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NASA NTRS2000

Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers

Optimal controller design is addressed for a class of linear, time-invariant systems which are dissipative with respect to a quadratic power function. The system matrices are assumed to be affine functions of uncertain parameters confined to a convex polytopic region in the parameter space. For such systems, a method is developed for designing a controller which is dissipative with respect to a given power function, and is simultaneously optimal in the linear-quadratic-Gaussian (LQG) sense. The resulting controller provides robust stability as well as optimal performance. Three important special cases, namely, passive, norm-bounded, and sector-bounded controllers, which are also LQG-optimal, are presented. The results give new methods for robust controller design in the presence of parametric uncertainties.

Joshi, Suresh M.↗
NASA NTRS2000

Extension of Efficient Low Dissipative High Order Schemes for 3-D Curvilinear Moving Grids

The efficient low dissipative high order schemes proposed by Yee et al. is formulated for 3-D curvilinear moving grids. These schemes consists of a high order base schemes combined with nonlinear characteristic filters. The amount of numerical dissipation is minimized by applying the schemes to the entropy splitting form of the inviscid flux derivatives. The analysis is given for a thermally perfect gas. The main difficulty in the extension of higher order schemes that were formulated in Cartesian coordinates to curvilinear moving grids is the higher order transformed metric evaluations. The higher order numerical evaluation of the transformed metric terms to insure freestream preservation is done in a coordinate invariant manner. The formulation is an improvement over existing formulation of high order scheme in curvilinear moving grids.

Vinokur, Marcel↗
NASA NTRS2001

Orbital, Rotational and Climatic Interactions: Energy Dissipation and Angular Momentum Exchange in the Earth-Moon System

A numerical ocean tide model has been developed and tested using highly accurate TOPEX/Poseidon (T/P) tidal solutions. The hydrodynamic model is based on time stepping a finite difference approximation to the non-linear shallow water equations. Two novel features of our implementation are a rigorous treatment of self attraction and loading (SAL), and a physically based parameterization for internal tide (IT) radiation drag. The model was run for a range of grid resolutions, and with variations in model parameters and bathymetry. For a rational treatment of SAL and IT drag, the model run at high resolution (1/12 degree) fits the T/P solutions to within 5 cm RMS in the open ocean. Both the rigorous SAL treatment and the IT drag parameterization are required to obtain solutions of this quality. The sensitivity of the solution to perturbations in bathymetry suggest that the fit to T/P is probably now limited by errors in this critical input. Since the model is not constrained by any data, we can test the effect of dropping sea-level to match estimated bathymetry from the last glacial maximum (LGM). Our results suggest that the 100 m drop in sea-level in the LGM would have significantly increased tidal amplitudes in the North Atlantic, and increased overall tidal dissipation by about 40%. However, details in tidal solutions for the past 20 ka are sensitive to the assumed stratification. IT drag accounts for a significant fraction of dissipation, especially in the LGM when large areas of present day shallow sea were exposed, and this parameter is poorly constrained at present.

Egbert, Gary D.↗
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 NTRS2002

Extension of Low Dissipative High Order Hydrodynamics Schemes for MHD Equations

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD (magnetohydrodynamic) equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvi-linear grids. The three features of the present MHD scheme over existing schemes in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion magnetized flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike existing schemes for the conservative MHD equations which suffer from ill-conditioned eigen-decompositions, the present scheme makes use of a well-conditioned eigen-decomposition to solve the conservative form of the MHD equations. This is due to, partly. the fact that the divergence of the magnetic field condition is a different type of constraint from its incompressible Navier-Stokes cousin. Third, a new approach to minimize the numerical error of the divergence free magnetic condition for high order scheme is introduced.

Yee, H. C.↗
NASA NTRS2002

A New Low Dissipative High Order Schemes for MHD Equations

The goal of this talk is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids.

Yee, H. C.↗
NASA NTRS2003

Shock Formation and Energy Dissipation of Slow Magnetosonic Waves in Coronal Plumes

We study the shock formation and energy dissipation of slow magnetosonic waves in coronal plumes. The wave parameters and the spreading function of the plumes as well as the base magnetic field strength are given by empirical constraints mostly from SOHO/UVCS. Our models show that shock formation occurs at low coronal heights, i.e., within 1.3 bun, depending on the model parameters. In addition, following analytical estimates, we show that scale height of energy dissipation by the shocks ranges between 0.15 and 0.45 Rsun. This implies that shock heating by slow magnetosonic waves is relevant at most heights, even though this type of waves is apparently not a solely operating energy supply mechanism.

