Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “high-order derivatives”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

149 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

A Systematic Methodology for Constructing High-Order Energy Stable WENO Schemes

A third-order Energy Stable Weighted Essentially Non{Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter [1] was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables "energy stable" modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.

Yamaleev, Nail K.↗
NASA NTRS2015

2nd-Order CESE Results For C1.1: Transonic Ringleb Flow

The Conservation Element and Solution Element (CESE) method was used as implemented in the NASA research code ez4d (an unstructured Navier-Stokes solver coded in C++ with serial and parallel versions available.) The CESE method is a time-accurate formulation with flux-conservation in both space and time. The method treats the discretized derivatives of space and time identically and while the 2nd-order accurate version was used, high-order versions exist.

Numerical Analysis↗
NASA NTRS2015

2nd-Order CESE Results For C1.4: Vortex Transport by Uniform Flow

The Conservation Element and Solution Element (CESE) method was used as implemented in the NASA research code ez4d. The CESE method is a time accurate formulation with flux-conservation in both space and time. The method treats the discretized derivatives of space and time identically and while the 2nd-order accurate version was used, high-order versions exist, the 2nd-order accurate version was used. In regards to the ez4d code, it is an unstructured Navier-Stokes solver coded in C++ with serial and parallel versions available. As part of its architecture, ez4d has the capability to utilize multi-thread and Messaging Passage Interface (MPI) for parallel runs.

Space-time CE/SE method↗
NASA NTRS2016

Hyperbolic Method for Dispersive PDEs: Same High-Order of Accuracy for Solution, Gradient, and Hessian

In this paper, we introduce a new hyperbolic first-order system for general dispersive partial differential equations (PDEs). We then extend the proposed system to general advection-diffusion-dispersion PDEs. We apply the fourth-order RD scheme of Ref. 1 to the proposed hyperbolic system, and solve time-dependent dispersive equations, including the classical two-soliton KdV and a dispersive shock case. We demonstrate that the predicted results, including the gradient and Hessian (second derivative), are in a very good agreement with the exact solutions. We then show that the RD scheme applied to the proposed system accurately captures dispersive shocks without numerical oscillations. We also verify that the solution, gradient and Hessian are predicted with equal order of accuracy.

Mazaheri, Alireza↗
NASA NTRS2019

High-Order Finite-Difference Nonlinear Filter Methods for Subsonic Turbulence Simulation with Stochastic Forcing

Numerical stability of high-order filter schemes developed by Yee & Sjogreen is tested on three-dimensional turbulence simulations with stochastic forcing and their performance is compared with that of TVD and WENO schemes. The best­ performing filter method employs an eighth-order central base scheme with the Kennedy & Gruber skew-symmetric splitting of the inviscid flux derivative, a wavelet-based local flow sensor, a nonlinear filter utilizing the dissipative portion of seventh-order \VENO scheme, and an explicit third - or fourth-order Runge­-Kutta time integration. We show that the filter scheme is more computational]y efficient and provides a wider spectral bandwidth compared to the seventh-order WENO scheme. The method also demonstrates robust long-time integration for moderately compressible turbulence. In contrast, the fifth- and seventh­ order WENO schemes show non-trivial evolution of the velocity and density power spectra. over a. few dozen dynamical times, where both TVD and filter schemes recover a so lid statistically stationary turbulent state

Kritsuk, Alexei G.↗