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NASA NTRS2004

Reliability of Complex Nonlinear Numerical Simulations

This work describes some of the procedure to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Yee, H. C.↗

NASA NTRS2004

Discontinuous Galerkin Finite Element Method for Parabolic Problems

In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.

Kaneko, Hideaki↗

NASA NTRS2004

Explanation Constraint Programming for Model-based Diagnosis of Engineered Systems

We can expect to see an increase in the deployment of unmanned air and land vehicles for autonomous exploration of space. In order to maintain autonomous control of such systems, it is essential to track the current state of the system. When the system includes safety-critical components, failures or faults in the system must be diagnosed as quickly as possible, and their effects compensated for so that control and safety are maintained under a variety of fault conditions. The Livingstone fault diagnosis and recovery kernel and its temporal extension L2 are examples of model-based reasoning engines for health management. Livingstone has been shown to be effective, it is in demand, and it is being further developed. It was part of the successful Remote Agent demonstration on Deep Space One in 1999. It has been and is being utilized by several projects involving groups from various NASA centers, including the In Situ Propellant Production (ISPP) simulation at Kennedy Space Center, the X-34 and X-37 experimental reusable launch vehicle missions, Techsat-21, and advanced life support projects. Model-based and consistency-based diagnostic systems like Livingstone work only with discrete and finite domain models. When quantitative and continuous behaviors are involved, these are abstracted to discrete form using some mapping. This mapping from the quantitative domain to the qualitative domain is sometimes very involved and requires the design of highly sophisticated and complex monitors. We propose a diagnostic methodology that deals directly with quantitative models and behaviors, thereby mitigating the need for these sophisticated mappings. Our work brings together ideas from model-based diagnosis systems like Livingstone and concurrent constraint programming concepts. The system uses explanations derived from the propagation of quantitative constraints to generate conflicts. Fast conflict generation algorithms are used to generate and maintain multiple candidates whose consistency can be tracked across multiple time steps.

Narasimhan, Sriram↗

NASA NTRS2003

A Discrete Constraint for Entropy Conservation and Sound Waves in Cloud-Resolving Modeling

Ideal cloud-resolving models contain little-accumulative errors. When their domain is so large that synoptic large-scale circulations are accommodated, they can be used for the simulation of the interaction between convective clouds and the large-scale circulations. This paper sets up a framework for the models, using moist entropy as a prognostic variable and employing conservative numerical schemes. The models possess no accumulative errors of thermodynamic variables when they comply with a discrete constraint on entropy conservation and sound waves. Alternatively speaking, the discrete constraint is related to the correct representation of the large-scale convergence and advection of moist entropy. Since air density is involved in entropy conservation and sound waves, the challenge is how to compute sound waves efficiently under the constraint. To address the challenge, a compensation method is introduced on the basis of a reference isothermal atmosphere whose governing equations are solved analytically. Stability analysis and numerical experiments show that the method allows the models to integrate efficiently with a large time step.

Zeng, Xi-Ping↗

NASA NTRS2004

Potential Predictability of U.S. Summer Climate with "Perfect" Soil Moisture

The potential predictability of surface-air temperature and precipitation over the United States continent was assessed for a GCM forced by observed sea surface temperatures and an estimate of observed ground soil moisture contents. The latter was obtained by substituting the GCM simulated precipitation, which is used to drive the GCM's land-surface component, with observed pentad-mean precipitation at each time step of the model's integration. With this substitution, the simulated soil moisture correlates well with an independent estimate of observed soil moisture in all seasons over the entire US continent. Significant enhancements on the predictability of surface-air temperature and precipitation were found in boreal late spring and summer over the US continent. Anomalous pattern correlations of precipitation and surface-air temperature over the US continent in the June-July-August season averaged for the 1979-2000 period increased from 0.01 and 0.06 for the GCM simulations without precipitation substitution to 0.23 and 0.3 1, respectively, for the simulations with precipitation substitution. Results provide an estimate for the limits of potential predictability if soil moisture variability is to be perfectly predicted. However, this estimate may be model dependent, and needs to be substantiated by other modeling groups.

Yang, Fanglin↗

NASA NTRS2004

Offline GCSS Intercomparison of Cloud-Radiation Interaction and Surface Fluxes

Simulations of deep tropical clouds by both cloud-resolving models (CRMs) and single-column models (SCMs) in the GEWEX Cloud System Study (GCSS) Working Group 4 (WG4; Precipitating Convective Cloud Systems), Case 2 (19-27 December 1992, TOGA-COARE IFA) have produced large differences in the mean heating and moistening rates (-1 to -5 K and -2 to 2 grams per kilogram respectively). Since the large-scale advective temperature and moisture "forcing" are prescribed for this case, a closer examination of two of the remaining external types of "forcing", namely radiative heating and air/sea hear and moisture transfer, are warranted. This paper examines the current radiation and surface flux of parameterizations used in the cloud models participating in the GCSS WG4, be executing the models "offline" for one time step (12 s) for a prescribed atmospheric state, then examining the surface and radiation fluxes from each model. The dynamic, thermodynamic, and microphysical fluids are provided by the GCE-derived model output for Case 2 during a period of very active deep convection (westerly wind burst). The surface and radiation fluxes produced from the models are then divided into prescribed convective, stratiform, and clear regions in order to examine the role that clouds play in the flux parameterizations. The results suggest that the differences between the models are attributed more to the surface flux parameterizations than the radiation schemes.

