from remote sensing data, efficient mission planning strategies, interpretation of current and future planetary data, calibration of spectroscopic data, and development of new instrument/spacecraft concepts.

Villanueva, G. L.↗
NASA NTRS2016

A Numerical Theory for Impedance Education in Three-Dimensional Normal Incidence Tubes

A method for educing the locally-reacting acoustic impedance of a test sample mounted in a 3-D normal incidence impedance tube is presented and validated. The unique feature of the method is that the excitation frequency (or duct geometry) may be such that high-order duct modes may exist. The method educes the impedance, iteratively, by minimizing an objective function consisting of the difference between the measured and numerically computed acoustic pressure at preselected measurement points in the duct. The method is validated on planar and high-order mode sources with data synthesized from exact mode theory. These data are then subjected to random jitter to simulate the effects of measurement uncertainties on the educed impedance spectrum. The primary conclusions of the study are 1) Without random jitter the method is in excellent agreement with that for known impedance samples, and 2) Random jitter that is compatible to that found in a typical experiment has minimal impact on the accuracy of the educed impedance.

Watson, Willie R.↗
NASA NTRS2021

Comparing Commercial and Research Computational Fluid Dynamic Codes Using High-Order Workshop Benchmark Problems

The commercial computational fluid dynamic (CFD) code ANSYS Fluent and multiple research CFD codes (ez4d with uses the conservation element and solution element (CESE) method and codes that use the flux reconstruction (FR) method) were tested using three different benchmark problems from the International Workshop for High-Order CFD Methods. The benchmark problems included the transonic Ringleb flow, vortex transport by uniform flow, and laminar boundary layer on a flat plate. Simulation results from all three benchmark problems showed that the Fluent solutions had less error than the ez4d solutions for a given degree of freedom. As expected, both the Fluent and ez4d solutions had larger errors for a given degree of freedom than the simulations that used the FR method because both Fluent and ez4d utilized a second-order scheme whereas the FR codes utilized a fourth-order scheme.

CFD↗
NASA NTRS2013

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

Fisher, Travis C.↗
NASA NTRS1994

Round-off error in long-term orbital integrations using multistep methods

Techniques for reducing roundoff error are compared by testing them on high-order Stormer and summetric multistep methods. The best technique for most applications is to write the equation in summed, function-evaluation form and to store the coefficients as rational numbers. A larger error reduction can be achieved by writing the equation in backward-difference form and performing some of the additions in extended precision, but this entails a larger central processing unit (cpu) cost.

Quinlan, Gerald D.↗
NASA NTRS1992

ULTRA-SHARP solution of the Smith-Hutton problem

Highly convective scalar transport involving near-discontinuities and strong streamline curvature was addressed in a paper by Smith and Hutton in 1982, comparing several different convection schemes applied to a specially devised test problem. First order methods showed significant artificial diffusion, whereas higher order methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of low order artificially diffusive schemes, especially in the numerical heat transfer industry. The present paper describes an alternate strategy of using non-artificially diffusive high order methods, while maintaining strictly monotonic transitions through the use of simple flux limited constraints. Limited third order upwinding is usually found to be the most cost effective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed.

Leonard, B. P.↗
NASA NTRS2014

High-Order Implicit-Explicit Multi-Block Time-stepping Method for Hyperbolic PDEs

This work seeks to explore and improve the current time-stepping schemes used in computational fluid dynamics (CFD) in order to reduce overall computational time. A high-order scheme has been developed using a combination of implicit and explicit (IMEX) time-stepping Runge-Kutta (RK) schemes which increases numerical stability with respect to the time step size, resulting in decreased computational time. The IMEX scheme alone does not yield the desired increase in numerical stability, but when used in conjunction with an overlapping partitioned (multi-block) domain significant increase in stability is observed. To show this, the Overlapping-Partition IMEX (OP IMEX) scheme is applied to both one-dimensional (1D) and two-dimensional (2D) problems, the nonlinear viscous Burger's equation and 2D advection equation, respectively. The method uses two different summation by parts (SBP) derivative approximations, second-order and fourth-order accurate. The Dirichlet boundary conditions are imposed using the Simultaneous Approximation Term (SAT) penalty method. The 6-stage additive Runge-Kutta IMEX time integration schemes are fourth-order accurate in time. An increase in numerical stability 65 times greater than the fully explicit scheme is demonstrated to be achievable with the OP IMEX method applied to 1D Burger's equation. Results from the 2D, purely convective, advection equation show stability increases on the order of 10 times the explicit scheme using the OP IMEX method. Also, the domain partitioning method in this work shows potential for breaking the computational domain into manageable sizes such that implicit solutions for full three-dimensional CFD simulations can be computed using direct solving methods rather than the standard iterative methods currently used.