Cuntz, M.↗
NASA NTRS2003

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Sjoegreen, Bjoern↗
NASA NTRS2000

A New Eddy Dissipation Rate Formulation for the Terminal Area PBL Prediction System(TAPPS)

The TAPPS employs the MASS model to produce mesoscale atmospheric simulations in support of the Wake Vortex project at Dallas Fort-Worth International Airport (DFW). A post-processing scheme uses the simulated three-dimensional atmospheric characteristics in the planetary boundary layer (PBL) to calculate the turbulence quantities most important to the dissipation of vortices: turbulent kinetic energy and eddy dissipation rate. TAPPS will ultimately be employed to enhance terminal area productivity by providing weather forecasts for the Aircraft Vortex Spacing System (AVOSS). The post-processing scheme utilizes experimental data and similarity theory to determine the turbulence quantities from the simulated horizontal wind field and stability characteristics of the atmosphere. Characteristic PBL quantities important to these calculations are determined based on formulations from the Blackadar PBL parameterization, which is regularly employed in the MASS model to account for PBL processes in mesoscale simulations. The TAPPS forecasts are verified against high-resolution observations of the horizontal winds at DFW. Statistical assessments of the error in the wind forecasts suggest that TAPPS captures the essential features of the horizontal winds with considerable skill. Additionally, the turbulence quantities produced by the post-processor are shown to compare favorably with corresponding tower observations.

Charney, Joseph J.↗
NASA NTRS2005

Adaptive Numerical Dissipation Control in High Order Schemes for Multi-D Non-Ideal MHD

The required type and amount of numerical dissipation/filter to accurately resolve all relevant multiscales of complex MHD unsteady high-speed shock/shear/turbulence/combustion problems are not only physical problem dependent, but also vary from one flow region to another. In addition, proper and efficient control of the divergence of the magnetic field (Div(B)) numerical error for high order shock-capturing methods poses extra requirements for the considered type of CPU intensive computations. The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multiresolution wavelets (WAV) (for the above types of flow feature). These filters also provide a natural and efficient way for the minimization of Div(B) numerical error.

Yee, H. C.↗
NASA NTRS2006

The Dissipation Mechanism in Collisionless Magnetic Reconnection

The dissipation mechanism of magnetic reconnection remains a subject of intense scientific interest. On one hand, one set of recent studies have shown that particle inertia-based processes, which include thermal and bulk inertial effects, provide the reconnection electric field in the diffusion region. On the other hand, a second set of studies emphasizes the role of wave-particle interactions in providing anomalous resistivity in the diffusion region. In this presentation, we present analytical theory results, as well as PIC simulations of guide-field magnetic reconnection. We will show that the thermal electron inertia-based dissipation mechanism, expressed through nongyrotropic electron pressure tensors, remains viable in three dimensions. We will demonstrate the thermal inertia effect through studies of electron distribution functions. Furthermore, we will show that the reconnection electric field provides a transient acceleration on particles traversing the inner reconnection region. This inertial effect can be described as a diffusion-like term of the current density, which matches key features of electron distribution functions.

Hesse, Michael↗
NASA NTRS2007

Dissipation in Relativistic Pair-Plasma Reconnection

We present an investigation of the relativistic dissipation in magnetic reconnection. The investigated system consists of an electron-positron plasma. A relativistic generalization of Ohm's law is derived. We analyze a set of numerical simulations, composed of runs with and without guide magnetic field, and of runs with different species temperatures. The calculations indicate that the thermal inertia-based dissipation process survives in relativistic plasmas. For anti-parallel reconnection, it is found that the pressure tensor divergence remains the sole contributor to the reconnection electric field, whereas relativistic guide field reconnection exhibits a similarly important role of the bulk inertia terms.