Tao, W.-K.↗

NASA NTRS1997

Correspondence between discrete and continuous models of excitable media: trigger waves

We present a theoretical framework for relating continuous partial differential equation (PDE) models of excitable media to discrete cellular automata (CA) models on a randomized lattice. These relations establish a quantitative link between the CA model and the specific physical system under study. We derive expressions for the CA model's plane wave speed, critical curvature, and effective diffusion constant in terms of the model's internal parameters (the interaction radius, excitation threshold, and time step). We then equate these expressions to the corresponding quantities obtained from solution of the PDEs (for a fixed excitability). This yields a set of coupled equations with a unique solution for the required CA parameter values. Here we restrict our analysis to "trigger" wave solutions obtained in the limiting case of a two-dimensional excitable medium with no recovery processes. We tested the correspondence between our CA model and two PDE models (the FitzHugh-Nagumo medium and a medium with a "sawtooth" nonlinear reaction source) and found good agreement with the numerical solutions of the PDEs. Our results suggest that the behavior of trigger waves is actually controlled by a small number of parameters.

Non-NASA Center↗

NASA NTRS2004

Recent Enhancements to USM3D Unstructured Flow Solver for Unsteady Flows

The NASA USM3D unstructured flow solver is undergoing extensions to address dynamic flow problems in support of NASA and NAVAIR efforts to study the applicability of Computational Fluid Dynamics tools for the prediction of aircraft stability and control characteristics. The initial extensions reported herein include two second-order time stepping schemes, Detached-Eddy Simulation, and grid motion. This paper reports the initial code verification and validation assessment of the dynamic flow capabilities of USM3D. The cases considered are the classic inviscid shock-tube problem, low Reynolds number wake shedding from a NACA 0012 airfoil, high Reynolds number DES-based wake shedding from a 4-to-1 length-to-diameter cylinder, and forced pitch oscillation of a NACA 0012 airfoil with inviscid and turbulent flow.

Pandya, Mohagna J.↗

NASA NTRS1998

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

Frink, N. T.↗

NASA NTRS1998

On Some Numerical Dissipation Schemes

Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar dissipation and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical solutions are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme. The coarse-grid accuracy for the original CUSP scheme is improved by modifying the limiter function used with the scheme, giving comparable accuracy to that obtained with the MATD scheme. The modifications reduce the background dissipation and provide control over the regions where the scheme can become first order.

Swanson, R. C.↗

NASA NTRS1997

Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids

An implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described. The foundation of the code is a backward Euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned Generalized Minimal Residual (GMRES) technique. For the GMRES calculations, several techniques are investigated for forming the matrix-vector product. Convergence acceleration is achieved through a multigrid scheme that uses non-nested coarse grids that are generated using a technique described in the present paper. Convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four-element airfoil. Viscous results, which are compared with experimental data, include the turbulent flow over a NACA 4412 airfoil, a three-element airfoil for which Mach number effects are investigated, and three-dimensional flow over a wing with a partial-span flap.

Anderson, W. Kyle↗

NASA NTRS2004

Validation of NASCAP-2K Spacecraft-Environment Interactions Calculations

The recently released Nascap-2k, version 2.0, three-dimensional computer code models interactions between spacecraft surfaces and low-earth-orbit, geosynchronous, auroral, and interplanetary plasma environments. It replaces the earlier three-dimensional spacecraft interactions codes NASCAP/GEO, NASCAP/LEO, POLAR, and DynaPAC. Nascap-2k has improved numeric techniques, a modern user interface, and a simple, interactive satellite surface definition module (Object ToolKit). We establish the accuracy of Nascap-2k both by comparing computed currents and potentials with analytic results and by comparing Nascap-2k results with published calculations using the earlier codes. Nascap-2k predicts Langmuir-Blodgett or Parker-Murphy current collection for a nearly spherical (100 surfaces) satellite in a short Debye length plasma depending on the absence or presence of a magnetic field. A low fidelity (in geometry and time) Nascap-2k geosynchronous charging calculation gives the same results as the corresponding low fidelity NASCAP/GEO calculation. A high fidelity calculation (using the Nascap-2k improved geometry and time stepping capabilities) gives higher potentials, which are more consistent with typical observations. Nascap-2k predicts the same current as a function of applied potential as was observed and calculated by NASCAP/LEO for the SPEAR I rocket with a bipolar sheath. A Nascap-2k DMSP charging calculation gives results similar to those obtained using POLAR and consistent with observation.

