Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “implicit methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 811 records · Page 45

Implicit dual control for general stochastic systems

A new implicit dual technique is presented for stochastic adaptive control synthesis. In this technique, denoted as the method of utility costs (MOUC), a new control policy is derived from a known starting control policy by using a single iteration in time-varying policy space. An important result is that the new control policy yields a corresponding improvement in adaptive performance relative to the known starting policy. Since the starting policy can be chosen arbitrarily, the new policy has potentially superior performance relative to any existing design. Unlike other implicit dual designs, the MOUC can be applied to systems having constrained inputs, discontinuities, discrete valued disturbances, as well as in situations where the variances of the associated process statistics are large. A numerical example is given in which a controller is synthesized to provide improved performance relative to the Open-Loop Feedback policy of Dreyfus.

Bayard, D. S.↗

Extended implicit model following as applied to integrated flight and propulsion control

An extended model-following control-synthesis method, including loop-transfer recovery, is presented and applied to synthesize control laws for integrated flight and propulsion control (IFPC). The vehicle considered is representative of an unstable modern fighter aircraft; with a two-dimensional thrust-vectoring and thrust-reversing nozzle. The linearized design model includes both airframe and engine dynamics. A model-following formulation of the LQR problem is extended to handle this hybrid problem. Compensators are then obtained to realize an output-feedback control law, by using a loop-transfer-recovery procedure. The airframe and engine responses are decoupled, and perfect airframe response following is obtained. The loop transfers also reveal good stability robustness and reasonable loop cross-over frequencies that would not lead to excessive actuation requirements.

Schmidt, David K.↗

An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

Jorgenson, Philip C. E.↗

Applying Formal Methods to Safety-Critical Systems

How do you know a proof is correct? Traditionally, mathematical proofs are socially verified – at least one human, following a set of implicit rules of natural language and logic, determines if the proof is believable. If the proof becomes overly tedious and/or is essential to some safety- or mission-critical application, it becomes necessary to determine the soundness to a higher standard. 'Formal methods' refer to mathematically rigorous techniques and tools that enable specification, design, and verification of hardware and software systems. The specification used in formal methods are statements in a mathematical logic while the formal verifications are deductions in that logic. Formal methods can be difficult or time/resource intensive, but offer a higher level of assurance than standard verification through testing or handwritten proofs. This talk will introduce formal methods, motivated by applications of interest to NASA, including uncrewed aircraft operations in the national airspace, urban air environments, and wildfire areas. The audience will be given a crash course in mechanically verified proofs in the Prototype Verification System (PVS), an interactive theorem prover.

Formal Methods↗

A finite element model of conduction, convection, and phase change near a solid/melt interface

Detailed understanding of heat transfer and fluid flow is required for many aerospace thermal systems. These systems often include phase change and operate over a range of accelerations or effective gravitational fields. An approach to analyzing such systems is presented which requires the simultaneous solution of the conservation laws of energy, momentum, and mass, as well as an equation of state. The variable property form of the governing equations are developed in two-dimensional Cartesian coordinates for a Newtonian fluid. A numerical procedure for solving the governing equations is presented and implemented in a computer program. The Galerkin form of the finite element method is used to solve the spatial variation of the field variables, along with the implicit Crank-Nicolson time marching algorithm. Quadratic Langrangian elements are used for the internal energy and the two components of velocity. Linear Lagrangian elements are used for the pressure. The location of the solid/liquid interface as well as the temperatures are determined form the calculated internal energy and pressure. This approach is quite general in that it can describe heat transfer without phase change, phase change with a sharp interface, and phase change without an interface. Analytical results from this model are compared to those of other researchers studying transient conduction, convection, and phase change and are found to be in good agreement. The numerical procedure presented requires significant computer resources, but this is not unusual when compared to similar studies by other researchers. Several methods are suggested to reduce the computational times.

Viterna, Larry A.↗

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗

Three-dimensional Euler time accurate simulations of fan rotor-stator interactions

A numerical method useful to describe unsteady 3-D flow fields within turbomachinery stages is presented. The method solves the compressible, time dependent, Euler conservation equations with a finite volume, flux splitting, total variation diminishing, approximately factored, implicit scheme. Multiblock composite gridding is used to partition the flow field into a specified arrangement of blocks with static and dynamic interfaces. The code is optimized to take full advantage of the processing power and speed of the Cray Y/MP supercomputer. The method is applied to the computation of the flow field within a single stage, axial flow fan, thus reproducing the unsteady 3-D rotor-stator interaction.

