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NASA NTRS2014

A Walsh Function Module Users' Manual

The solution of partial differential equations (PDEs) with Walsh functions offers new opportunities to simulate many challenging problems in mathematical physics. The approach was developed to better simulate hypersonic flows with shocks on unstructured grids. It is unique in that integrals and derivatives are computed using simple matrix multiplication of series representations of functions without the need for divided differences. The product of any two Walsh functions is another Walsh function - a feature that radically changes an algorithm for solving PDEs. A FORTRAN module for supporting Walsh function simulations is documented. A FORTRAN code is also documented with options for solving time-dependent problems: an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the usage of the Walsh function module including such features as operator overloading, Fast Walsh Transforms in multi-dimensions, and a Fast Walsh reciprocal.

Gnoffo, Peter A.↗
NASA NTRS2013

The Challenges in Applying Magnetroesistive Sensors on the 'Curiosity' Rover

Magnetoresistive Sensors were selected for use on the motor encoders throughout the Curiosity Rover for motor position feedback devices. The Rover contains 28 acuators with a corresponding number of encoder assemblies. The environment on Mars provides opportunities for challenges to any hardware design. The encoder assemblies presented several barriers that had to be vaulted in order to say the rover was ready to fly. The environment and encoder specific design features provided challenges that had to be solved in time to fly.

Radioisotope Thermoelectric Gererator (RTG)↗
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

Accelerated Simulation of Air Pollution Using NVIDIA RAPIDS

Atmospheric chemistry models are a central tool to study and forecast the impact of air pollution on the environment, vegetation, and human health. However, the numerical simulation of chemical kinetics is computationally expensive due to the stiffness of the system of ordinary differential equations that describes atmospheric chemistry. Here we present an alternative approach to the computation of atmospheric chemistry based on machine learning. Our training data set is produced using the NASA Goddard Earth Observing System (GEOS) model with GEOS-Chem chemistry, run on the NASA Center for Climate Simulation (NCCS) Discover supercomputing cluster on 384 Intel Xeon Haswell cores. This model spends more than 50% of total run time on solving atmospheric chemistry. The data set contains as input features the air pollution concentrations before solving the differential equations, together with some key physical parameters such as temperature and sun intensity. As target variables we define the air pollution concentrations after solving the differential equations. Using Dask-cuDF and Dask-XGBoost on the NVIDIA RAPIDS platform on 8 Tesla V100 GPUs, we generate from this training set gradient boosted decision tree models that can reproduce the simulation of chemical kinetics. We do this on the NCCS Advanced Data Analytics Platform (ADAPT) science cloud environment. Our application takes full advantage of recent advances in Dask-XGBoost, such as multi-node and multi-GPU scaling for distributed training with large data sets. The increase in training data size enabled by this is critical to capture the full range of chemical environments encountered across the globe and all annual seasons.The boosted tree models offer good predictability and show many of the features of the full chemistry reference simulation. Further improvements can be achieved through mass balance considerations and by accounting for error correlations. We incorporate the boosted tree models into the GEOS reference model using XGBoost's C API. This enables a seamless integration of the GPU trained models into GEOS-Chem, which is written in Fortran and optimized for use in a massively parallel CPU environment. We show the benefits of this approach and discuss the potential speedup of this machine learning accelerated atmospheric chemistry model.

Keller, Christoph A.↗
NASA NTRS2024

Machine Learning for the Prediction of Local Asteroid Damages

Risk assessment studies of local asteroid hazards traditionally simulate the physics of meteors with engineering models tailored to analyze tens-of-millions of scenarios. However, these simplified approaches still need to solve time-dependent ODEs to model the entry process and the resulting ground damage. With a computational cost of O(0.01 CPU.s) per scenario, simulating these large numbers of potential entry conditions in risk assessment studies can take several days on local computers. To improve computational efficiency, we propose in this paper an orthogonal approach based on machine learning models to predict the size of damaged areas given a list of entry parameters. We train 5 machine learning methods and compare the predictions to the outputs of the PAIR model, first only with primitive entry condition variables, and then with more advanced features. We find that complex models like neural networks are well-suited to estimate blast hazards, while simpler linear models can accurately assess thermal damage. For both types of hazards, the radii of damaged areas can be predicted with around 10% average errors and a coefficient of determination (R2) of 0.99. The CPU time is decreased by a factor O(10 3 ) compared to the PAIR model, which enables the simulation of millions of scenarios in minutes, on a local computer. We then use the same machine learning approaches for a classification task where the models are trained to predict if an asteroid will produce a given level of damage. Results show that complex models like the gradient boosting classifier and the neural network can perform this task with 98% accuracy. Beyond surrogate models, we finally incorporate the machine learning algorithms to the state-of-the-art Shapley sensitivity analysis and present a ranking of the entry parameters based on their contributions to ground damages.