Nielsen, Tanner B.↗
DOE OSTI2026

PDE-constrained high-order mesh optimization

Here, we present a novel framework for PDE-constrained r-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality metric and a measure of the accuracy of the PDE solution obtained via finite element discretization. The proposed formulation achieves optimized, well-defined high-order meshes by integrating mesh quality control, PDE solution accuracy, and robust gradient regularization. We adopt the Target-Matrix Optimization Paradigm to control geometric properties across the mesh, independent of the PDE of interest. To incorporate the accuracy of the PDE solution, we introduce error measures that control the finite element discretization error. The implicit dependence of these error measures on the mesh nodal positions is accurately captured by adjoint sensitivity analysis. Additionally, a convolution-based gradient regularization strategy is used to ensure stable and effective adaptation of high-order meshes. We demonstrate that the proposed framework can improve mesh quality and reduce the error by up to 10 times for the solution of Poisson and linear elasto-static problems. The approach is general with respect to the dimensionality, the order of the mesh, the types of mesh elements, and can be applied to any PDE that admits well-defined adjoint operators.

Computer science↗
NASA NTRS1987

Constrained optimization techniques for active control of aeroelastic response

Active control of aeroelastic response is a complex problem in which the designer usually tries to satisfy many design criteria which are often conflicting in nature. To further complicate the design problem, the state space equations describing this type of control problem are usually of high order, involving a large number of states to represent the flexible structure and unsteady aerodynamics. Control laws based on the standard Linear - Quadratic - Gaussian method are of the same high order as the aeroelastic plant and may be difficult to implement in the flight computer. To overcome this disadvantage a new approach was developed for designing low-order optimized robust control laws. In this approach, a nonlinear programming algorithm is used to search for the values of control law design variables that minimize a performance index while satisfying several inequality constraints that describe the design criteria on the stability robustness and responses. The method is applied to a gust load alleviation problem and a stability robustness improvement problem of a drone aircraft.

Mukhopadhyay, Vivekananda↗
NASA NTRS1981

Application of constrained optimization to active control of aeroelastic response

Active control of aeroelastic response is a complex in which the designer usually tries to satisfy many criteria which are often conflicting. To further complicate the design problem, the state space equations describing this type of control problem are usually of high order, involving a large number of states to represent the flexible structure and unsteady aerodynamics. Control laws based on the standard Linear-Quadratic-Gaussian (LQG) method are of the same high order as the aeroelastic plant. To overcome this disadvantage of the LQG mode, an approach developed for designing low order optimal control laws which uses a nonlinear programming algorithm to search for the values of the control law variables that minimize a composite performance index, was extended to the constrained optimization problem. The method involves searching for the values of the control law variables that minimize a basic performance index while satisfying several inequality constraints that describe the design criteria. The method is applied to gust load alleviation of a drone aircraft.

Newsom, J. R.↗
DOE OSTI2026

A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method that maintains high-order temporal accuracy in both velocity and pressure for steady and unsteady velocity boundary conditions. Fourth order spatial accuracy is achieved through a novel fifth order IIM discretization scheme for the advection term, as well as existing high-order interface-corrected finite difference schemes for the other differential operators. Using a set of manufactured flow problems with stationary and moving boundaries, we demonstrate fourth order convergence of velocity and pressure in the infinity norm, both inside the domain and on the immersed boundaries. The solver’s performance is further validated through a range of practical flow simulations, highlighting its efficiency over a second order scheme. Finally, we showcase the ability of our immersed discretization scheme to handle interface-coupled multiphysics problems by solving a conjugate heat transfer problem with multiple immersed solids. Overall, the proposed approach robustly combines the efficiency of high order discretization schemes with the flexibility of immersed discretizations for flow problems with complex, moving boundaries and interfaces.

