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NASA NTRS1991

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

Chen, H. C.↗

NASA NTRS1985

Advanced reliability methods for structural evaluation

Fast probability integration (FPI) methods, which can yield approximate solutions to such general structural reliability problems as the computation of the probabilities of complicated functions of random variables, are known to require one-tenth the computer time of Monte Carlo methods for a probability level of 0.001; lower probabilities yield even more dramatic differences. A strategy is presented in which a computer routine is run k times with selected perturbed values of the variables to obtain k solutions for a response variable Y. An approximating polynomial is fit to the k 'data' sets, and FPI methods are employed for this explicit form.

Wirsching, P. H.↗

NASA NTRS1998

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Koppenhoefer, Kyle C.↗

NASA NTRS2026

Integrated Computational Materials Engineering (ICME) Capability Maturity Levels for Ecosystems Enabling Digital Transformation

Digital engineering (DE) and integrated computational materials engineering (ICME) are widely recognized as critical enablers of faster, more affordable, and more reliable aerospace systems. However, many organizations have struggled to realize the promised return on investment (ROI) from digital initiatives. A primary reason is the absence of a shared, decision-focused framework that distinguishes simple digitization of existing workflows from true digital transformation that fundamentally changes how engineering decisions are made. This paper introduces an ICME capability maturity framework that fills this gap. The framework defines six cumulative ICME capability maturity levels (CMLs), explicitly tied to decision authority, engineering integration, optimization, and uncertainty management across material, process, structure, and performance scales. It is designed to complement established readiness metrics such as technology readiness levels (TRLs), manufacturing readiness levels (MRLs), and integration readiness levels (IRLs), by addressing a missing dimension: the conditions required for model-informed decision authority across scales. A unifying figure and capability table illustrate the six-level ICME Capability Maturity Framework, showing how organizations progress from digitization—with limited or negative ROI—to true digital transformation, where ICME-enabled workflows deliver measurable improvements in decision quality, cycle time, risk reduction, and reuse. The framework is intended for both technical practitioners and executive leadership, providing a common language to assess current state, guide roadmaps, align software ecosystem investments, and set realistic expectations for digital transformation outcomes. A regulatory-relevant statement clarifying the relationship between ICME capability and existing certification frameworks is provided.

ICME↗

NASA NTRS2011

Conjugate Compressible Fluid Flow and Heat Transfer in Ducts

A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.

Cross, M. F.↗

NASA NTRS2016

Introducing a Degree of Freedom in the Family of Generalized Logarithmic Spirals

The versatility of the family of generalized logarithmic spirals is improved by introducing a degree of freedom in the solution. The low-thrust acceleration profile now includes a control term that affects both the magnitude and the direction of the thrust. Exact and fully analytic solutions to the trajectory, the velocity, the time of flight, etc. are made available. Two integrals of motion are preserved. The first one is a generalization of the equation of the energy and depends on the values of the control parameter. The second one relates to the equation of the angular momentum. The problem of finding spiral transfers between two arbitrary state vectors reduces to solving one algebraic equation with one unknown. The degree of freedom allows fixing the time of flight of the transfer. If the time of flight is fixed, then there are two equations with two unknowns. No other iterative procedures are required. Coast arcs can be introduced in the solution naturally. An explicit expression for the maximum acceleration reached along the transfer is provided. Thanks to the symmetry properties of the solution a simple algorithm for generating periodic orbits is presented. An arbitrary number of intermediate nodes can be introduced to improve the flexibility of the solution when facing optimization problems. An example of a low-thrust gravity-assist Earth-Mars-Ceres trajectory shows that the solution is comparable to that obtained with other preliminary design techniques.

Roa, Javier↗

NASA NTRS1993

Floquet operator as integral of motion

Nonstationary quantum systems have no energy levels. However, for time-dependent periodical quantum systems, the notion of quasi-energy levels has been introduced. The main point of the quasi-energy concept is to relate quasi-energies to eigenvalues of the Floquet operator or monodromy operators which is equal to the evolution operator of a quantum system taken at the moment coinciding with the period of the system. The purpose of this article is to relate the Floquet operator to integrals of the motion and to introduce a new operator which is the integral of motion and has the same quasi-energy spectrum that the Floquet operator has. We wish to discuss an explicit formula for this new integral of motion.