Davis, V. A.↗

NASA NTRS2004

Simulation of Synthetic Jets in Quiescent Air Using Unsteady Reynolds Averaged Navier-Stokes Equations

We report research experience in applying an Unsteady Reynolds-Averaged Navier-Stokes (URANS) solver for the prediction of time-dependent flows in the presence of an active flow control device. The configuration under consideration is a synthetic jet created by a single diaphragm piezoelectric actuator in quiescent air. Time-averaged and instantaneous data for this case were obtained at Langley Research Center, using multiple measurement techniques. Computational results for this case using one-equation Spalart-Allmaras and two-equation Menter s turbulence models are presented here along with comparisons with the experimental data. The effect of grid refinement, preconditioning and time-step variation are also examined.

Vatsa, Veer N.↗

NASA NTRS2004

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

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 of 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 multi-resolution wavelets (WAV) (for the above types of flow feature). These filter approaches also provide a natural and efficient way for the minimization of Div(B) numerical error. The filter scheme consists of spatially sixth order or higher non-dissipative spatial difference operators as the base scheme for the inviscid flux derivatives. If necessary, a small amount of high order linear dissipation is used to remove spurious high frequency oscillations. For example, an eighth-order centered linear dissipation (AD8) might be included in conjunction with a spatially sixth-order base scheme. The inviscid difference operator is applied twice for the viscous flux derivatives. After the completion of a full time step of the base scheme step, the solution is adaptively filtered by the product of a 'flow detector' and the 'nonlinear dissipative portion' of a high-resolution shock-capturing scheme. In addition, the scheme independent wavelet flow detector can be used in conjunction with spatially compact, spectral or spectral element type of base schemes. The ACM and wavelet filter schemes using the dissipative portion of a second-order shock-capturing scheme with sixth-order spatial central base scheme for both the inviscid and viscous MHD flux derivatives and a fourth-order Runge-Kutta method are denoted.

Yee, H. C.↗

NASA NTRS2005

The Flora Mission for Ecosystem Composition, Disturbance and Productivity

Global land use and climate variability alter ecosystem conditions - including structure, function, and biological diversity - at a pace that requires unambiguous observations from satellite vantage points. Current global measurements are limited to general land cover, some disturbances, vegetation leaf area index, and canopy energy absorption. Flora is a pathfinding mission that provides new measurements of ecosystem structure, function, and diversity to understand the spatial and temporal dynamics of human and natural disturbances, and the biogeochemical and physiological responses of ecosystems to disturbance. The mission relies upon high-fidelity imaging spectroscopy to deliver full optical spectrum measurements (400-2500 nm) of the global land surface on a monthly time step at 45 meter spatial resolution for three years. The Flora measurement objectives are: (i) fractional cover of biological materials, (ii) canopy water content, (iii) vegetation pigments and light-use efficiency, (iv) plant functional types, (v) fire fuel load and fuel moisture content, and (vi) disturbance occurrence, type and intensity. These measurements are made using a multi-parameter, spectroscopic analysis approach afforded by observation of the full optical spectrum. Combining these measurements, along with additional observations from multispectral sensors, Flora will far advance global studies and models of ecosystem dynamics and change.

Asner, Gregory P.↗

NASA NTRS1999

Numerical System Solver Developed for the National Cycle Program

As part of the National Cycle Program (NCP), a powerful new numerical solver has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.

Binder, Michael P.↗

NASA NTRS2005

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations.

Yee, H. C.↗

NASA NTRS2005

Quicker Q-Learning in Multi-Agent Systems

Multi-agent learning in Markov Decisions Problems is challenging because of the presence ot two credit assignment problems: 1) How to credit an action taken at time step t for rewards received at t' greater than t; and 2) How to credit an action taken by agent i considering the system reward is a function of the actions of all the agents. The first credit assignment problem is typically addressed with temporal difference methods such as Q-learning OK TD(lambda) The second credit assi,onment problem is typically addressed either by hand-crafting reward functions that assign proper credit to an agent, or by making certain independence assumptions about an agent's state-space and reward function. To address both credit assignment problems simultaneously, we propose the Q Updates with Immediate Counterfactual Rewards-learning (QUICR-learning) designed to improve both the convergence properties and performance of Q-learning in large multi-agent problems. Instead of assuming that an agent s value function can be made independent of other agents, this method suppresses the impact of other agents using counterfactual rewards. Results on multi-agent grid-world problems over multiple topologies show that QUICR-learning can achieve up to thirty fold improvements in performance over both conventional and local Q-learning in the largest tested systems.

Agogino, Adrian K.↗