42 ENGINEERING↗
NASA NTRS2016

Development of a Perfectly Matched Layer Technique for a Discontinuous-Galerkin Spectral-Element Method

The numerical simulation of many aerodynamic non-periodic flows of practical interest involves discretized computational domains that often must be artificially truncated. Appropriate boundary conditions are required at these truncated domain boundaries, and ideally, these boundary conditions should be perfectly "absorbing" or "nonreflecting" so that they do not contaminate the flow field in the interior of the domain. The proper specification of these boundaries is critical to the stability, accuracy, convergence, and quality of the numerical solution, and has been the topic of considerable research. The need for accurate boundary specification has been underscored in recent years with efforts to apply higher-fidelity methods (DNS, LES) in conjunction with high-order low-dissipation numerical schemes to realistic flow configurations. One of the most popular choices for specifying these boundaries is the characteristics-based boundary condition where the linearized flow field at the boundaries are decomposed into characteristic waves using either one-dimensional Riemann or other multi-dimensional Riemann approximations. The values of incoming characteristics are then suitably modified. The incoming characteristics are specified at the in flow boundaries, and at the out flow boundaries the variation of the incoming characteristic is zeroed out to ensure no reflection. This, however, makes the problem ill-posed requiring the use of an ad-hoc parameter to allow small reflections that make the solution stable. Generally speaking, such boundary conditions work reasonably well when the characteristic flow direction is normal to the boundary, but reflects spurious energy otherwise. An alternative to the characteristic-based boundary condition is to add additional "buffer" regions to the main computational domain near the artificial boundaries, and solve a different set of equations in the buffer region in order to minimize acoustic reflections. One approach that has been used involves modeling the pressure fluctuations as acoustic waves propagating in the far-field relative to a single noise-source inside the buffer region. This approach treats vorticity-induced pressure fluctuations the same as acoustic waves. Another popular approach, often referred to as the "sponge layer," attempts to dampen the flow perturbations by introducing artificial dissipation in the buffer region. Although the artificial dissipation removes all perturbations inside the sponge layer, incoming waves are still reflected from the interface boundary between the computational domain and the sponge layer. The effect of these refkections can be somewhat mitigated by appropriately selecting the artificial dissipation strength and the extent of the sponge layer. One of the most promising variants on the buffer region approach is the Perfectly Matched Layer (PML) technique. The PML technique mitigates spurious reflections from boundaries and interfaces by dampening the perturbation modes inside the buffer region such that their eigenfunctions remain unchanged. The technique was first developed by Berenger for application to problems involving electromagnetic wave propagation. It was later extended to the linearized Euler, Euler and Navier-Stokes equations by Hu and his coauthors. The PML technique ensures the no-reflection property for all waves, irrespective of incidence angle, wavelength, and propagation direction. Although the technique requires the solution of a set of auxiliary equations, the computational overhead is easily justified since it allows smaller domain sizes and can provide better accuracy, stability, and convergence of the numerical solution. In this paper, the PML technique is developed in the context of a high-order spectral-element Discontinuous Galerkin (DG) method. The technique is compared to other approaches to treating the in flow and out flow boundary, such as those based on using characteristic boundary conditions and sponge layers. The superiority of the current PML technique over other approaches is demonstrated for a range of test cases, viz., acoustic pulse propagation, convective vortex, shear layer flow, and low-pressure turbine cascade flow. The paper is structured as follows. We first derive the PML equations from the non{linear Euler equations. A short description of the higher-order DG method used is then described. Preliminary results for the four test cases considered are then presented and discussed. Details regarding current work that will be included in the final paper are also provided.