Boretti, A. A.↗

On the Coupling of CDISC Design Method with FPX Rotor Code

A rotor section aerodynamics design package is developed by coupling Constrained Direct Iterative Surface Curvature (CDISC) design method with the FPX rotor code. The coupling between the CDISC design and the FPX flow analysis is fully automated. The CDISC design method employs a predictor-corrector procedure iteratively to determine a surface geometry which produces a target pressure distribution, where the target pressure distributions is either pre-defined or automatically generated through flow and geometry constraints. The FPX code is an eXtended Full-Potential rotor Computational Fluid Dynamics (CFD) code, which solves the three-dimensional unsteady full-potential equation in a strong conservative form using an implicit approximate factorization finite-difference scheme with entropy and viscosity corrections. Application of the CDISC design method coupled with the FPX rotor code is made for rotor blades in hovering motions. Several design examples are presented to demonstrate the capability of the new package in rotor section design.

Hu, Hong↗

A comparison of artificial compressibility and fractional step methods for incompressible flow computations

We have applied and compared the efficiency and accuracy of two commonly used numerical methods for the solution of Navier-Stokes equations. The artificial compressibility method augments the continuity equation with a transient pressure term and allows one to solve the modified equations as a coupled system. Due to its implicit nature, one can have the luxury of taking a large temporal integration step at the expense of higher memory requirement and larger operation counts per step. Meanwhile, the fractional step method splits the Navier-Stokes equations into a sequence of differential operators and integrates them in multiple steps. The memory requirement and operation count per time step are low, however, the restriction on the size of time marching step is more severe. To explore the strengths and weaknesses of these two methods, we used them for the computation of a two-dimensional driven cavity flow with Reynolds number of 100 and 1000, respectively. Three grid sizes, 41 x 41, 81 x 81, and 161 x 161 were used. The computations were considered after the L2-norm of the change of the dependent variables in two consecutive time steps has fallen below 10(exp -5).

Chan, Daniel C.↗

Choosing a software design method for real-time Ada applications: JSD process inversion as a means to tailor a design specification to the performance requirements and target machine

The validity of real-time software is determined by its ability to execute on a computer within the time constraints of the physical system it is modeling. In many applications the time constraints are so critical that the details of process scheduling are elevated to the requirements analysis phase of the software development cycle. It is not uncommon to find specifications for a real-time cyclic executive program included to assumed in such requirements. It was found that prelininary designs structured around this implementation abscure the data flow of the real world system that is modeled and that it is consequently difficult and costly to maintain, update and reuse the resulting software. A cyclic executive is a software component that schedules and implicitly synchronizes the real-time software through periodic and repetitive subroutine calls. Therefore a design method is sought that allows the deferral of process scheduling to the later stages of design. The appropriate scheduling paradigm must be chosen given the performance constraints, the largest environment and the software's lifecycle. The concept of process inversion is explored with respect to the cyclic executive.

Withey, James V.↗

A numerical simulation of two-dimensional inlet flow fields

Inlet flow fields for airbreathing missiles are calculated by the adaptation of a two-dimensional computational method developed for the flow around airfoils. A supersonic free stream is assumed to allow the forebody calculation to be uncoupled from the inlet calculation. The inlet calculation employs an implicit, time-marching finite-difference procedure to solve the thin-layer Navier-Stokes equations formulated in body-fitted coordinates. Because the method can be used for a flow field with both subsonic and supersonic regions, it is applicable to subcritical as well as supercritical inlet operation.

Biringen, S.↗

An Inviscid Decoupled Method for the Roe FDS Scheme in the Reacting Gas Path of FUN3D

An approach is described to decouple the species continuity equations from the mixture continuity, momentum, and total energy equations for the Roe flux difference splitting scheme. This decoupling simplifies the implicit system, so that the flow solver can be made significantly more efficient, with very little penalty on overall scheme robustness. Most importantly, the computational cost of the point implicit relaxation is shown to scale linearly with the number of species for the decoupled system, whereas the fully coupled approach scales quadratically. Also, the decoupled method significantly reduces the cost in wall time and memory in comparison to the fully coupled approach. This work lays the foundation for development of an efficient adjoint solution procedure for high speed reacting flow.