SMD↗
NASA NTRS1988

Time-accurate unsteady aerodynamic and aeroelastic calculations for wings using Euler equations

A time-accurate approach to simultaneously solve the Euler flow equations and modal structural equations of motion is presented for computing aeroelastic responses of wings. The Euler flow eauations are solved by a time-accurate finite difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear acceleration method. The aeroelastic configuration adaptive dynamic grids are time accurately generated using the aeroelastically deformed shape of the wing. The unsteady flow calculations are validated wih experiment, both for a semi-infinite wing and a wall-mounted cantilever rectangular wings. Aeroelastic responses are computed for a rectangular wing using the modal data generated by the finite-element method. The robustness of the present approach in computing unsteady flows and aeroelastic responses that are beyond the capability of earlier approaches using the potential equations are demonstrated.

Guruswamy, Guru P.↗
NASA NTRS2004

Category 3: Sound Generation by Interacting with a Gust

The cascade-gust interaction problem is solved employing a time-domain approach. The purpose of this problem is to test the ability of a CFD/CAA code to accurately predict the unsteady aerodynamic and aeroacoustic response of a single airfoil to a two-dimensional, periodic vortical gust.Nonlinear time dependent Euler equations are solved using higher order spatial differencing and time marching techniques. The solutions indicate the generation and propagation of expected mode orders for the given configuration and flow conditions. The blade passing frequency (BPF) is cut off for this cascade while higher harmonic, 2BPF and 3BPF, modes are cut on.

Scott, James R.↗
NASA NTRS2016

Addressing Thermal Model Run Time Concerns of the Wide Field Infrared Survey Telescope using Astrophysics Focused Telescope Assets (WFIRST-AFTA)

The Wide Field Infrared Survey Telescope using Astrophysics Focused Telescope Assets (WFIRST-AFTA) utilizes an existing 2.4 m diameter Hubble sized telescope donated from elsewhere in the federal government for near-infrared sky surveys and Exoplanet searches to answer crucial questions about the universe and dark energy. The WFIRST design continues to increase in maturity, detail, and complexity with each design cycle leading to a Mission Concept Review and entrance to the Mission Formulation Phase. Each cycle has required a Structural-Thermal-Optical-Performance (STOP) analysis to ensure the design can meet the stringent pointing and stability requirements. As such, the models have also grown in size and complexity leading to increased model run time. This paper addresses efforts to reduce the run time while still maintaining sufficient accuracy for STOP analyses. A technique was developed to identify slews between observing orientations that were sufficiently different to warrant recalculation of the environmental fluxes to reduce the total number of radiation calculation points. The inclusion of a cryocooler fluid loop in the model also forced smaller time-steps than desired, which greatly increases the overall run time. The analysis of this fluid model required mitigation to drive the run time down by solving portions of the model at different time scales. Lastly, investigations were made into the impact of the removal of small radiation couplings on run time and accuracy. Use of these techniques allowed the models to produce meaningful results within reasonable run times to meet project schedule deadlines.

Thermal Analysis↗
NASA NTRS2003

Choice of Variables and Preconditioning for Time Dependent Problems

We consider the use of low speed preconditioning for time dependent problems. These are solved using a dual time step approach. We consider the effect of this dual time step on the parameter of the low speed preconditioning. In addition, we compare the use of two sets of variables, conservation and primitive variables, to solve the system. We show the effect of these choices on both the convergence to a steady state and the accuracy of the numerical solutions for low Mach number steady state and time dependent flows.

Turkel, Eli↗
NASA NTRS2002

A Nonlinear, Human-Centered Approach to Motion Cueing with a Neurocomputing Solver

This paper discusses the continuation of research into the development of new motion cueing algorithms first reported in 1999. In this earlier work, two viable approaches to motion cueing were identified: the coordinated adaptive washout algorithm or 'adaptive algorithm', and the 'optimal algorithm'. In this study, a novel approach to motion cueing is discussed that would combine features of both algorithms. The new algorithm is formulated as a linear optimal control problem, incorporating improved vestibular models and an integrated visual-vestibular motion perception model previously reported. A control law is generated from the motion platform states, resulting in a set of nonlinear cueing filters. The time-varying control law requires the matrix Riccati equation to be solved in real time. Therefore, in order to meet the real time requirement, a neurocomputing approach is used to solve this computationally challenging problem. Single degree-of-freedom responses for the nonlinear algorithm were generated and compared to the adaptive and optimal algorithms. Results for the heave mode show the nonlinear algorithm producing a motion cue with a time-varying washout, sustaining small cues for a longer duration and washing out larger cues more quickly. The addition of the optokinetic influence from the integrated perception model was shown to improve the response to a surge input, producing a specific force response with no steady-state washout. Improved cues are also observed for responses to a sway input. Yaw mode responses reveal that the nonlinear algorithm improves the motion cues by reducing the magnitude of negative cues. The effectiveness of the nonlinear algorithm as compared to the adaptive and linear optimal algorithms will be evaluated on a motion platform, the NASA Langley Research Center Visual Motion Simulator (VMS), and ultimately the Cockpit Motion Facility (CMF) with a series of pilot controlled maneuvers. A proposed experimental procedure is discussed. The results of this evaluation will be used to assess motion cueing performance.