Spectral↗
DOE OSTI2025

Boundary Corrections for Kernel Approximation to Differential Operators

The kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same computational cost as an explicit finite difference scheme but can exhibit order reduction at boundaries. In previous work on periodic domains, order reduction was addressed, yielding high-order accuracy. The issue addressed in this work is the elimination of order reduction of the kernel-based approach for a more general set of boundary conditions. Further, we consider the case of both first and second order operators. To demonstrate the theory, we provide not only the mathematical proofs but also experimental results by applying various boundary conditions to different types of equations. The results agree with the theory, demonstrating a systematic path to high order for kernel-based methods on bounded domains.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

Jiang, Bo-Nan↗
DOE OSTI2024

Implicit–explicit multirate infinitesimal stage-restart methods

Implicit–Explicit (IMEX) methods are flexible numerical time integration methods which solve an initial-value problem (IVP) that is split into stiff and nonstiff processes with the goal of lower computational costs than a purely implicit or explicit approach. A complementary form of flexible IVP solvers are multirate infinitesimal methods for problems split into fast- and slow-changing dynamics, that solve a multirate IVP by evolving a sequence of “fast” IVPs using any suitably accurate algorithm. This article introduces a new class of high-order implicit–explicit multirate methods that are designed for multirate IVPs in which the slow-changing dynamics are further split in an IMEX fashion. This new class, which we call implicit–explicit multirate infinitesimal stage-restart (IMEX-MRI-SR), both improves upon the previous implicit–explicit multirate infinitesimal generalized-structure additive Runge Kutta (IMEX-MRI-GARK) methods by allowing for far easier creation of new embedded methods, and extends multirate exponential Runge Kutta (MERK) methods by allowing the fast-changing dynamics to be nonlinear and the methods to be implicit. We leverage GARK theory to derive conditions for orders of accuracy up to four, and we provide second- and third-order accurate example methods, which are the first known embedded MRI methods with IMEX structure. We then perform numerical simulations demonstrating convergence rates and computational performance in both fixed-step and adaptive-step settings.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
NASA NTRS2019

Predictions of Slat Noise from the 30P30N at High Angles of Attack Using Zonal Hybrid RANS-LES

Aeroacoustic predictions of slat noise from the 30P30N three-element high-lift system at high angles of attack are presented using a zonal hybrid RANS-LES method. The simulations are part of the 5th AIAA Benchmark problems for Airframe Noise Computations (BANC-V) Workshop. An economical approach utilizing structured overset grids with spatially varying span-wise grid resolution and a high-order accurate finite difference method is described. The method is utilized for near-field predictions at three angles of attack: α = 5.5, 9.5, and 14.0 degrees. Far-field noise is obtained by propagating the near-field solution using a permeable surface Ffowcs Williams-Hawkings (FWH) method. Good agreement is obtained with both near-field and far-field Power Spectral Density (PSD) data from an experimental study of the 30P30N in the 2m x 2m Kevlar-wall wind tunnel at the Japan Aerospace Exploration Agency (JAXA). Specifically, the reduction in narrow band peaks and overall broadband noise levels with increasing angle of attack is captured well using the zonal hybrid RANS-LES method.

Housman, Jeffrey A.↗
NASA NTRS2016

Validation of High-Fidelity CFD/CAA Framework for Launch Vehicle Acoustic Environment Simulation against Scale Model Test Data

A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed for launch vehicle liftoff acoustic environment predictions. The framework couples the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate discontinuous Galerkin solver developed in the same production framework, Loci/THRUST, to accurately resolve and propagate acoustic physics across the entire launch environment. Time-accurate, Hybrid RANS/LES CFD modeling is applied for predicting the acoustic generation physics at the plume source, and a high-order accurate unstructured discontinuous Galerkin (DG) method is employed to propagate acoustic waves away from the source across large distances using high-order accurate schemes. The DG solver is capable of solving 2nd, 3rd, and 4th order Euler solutions for non-linear, conservative acoustic field propagation. Initial application testing and validation has been carried out against high resolution acoustic data from the Ares Scale Model Acoustic Test (ASMAT) series to evaluate the capabilities and production readiness of the CFD/CAA system to resolve the observed spectrum of acoustic frequency content. This paper presents results from this validation and outlines efforts to mature and improve the computational simulation framework.

Liever, Peter A.↗