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Results for “High-order accuracy”

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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171 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

High-Order Energy Stable WENO Schemes

A new third-order Energy Stable Weighted Essentially NonOscillatory (ESWENO) finite difference scheme for scalar and vector linear hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. A rigorous truncation error analysis is presented showing that the accuracy of the 3rd-order ESWENO scheme is drastically improved if the tuning parameters of the weight functions satisfy certain criteria. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO finite difference scheme of Jiang and Shu in terms of accuracy, while providing essentially nonoscillatory solutions near strong discontinuities.

Yamaleev, Nail K.↗
NASA NTRS2009

Parametric Optimization of Ares I Propellant Slosh Characteristics Using Frequency Response Criteria

A novel technique for developing propellant slosh damping requirements with respect to the stability characteristics of large flexible launch vehicles is presented. A numerical algorithm is devised which allows an automated software program to rapidly converge to pseudo-optimal solutions that minimize required propellant slosh damping for multiple tanks while maintaining constraints on the frequency response characteristics of a particular open-loop plant transfer function. An implementation of the algorithm using a high-order linear model of the Ares I plant dynamics considers all relevant dynamic interactions of flexible body modes, propellant slosh, and nozzle inertia effects. A high-resolution propellant damping requirements table is produced that can be used for baffle design. The method is demonstrated to provide exceptional speed and accuracy when compared with the alternative human-in-the-loop approach.

Orr, Jeb S.↗
NASA NTRS2011

Development and Validation of a Multidisciplinary Tool for Accurate and Efficient Rotorcraft Noise Prediction (MUTE)

A physics-based, systematically coupled, multidisciplinary prediction tool (MUTE) for rotorcraft noise was developed and validated with a wide range of flight configurations and conditions. MUTE is an aggregation of multidisciplinary computational tools that accurately and efficiently model the physics of the source of rotorcraft noise, and predict the noise at far-field observer locations. It uses systematic coupling approaches among multiple disciplines including Computational Fluid Dynamics (CFD), Computational Structural Dynamics (CSD), and high fidelity acoustics. Within MUTE, advanced high-order CFD tools are used around the rotor blade to predict the transonic flow (shock wave) effects, which generate the high-speed impulsive noise. Predictions of the blade-vortex interaction noise in low speed flight are also improved by using the Particle Vortex Transport Method (PVTM), which preserves the wake flow details required for blade/wake and fuselage/wake interactions. The accuracy of the source noise prediction is further improved by utilizing a coupling approach between CFD and CSD, so that the effects of key structural dynamics, elastic blade deformations, and trim solutions are correctly represented in the analysis. The blade loading information and/or the flow field parameters around the rotor blade predicted by the CFD/CSD coupling approach are used to predict the acoustic signatures at far-field observer locations with a high-fidelity noise propagation code (WOPWOP3). The predicted results from the MUTE tool for rotor blade aerodynamic loading and far-field acoustic signatures are compared and validated with a variation of experimental data sets, such as UH60-A data, DNW test data and HART II test data.

Liu, Yi↗
NASA NTRS2013

Performance of Improved High-Order Filter Schemes for Turbulent Flows with Shocks

The performance of the filter scheme with improved dissipation control κ has been demonstrated for different flow types. The scheme with local κ is shown to obtain more accurate results than its counterparts with global or constant κ. At the same time no additional tuning is needed to achieve high accuracy of the method when using the local κ technique. However, further improvement of the method might be needed for even more complex and/or extreme flows.

Flows↗
NASA NTRS2014

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

Mazaheri, Alireza R.↗
NASA NTRS2015

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Mazaheri, Alireza↗
NASA NTRS2016

High-Order Residual-Distribution Schemes for Discontinuous Problems on Irregular Triangular Grids

In this paper, we develop second- and third-order non-oscillatory shock-capturing hyperbolic residual distribution schemes for irregular triangular grids, extending our second- and third-order schemes to discontinuous problems. We present extended first-order N- and Rusanov-scheme formulations for hyperbolic advection-diffusion system, and demonstrate that the hyperbolic diffusion term does not affect the solution of inviscid problems for vanishingly small viscous coefficient. We then propose second- and third-order blended hyperbolic residual-distribution schemes with the extended first-order Rusanov-scheme. We show that these proposed schemes are extremely accurate in predicting non-oscillatory solutions for discontinuous problems. We also propose a characteristics-based nonlinear wave sensor for accurately detecting shocks, compression, and expansion regions. Using this proposed sensor, we demonstrate that the developed hyperbolic blended schemes do not produce entropy-violating solutions (unphysical stocks). We then verify the design order of accuracy of these blended schemes on irregular triangular grids.

Mazaheri, Alireza↗
NASA NTRSDate not supplied

Scale-Resolving Simulations of a Supersonic Retro-Propulsion Concept For Mars Entry, Descent, and Landing

Supersonic retro-propulsion (SRP) is a deceleration technology that could enable largerpayloads and potentially humans to be brought from space to the surface of Mars safely.Accurate and reliable CFD predictions are needed to help design future Mars entry, descent,and landing (EDL) vehicles due to the cost and limitations of wind tunnel tests. TypicalCFD approaches struggle at points along the Mars EDL trajectory with high enough altitude(low enough ambient pressure) that the SRP motor plumes are over-expanded. This workdemonstrates how high-order scale-resolving simulations on Cartesian AMR grids can provideaccurate and reliable time-averaged aerodynamic loads on the vehicle for this challengingflow regime. Greater than second order convergence in the time-averaged integrated axialforce𝐶𝐴is obtained across the three finest mesh resolutions simulated, and the estimateduncertainty is smaller than the unsteady standard deviation – demonstrating the accuracy andreliability of the method. Although costly, this approach can yield higher confidence in𝐶𝐴thanpreviously obtained in a reasonable turnaround time and is within reach for a few points in thetrajectory (i.e. Mach 2.4, 2.52, and 2.78). Further computational performance and numericalmethods improvements are needed to reduce the cost enough to bring this method into the EDLengineering design cycle.

S&M↗
NASA NTRSDate not supplied

Shock Capturing via Limiting for High-Order Methods Including Discontinuous Galerkin

As is well-known, popular high-order methods such as discontinuous Galerkin (DG) and flux reconstruction (FR) tend to generate oscillations near shocks and discontinuities, which can lead to negative pressure or density, ultimately causing code breakdown. For standard second-order methods, one approach to mitigating oscillations is to impose constraints on the calculated slopes, ensuring they do not become excessively steep. This limiting process is rooted in the idea of preserving monotonicity introduced by Van Leer (1974): when the data are monotone, limiting the slopes result in a monotone piecewise linear solution. However, a drawback of this approach is the loss of accuracy near extrema, where the non-monotone solution is somewhat flattened and achieves only first-order accuracy.

numerical methods↗