Telban, Robert J.↗
NASA NTRS1993

Simulation of tail buffet using delta wing-vertical tail configuration

Computational simulation of the vertical tail buffet problem is accomplished using a delta wing-vertical tail configuration. Flow conditions are selected such that the wing primary-vortex cores experience vortex breakdown and the resulting flow interacts with the vertical tail. This multidisciplinary problem is solved successively using three sets of equations for the fluid flow, aeroelastic deflections and grid displacements. For the fluid dynamics part, the unsteady, compressible, full Navier-Stokes equations are solved accurately in time using an implicit, upwind, flux-difference splitting, finite-volume scheme. For the aeroelastic part, the aeroelastic equation for bending vibrations is solved accurately in time using the Galerkin method and the four-stage Runge-Kutta scheme. The grid for the fluid dynamics computations is updated every few time steps using a third set of interpolation equations. The computational application includes a delta wing of aspect ratio 1 and a rectangular vertical tail of aspect ratio 2, which is placed at 0.5 root-chord length downstream of the wing trailing edge. The wing angle of attack is 35 deg and the flow Mach number and Reynolds number are 0.4 and 10,000, respectively.

Kandil, Osama A.↗
NASA NTRS1999

Large Eddy Simulation in the Computation of Jet Noise

Noise can be predicted by solving Full (time-dependent) Compressible Navier-Stokes Equation (FCNSE) with computational domain. The fluctuating near field of the jet produces propagating pressure waves that produce far-field sound. The fluctuating flow field as a function of time is needed in order to calculate sound from first principles. Noise can be predicted by solving the full, time-dependent, compressible Navier-Stokes equations with the computational domain extended to far field - but this is not feasible as indicated above. At high Reynolds number of technological interest turbulence has large range of scales. Direct numerical simulations (DNS) can not capture the small scales of turbulence. The large scales are more efficient than the small scales in radiating sound. The emphasize is thus on calculating sound radiated by large scales.

Mankbadi, R. R.↗
NASA NTRS1991

A new numerical framework for solving conservation laws: The method of space-time conservation element and solution element

A new numerical framework for solving conservation laws is being developed. It employs: (1) a nontraditional formulation of the conservation laws in which space and time are treated on the same footing, and (2) a nontraditional use of discrete variables such as numerical marching can be carried out by using a set of relations that represents both local and global flux conservation.

Chang, Sin-Chung↗
NASA NTRS1993

Finite difference time domain analysis of chirped dielectric gratings

The finite difference time domain (FDTD) method for solving Maxwell's time-dependent curl equations is accurate, computationally efficient, and straight-forward to implement. Since both time and space derivatives are employed, the propagation of an electromagnetic wave can be treated as an initial-value problem. Second-order central-difference approximations are applied to the space and time derivatives of the electric and magnetic fields providing a discretization of the fields in a volume of space, for a period of time. The solution to this system of equations is stepped through time, thus, simulating the propagation of the incident wave. If the simulation is continued until a steady-state is reached, an appropriate far-field transformation can be applied to the time-domain scattered fields to obtain reflected and transmitted powers. From this information diffraction efficiencies can also be determined. In analyzing the chirped structure, a mesh is applied only to the area immediately around the grating. The size of the mesh is then proportional to the electric size of the grating. Doing this, however, imposes an artificial boundary around the area of interest. An absorbing boundary condition must be applied along the artificial boundary so that the outgoing waves are absorbed as if the boundary were absent. Many such boundary conditions have been developed that give near-perfect absorption. In this analysis, the Mur absorbing boundary conditions are employed. Several grating structures were analyzed using the FDTD method.

Hochmuth, Diane H.↗
NASA NTRS1995

Implicit method for the computation of unsteady flows on unstructured grids

An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed.

Venkatakrishnan, V.↗
NASA NTRS2000

Parallel CE/SE Computations via Domain Decomposition

This paper describes the parallelization strategy and achieved parallel efficiency of an explicit time-marching algorithm for solving conservation laws. The Space-Time Conservation Element and Solution Element (CE/SE) algorithm for solving the 2D and 3D Euler equations is parallelized with the aid of domain decomposition. The parallel efficiency of the resultant algorithm on a Silicon Graphics Origin 2000 parallel computer is checked.

Himansu, Ananda↗
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 NTRS1992

A brief description of a new numerical framework for solving conservation laws: The method of space-time conservation element and solution element

A new numerical method for solving conservation laws is being developed. It differs substantially from the well established methods, i.e., finite difference, finite volume, finite element, and spectral methods, in both concept and methodology. It is much simpler than a typical high resolution method. No flux limiter or any technique related to characteristics is involved. No artificial viscosity or smoothing is introduced, and no moving mesh is used. Yet this method is capable of generating highly accurate shock tube solutions. The slight numerical overshoot and/or oscillations generated can be removed if a simple averaging formula initially used is replaced by a weighted formula. This modification has little effect on other parts of the solution. Because of its simplicity, generalization of this new method for multi-dimensional problems is straightforward.

Chang, Sin-Chung↗