Engineering topics

Yee, Helen C.

Publications and source records attributed to Yee, Helen C..

7 records

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.↗

NASA NTRS2002

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

Sjoegreen, Bjoern↗

NASA NTRS2001

Adaptive Numerical Dissipation Controls for High Order Methods

A numerical scheme for direct numerical simulation of shock-turbulence interactions of high speed compressible flows would ideally not be significantly more expensive than the standard fourth or sixth-order compact or non-compact central differencing scheme. It should be possible to resolve all scales down to scales of order of the Kolmogorov scales of turbulence accurately and efficiently, while at the same time being able to capture steep gradients occurring at much smaller scales efficiently. The goal of this lecture is to review the progress and new development of the low dissipative high order shock-capturing schemes proposed by Yee et al. Comparison on the efficiency and accuracy of this class of schemes with spectral and the fifth-order WENO (weighted essentially nonoscillatory) scheme will be presented. A new approach to dynamically sense the appropriate amount of numerical dissipation to be added at each grid point using non-orthogonal wavelets will be discussed.

Yee, Helen C.↗

NASA NTRS2001

Designing Adaptive Low-Dissipative High Order Schemes for Long-Time Integrations

A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible; (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred; (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used; and (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for nonlinear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows. The minimization of employing very fine grids to overcome the production of spurious numerical solutions and/or instability due to under-resolved grids is also sought. The incremental studies to illustrate the performance of the approach are summarized. Extensive testing and full implementation of the approach is forthcoming. The results shown so far are very encouraging.

Yee, Helen C.↗

NASA NTRS1997

Dynamics of Numerics & Spurious Behaviors in CFD Computations

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

Yee, Helen C.↗

NASA NTRS1996

Some Aspects of Nonlinear Dynamics and CFD

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with examples of spurious behavior observed in CFD computations.

Yee, Helen C.↗

NASA NTRS1994

On the dynamics of some grid adaption schemes

The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.

Sweby, Peter K.↗