Manko, V. I.↗

NASA NTRS1985

Errors in reduction methods

A mathematical basis is given for comparing the relative merits of various techniques used to reduce the order of large linear and nonlinear dynamics problems during their numerical integration. In such techniques as Guyan-Irons, path derivatives, selected eigenvectors, Ritz vectors, etc., the nth order initial value problem of /y(dot) = f(y) for t greater than 0, y(0) given/ is typically reduced to the mth order (m is much less than n) problem of /z(dot) = g(z) for t greater than 0, z(0) given/ by the transformation y = Pz where P changes from technique to technique. This paper gives an explicit approximate expression for the reduction error e-i in terms of P and the Jacobian of f. It is shown that: (a) reduction techniques are more accurate when the time rate of change of the response y is relatively small; (b) the change in response between two successive stations contributes to the errors at future stations after the change in response is transformed by a filtering matrix H, defined in terms of P; (c) the error committed at a station propagates to future stations by a mixing and scaling matrix G, defined in terms of P, Jacobian and of f, and time increment h. The paper discusses the conditions under which the reduction errors may be minimized and gives guidelines for selecting the reduction basis vector, i.e., the columns of P.

Utku, S.↗

NASA NTRS2003

Design for Verification: Using Design Patterns to Build Reliable Systems

Components so far have been mainly used in commercial software development to reduce time to market. While some effort has been spent on formal aspects of components, most of this was done in the context of programming language or operating system framework integration. As a consequence, increased reliability of composed systems is mainly regarded as a side effect of a more rigid testing of pre-fabricated components. In contrast to this, Design for Verification (D4V) puts the focus on component specific property guarantees, which are used to design systems with high reliability requirements. D4V components are domain specific design pattern instances with well-defined property guarantees and usage rules, which are suitable for automatic verification. The guaranteed properties are explicitly used to select components according to key system requirements. The D4V hypothesis is that the same general architecture and design principles leading to good modularity, extensibility and complexity/functionality ratio can be adapted to overcome some of the limitations of conventional reliability assurance measures, such as too large a state space or too many execution paths.

Mehlitz, Peter C.↗

NASA NTRS1991

Analysis of Issues for Project Scheduling by Multiple, Dispersed Schedulers (distributed Scheduling) and Requirements for Manual Protocols and Computer-based Support

Although computerized operations have significant gains realized in many areas, one area, scheduling, has enjoyed few benefits from automation. The traditional methods of industrial engineering and operations research have not proven robust enough to handle the complexities associated with the scheduling of realistic problems. To address this need, NASA has developed the computer-aided scheduling system (COMPASS), a sophisticated, interactive scheduling tool that is in wide-spread use within NASA and the contractor community. Therefore, COMPASS provides no explicit support for the large class of problems in which several people, perhaps at various locations, build separate schedules that share a common pool of resources. This research examines the issue of distributing scheduling, as applied to application domains characterized by the partial ordering of tasks, limited resources, and time restrictions. The focus of this research is on identifying issues related to distributed scheduling, locating applicable problem domains within NASA, and suggesting areas for ongoing research. The issues that this research identifies are goals, rescheduling requirements, database support, the need for communication and coordination among individual schedulers, the potential for expert system support for scheduling, and the possibility of integrating artificially intelligent schedulers into a network of human schedulers.

Richards, Stephen F.↗

NASA NTRS1995

Diabatic forcing and intialization with assimilation of cloud water and rainwater in a forecast model

In this study, diabatic forcing, and liquid water assimilation techniques are tested in a semi-implicit hydrostatic regional forecast model containing explicit representations of grid-scale cloud water and rainwater. Diabatic forcing, in conjunction with diabatic contributions in the initialization, is found to help the forecast retain the diabatic signal found in the liquid water or heating rate data, consequently reducing the spinup time associated with grid-scale precipitation processes. Both observational Special Sensor Microwave/Imager (SSM/I) and model-generated data are used. A physical retrieval method incorporating SSM/I radiance data is utilized to estimate the 3D distribution of precipitating storms. In the retrieval method the relationship between precipitation distributions and upwelling microwave radiances is parameterized, based upon cloud ensemble-radiative model simulations. Regression formulae relating vertically integrated liquid and ice-phase precipitation amounts to latent heating rates are also derived from the cloud ensemble simulations. Thus, retrieved SSM/I precipitation structures can be used in conjunction with the regression-formulas to infer the 3D distribution of latent heating rates. These heating rates are used directly in the forecast model to help initiate Tropical Storm Emily (21 September 1987). The 14-h forecast of Emily's development yields atmospheric precipitation water contents that compare favorably with coincident SSM/I estimates.