Thompson, Kyle B.↗

Comparison of GOES Cloud Classification Algorithms Employing Explicit and Implicit Physics

Cloud-type classification based on multispectral satellite imagery data has been widely researched and demonstrated to be useful for distinguishing a variety of classes using a wide range of methods. The research described here is a comparison of the classifier output from two very different algorithms applied to Geostationary Operational Environmental Satellite (GOES) data over the course of one year. The first algorithm employs spectral channel thresholding and additional physically based tests. The second algorithm was developed through a supervised learning method with characteristic features of expertly labeled image samples used as training data for a 1-nearest-neighbor classification. The latter's ability to identify classes is also based in physics, but those relationships are embedded implicitly within the algorithm. A pixel-to-pixel comparison analysis was done for hourly daytime scenes within a region in the northeastern Pacific Ocean. Considerable agreement was found in this analysis, with many of the mismatches or disagreements providing insight to the strengths and limitations of each classifier. Depending upon user needs, a rule-based or other postprocessing system that combines the output from the two algorithms could provide the most reliable cloud-type classification.

EXPLICIT PHYSICS ALGORITHMS↗

Numerical simulation of turbulent jet noise, part 2

Results on the numerical simulation of jet flow fields were used to study the radiated sound field, and in addition, to extend and test the capabilities of the turbulent jet simulation codes. The principal result of the investigation was the computation of the radiated sound field from a turbulent jet. In addition, the computer codes were extended to account for the effects of compressibility and eddy viscosity, and the treatment of the nonlinear terms of the Navier-Stokes equations was modified so that they can be computed in a semi-implicit way. A summary of the flow model and a description of the numerical methods used for its solution are presented. Calculations of the radiated sound field are reported. In addition, the extensions that were made to the fundamental dynamical codes are described. Finally, the current state-of-the-art for computer simulation of turbulent jet noise is summarized.

Metcalfe, R. W.↗

Numerical simulation of homogeneous, isotropic, compressible turbulence

A new numerical algorithm is developed and applied to the direct simulation of compressible, homogeneous turbulent flows at low Mach numbers. A split method in time first solves a subset of the equations explicitly, followed by an implicit treatment of the pressure terms. The definition of an average sound speed over the entire field allows the implicit equations to be solved analytically, while relaxing the severe time limit imposed by the large sound speeds. Results from direct simulations on 96(3) grids provide a data base against which a new subgrid-scale model for compressible homogeneous turbulence is tested. This model reduces to the linear combination model in the absence of compressibility.

Erlebacher, G.↗

Multigrid solution of the Navier-Stokes equations on triangular meshes

A new Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite-element Galerkin approximation, which can be shown to be equivalent to a finite-volume approximation for regular equilateral triangular meshes. Integration to steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. The convergence efficiency of the present method is shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, D. J.↗

A circular median filter approach for resolving directional ambiguities in wind fields retrieved from spaceborne scatterometer data

The retrieval algorithm for spaceborne scatterometry proposed by Schultz (1985) is extended. A circular median filter (CMF) method is presented, which operates on wind directions independently of wind speed, removing any implicit wind speed dependence. A cell weighting scheme is included in the algorithm, permitting greater weights to be assigned to more reliable data. The mathematical properties of the ambiguous solutions to the wind retrieval problem are reviewed. The CMF algorithm is tested on twelve simulated data sets. The effects of spatially correlated likelihood assignment errors on the performance of the CMF algorithm are examined. Also, consideration is given to a wind field smoothing technique that uses a CMF.

Schultz, Howard↗

Finite element computation of compressible flows with the SUPG formulation

Finite element computation of compressible Euler equations is presented in the context of the streamline-upwind/Petrov-Galerkin (SUPG) formulation. The SUPG formulation, which is based on adding stabilizing terms to the Galerkin formulation, is further supplemented with a shock capturing operator which addresses the difficulty in maintaining a satisfactory solution near discontinuities in the solution field. The shock capturing operator, which has been derived from work done in entropy variables for a similar operator, is shown to lead to an appropriate level of additional stabilization near shocks, without resulting in excessive numerical diffusion. An implicit treatment of the impermeable wall boundary condition is also presented. This treatment of the no-penetration condition offers increased stability for large Courant numbers, and accelerated convergence of the computations for both implicit and explicit applications. Several examples are presented to demonstrate the ability of this method to solve the equations governing compressible fluid flow.

Le Beau, G. J.↗