Hesse, Michael↗
NASA NTRS2011

Observational Evidence of How Magnetofluid Turbulence in the Solar Wind Dissipates

The solar wind appears to be a fully developed turbulent magnetofluid. As this magnetofluid expands into the heliosphere, it cools significantly less rapidly than would be expected of an adiabatically expanding gas. The evolution of the temperature with distance is roughly what would be expected if the turbulence dissipated by heating the thermal plasma. Several physical mechanisms have been proposed, including resonance absorption of waves and Landau damping. Recently, high-time resolution magnetic field data from the four Cluster spacecraft have illustrated damping of the fluctuations out to the electron inertial scale. Use of the wave telescope/k-filtering technique during two intervals of busrt mode data suggests that dissipation of the fluctuations is due to Landau damping, first on protons, then on electrons.

Goldstein, Melvyn L.↗
NASA NTRS2012

Estimation of Eddy Dissipation Rates from Mesoscale Model Simulations

The Eddy Dissipation Rate is an important metric for representing the intensity of atmospheric turbulence and is used as an input parameter for predicting the decay of aircraft wake vortices. In this study, the forecasts of eddy dissipation rates obtained from the current state-of-the-art mesoscale model are evaluated for terminal area applications. The Weather Research and Forecast mesoscale model is used to simulate the planetary boundary layer at high horizontal and vertical mesh resolutions. The Bougeault-Lacarrer and the Mellor-Yamada-Janji schemes implemented in the Weather Research and Forecast model are evaluated against data collected during the National Aeronautics and Space Administration s Memphis Wake Vortex Field Experiment. Comparisons with other observations are included as well.

Ahmad, Nashat N.↗
NASA NTRS2012

Does the Rate of Collisionless Reconnection Depend on the Dissipation Mechanism?

The importance of the electron dissipation effect on the reconnection rate is investigated in the general case of asymmetric collisionless magnetic reconnection. Contrary to the standard collisionless reconnection model, it is found that the reconnection rate, and them acroscopic evolution of the reconnecting system, crucially depend on the nature of the dissipation mechanism and that the Hall effect alone is not able to sustain fast reconnection.

Aunai, Nicolas↗
NASA NTRS2012

Effects of Subscale Size and Shape on Global Energy Dissipation in a Multiscale Model of a Fiber-Reinforced Composite Exhibiting Post-Peak Strain Softening Using Abaqus and FEAMAC

A mesh objective crack band model is implemented in the generalized method of cells (GMC) micromechanics model to predict failure of a composite repeating unit cell (RUC). The micromechanics calculations are achieved using the MAC/GMC core engine within the ImMAC suite of micromechanics codes, developed at the NASA Glenn Research Center. The microscale RUC is linked to a macroscale Abaqus/Standard finite element model using the FEAMAC multiscale framework (included in the ImMAC suite). The effects of the relationship between the characteristic length of the finite element and the size of the microscale RUC on the total energy dissipation of the multiscale model are investigated. A simple 2-D composite square subjected to uniaxial tension is used to demonstrate the effects of scaling the dimensions of the RUC such that the length of the sides of the RUC are equal to the characteristic length of the finite element. These results are compared to simulations where the size of the RUC is fixed, independent of the element size. Simulations are carried out for a variety of mesh densities and element shapes, including square and triangular. Results indicate that a consistent size and shape must be used to yield preserve energy dissipation across the scales.

Pineda, Evan, J.↗
NASA NTRS2012

Does the Rate of Collisionless Magnetic Reconnection Depend on the Dissipation Mechanism?

The importance of the electron dissipation effect on the reconnection rate is investigated in the general case of asymmetric collisionless magnetic reconnection. Contrary to the standard collisionless reconnection model, it is found that the reconnection rate, and the macroscopic evolution of the reconnecting system, crucially depend on the nature of the dissipation mechanism and that the Hall effect alone is not able to sustain fast reconnection.

Aunai, Nicolas↗
NASA NTRS2012

New Measure of the Dissipation Region in Collisionless Magnetic Reconnection

A new measure to identify a small-scale dissipation region in collisionless magnetic reconnection is proposed. The energy transfer from the electromagnetic field to plasmas in the electron s rest frame is formulated as a Lorentz-invariant scalar quantity. The measure is tested by two-dimensional particle-in-cell simulations in typical configurations: symmetric and asymmetric reconnection, with and without the guide field. The innermost region surrounding the reconnection site is accurately located in all cases. We further discuss implications for nonideal MHD dissipation.

Zenitani, Seiji↗