Raymond, William H.↗

NASA NTRS2004

Meeting the Deadline: Why, When and How

A normative system is defined as any set of interacting agents whose behavior can usefully be regarded as norm-directed. Most organizations, and more specifically institutions, fall under this definition. Interactions in these normative systems are regulated by normative templates that describe desired behavior in terms of deontic concepts (obligations, prohibitions and permissions), deadlines, violations and sanctions. Agreements between agents, and between an agent and the society, can then be specified by means of contracts. Contracts provide flexible but verifiable means to integrate society requirements and agent autonomy. and are an adequate means for the explicit specification of interactions. From the society perspective, it is important that these contracts adhere to the specifications described in the model of the organization. If we want to automate such verifications, we have to formalize the languages used for contracts and for the specification of organizations. The logic LCR is based on deontic temporal logic. LCR is an expressive language for describing interaction in multi-agent systems, including obligations with deadlines. Deadlines are important norms in most interactions between agents. Intuitively, a deadline states that an agent should perform an action before a certain point in time. The obligation to perform the action starts at the moment the deadline becomes active. E.g. when a contract is signed or approved. If the action is not performed in time a violation of the deadline occurs. It can be specified independently what measure has to be taken in this case. In this paper we investigate the deadline concept in more detail. The paper is organized as follows. Section 2 defines the variant of CTL we use. In section 3, we discuss the basic intuitions of deadlines. Section 4 presents a first intuitive formalization for deadlines. In section 5, we look at a more complex model for deadlines trying to catch some more practical aspects. Finally, in section 6 we present issues for future work and our conciusions.

Dignum, Frank↗

NASA NTRS1974

Program manual for HILTOP, a heliocentric interplanetary low thrust trajectory optimization program. Part 1: User's guide

A performance-analysis computer program, that was developed explicitly to generate optimum electric propulsion trajectory data for missions of interest in the exploration of the solar system is presented. The program was primarily designed to evaluate the performance capabilities of electric propulsion systems, and in the simulation of a wide variety of interplanetary missions. A numerical integration of the two-body, three-dimensional equations of motion and the Euler-Lagrange equations was used in the program. Transversality conditions which permit the rapid generation of converged maximum-payload trajectory data, and the optimization of numerous other performance indices for which no transversality conditions exist are included. The ability to simulate constrained optimum solutions, including trajectories having specified propulsion time and constant thrust cone angle, is also in the program. The program was designed to handle multiple-target missions with various types of encounters, such as rendezvous, stopover, orbital capture, and flyby. Performance requirements for a variety of launch vehicles can be determined.

Mann, F. I.↗

NASA NTRS2010

Trajectory Optimization: OTIS 4

The latest release of the Optimal Trajectories by Implicit Simulation (OTIS4) allows users to simulate and optimize aerospace vehicle trajectories. With OTIS4, one can seamlessly generate optimal trajectories and parametric vehicle designs simultaneously. New features also allow OTIS4 to solve non-aerospace continuous time optimal control problems. The inputs and outputs of OTIS4 have been updated extensively from previous versions. Inputs now make use of objectoriented constructs, including one called a metastring. Metastrings use a greatly improved calculator and common nomenclature to reduce the user s workload. They allow for more flexibility in specifying vehicle physical models, boundary conditions, and path constraints. The OTIS4 calculator supports common mathematical functions, Boolean operations, and conditional statements. This allows users to define their own variables for use as outputs, constraints, or objective functions. The user-defined outputs can directly interface with other programs, such as spreadsheets, plotting packages, and visualization programs. Internally, OTIS4 has more explicit and implicit integration procedures, including high-order collocation methods, the pseudo-spectral method, and several variations of multiple shooting. Users may switch easily between the various methods. Several unique numerical techniques such as automated variable scaling and implicit integration grid refinement, support the integration methods. OTIS4 is also significantly more user friendly than previous versions. The installation process is nearly identical on various platforms, including Microsoft Windows, Apple OS X, and Linux operating systems. Cross-platform scripts also help make the execution of OTIS and post-processing of data easier. OTIS4 is supplied free by NASA and is subject to ITAR (International Traffic in Arms Regulations) restrictions. Users must have a Fortran compiler, and a Python interpreter is highly recommended.

Riehl, John P.↗

NASA NTRS1990

Staggered solution procedures for multibody dynamics simulation

The numerical solution procedure for multibody dynamics (MBD) systems is termed a staggered MBD solution procedure that solves the generalized coordinates in a separate module from that for the constraint force. This requires a reformulation of the constraint conditions so that the constraint forces can also be integrated in time. A major advantage of such a partitioned solution procedure is that additional analysis capabilities such as active controller and design optimization modules can be easily interfaced without embedding them into a monolithic program. After introducing the basic equations of motion for MBD system in the second section, Section 3 briefly reviews some constraint handling techniques and introduces the staggered stabilized technique for the solution of the constraint forces as independent variables. The numerical direct time integration of the equations of motion is described in Section 4. As accurate damping treatment is important for the dynamics of space structures, we have employed the central difference method and the mid-point form of the trapezoidal rule since they engender no numerical damping. This is in contrast to the current practice in dynamic simulations of ground vehicles by employing a set of backward difference formulas. First, the equations of motion are partitioned according to the translational and the rotational coordinates. This sets the stage for an efficient treatment of the rotational motions via the singularity-free Euler parameters. The resulting partitioned equations of motion are then integrated via a two-stage explicit stabilized algorithm for updating both the translational coordinates and angular velocities. Once the angular velocities are obtained, the angular orientations are updated via the mid-point implicit formula employing the Euler parameters. When the two algorithms, namely, the two-stage explicit algorithm for the generalized coordinates and the implicit staggered procedure for the constraint Lagrange multipliers, are brought together in a staggered manner, they constitute a staggered explicit-implicit procedure which is summarized in Section 5. Section 6 presents some example problems and discussions concerning several salient features of the staggered MBD solution procedure are offered in Section 7.

Park, K. C.↗

NASA NTRS2000

Efficient Use of Distributed Systems for Scientific Applications

Distributed computing has been regarded as the future of high performance computing. Nationwide high speed networks such as vBNS are becoming widely available to interconnect high-speed computers, virtual environments, scientific instruments and large data sets. One of the major issues to be addressed with distributed systems is the development of computational tools that facilitate the efficient execution of parallel applications on such systems. These tools must exploit the heterogeneous resources (networks and compute nodes) in distributed systems. This paper presents a tool, called PART, which addresses this issue for mesh partitioning. PART takes advantage of the following heterogeneous system features: (1) processor speed; (2) number of processors; (3) local network performance; and (4) wide area network performance. Further, different finite element applications under consideration may have different computational complexities, different communication patterns, and different element types, which also must be taken into consideration when partitioning. PART uses parallel simulated annealing to partition the domain, taking into consideration network and processor heterogeneity. The results of using PART for an explicit finite element application executing on two IBM SPs (located at Argonne National Laboratory and the San Diego Supercomputer Center) indicate an increase in efficiency by up to 36% as compared to METIS, a widely used mesh partitioning tool. The input to METIS was modified to take into consideration heterogeneous processor performance; METIS does not take into consideration heterogeneous networks. The execution times for these applications were reduced by up to 30% as compared to METIS. These results are given in Figure 1 for four irregular meshes with number of elements ranging from 30,269 elements for the Barth5 mesh to 11,451 elements for the Barth4 mesh. Future work with PART entails using the tool with an integrated application requiring distributed systems. In particular this application, illustrated in the document entails an integration of finite element and fluid dynamic simulations to address the cooling of turbine blades of a gas turbine engine design. It is not uncommon to encounter high-temperature, film-cooled turbine airfoils with 1,000,000s of degrees of freedom. This results because of the complexity of the various components of the airfoils, requiring fine-grain meshing for accuracy. Additional information is contained in the original.

Taylor, Valerie↗

NASA NTRS1989

Integrating planning and reactive control

Artificial intelligence research on planning is concerned with designing control systems that choose actions by manipulating explicit descriptions of the world state, the goal to be achieved, and the effects of elementary operations available to the system. Because planning shifts much of the burden of reasoning to the machine, it holds great appeal as a high-level programming method. Experience shows, however, that it cannot be used indiscriminately because even moderately rich languages for describing goals, states, and the elementary operators lead to computational inefficiencies that render the approach unsuitable for realistic applications. This inadequacy has spawned a recent wave of research on reactive control or situated activity in which control systems are modeled as reacting directly to the current situation rather than as reasoning about the future effects of alternative action sequences. While this research has confronted the issue of run-time tractability head on, in many cases it has done so by sacrificing the advantages of declarative planning techniques. Ways in which the two approaches can be unified are discussed. The authors begin by modeling reactive control systems as state machines that map a stream of sensory inputs to a stream of control outputs. These machines can be decomposed into two continuously active subsystems: the planner and the execution module. The planner computes a plan, which can be seen as a set of bits that control the behavior of the execution module. An important element of this work is the formulation of a precise semantic interpretation for the inputs and outputs of the planning system. They show that the distinction between planned and reactive behavior is largely in the eye of the beholder: systems that seem to compute explicit plans can be redescribed in situation-action terms and vice versa. They also discuss practical programming techniques that allow the advantages of declarative programming and guaranteed reactive response to be achieved simultaneously.

Rosenschein, Stanley J.↗

NASA NTRS1991

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Tamma, Kumar K.↗