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Results for “boundary value problems”

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.

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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Additive manufacturing system and method having toolpath analysis

An additive manufacturing (AM) system is disclosed for constructing a three dimensional (3D) part with optimized orthotropy. The system combines an electronic processor which calculates an optimal set of physically achievable toolpaths to meet a given design objective, and a 3D printing direct ink write machine capable of printing inks with reinforcing particles that result in orthotropic materials. The electronic processor may combine a Domain of Interest subsystem that transforms a mathematical description of a desired part orthotropy to a plurality of guidepaths, a toolpath generate subsystem that develops a plurality of physically realizable toolpaths from those guidepaths with a minimum number of starts and stops, a finite element subsystem that computes spatially varying material orthotropy from those toolpaths and then solves a boundary value problem to determine a figure of merit for the design, and an optimization subsystem that uses that figure of merit to update the mathematical description of the part orthotropy to iteratively develop an improved part. The optimization subsystem also includes convergence criteria to indicate when toolpaths have been achieved that yield a sufficiently optimal part has been achieved. The toolpath generate can then output the final toolpaths, which are converted to suitable code that controls the motion of the 3D printer toolhead and allows the optimized 3D part to be manufactured.

King, Michael J.↗
DOE OSTI2016

A Coarse-Mesh Nonlinear Diffusion Acceleration Scheme with Local Refinement for Neutron Transport Calculations

The coarse-mesh nonlinear diffusion acceleration (CM-NDA) technique, or commonly known as coarse-mesh finite difference (CMFD), is one of the most widely used acceleration methods for numerical transport calculations. Although CM-NDA is very effective to reduce the iteration number of neutron transport sweep, it can sometimes become unstable, in particularly when the coarse mesh size becomes large. Over the last two decades a number of ad hoc techniques have been developed to stabilize the CM-NDA scheme. In this paper, we present a new scheme, LR-NDA, which is based on CM-NDA with local refinement. Within the CM-NDA framework, the LR-NDA scheme incorporates solving an additional local boundary-value problem (BVP) of the neutron flux on each individual coarse mesh cell, yielding a finer flux profile than CMNDA. Our assessments show that this new scheme can significantly improve the effectiveness of CM-NDA, and more importantly it is very stable even for extremely high optical thickness. A great feature of LR-NDA is that it is fully adaptive, which means that it can be easily applied to any local region of the problem domain, and local refinement can be performed using any numerical method (e.g., finite difference, finite element, or spectral element, etc.). (authors)

42 ENGINEERING↗
NASA NTRS1974

The application of MINIQUASI to thermal program boundary and initial value problems

The feasibility of applying the solution techniques of Miniquasi to the set of equations which govern a thermoregulatory model is investigated. For solving nonlinear equations and/or boundary conditions, a Taylor Series expansion is required for linearization of both equations and boundary conditions. The solutions are iterative and in each iteration, a problem like the linear case is solved. It is shown that Miniquasi cannot be applied to the thermoregulatory model as originally planned.

Source record↗
DOE OSTI2018

An asymmetric backward problem for the inhomogeneous parabolic equation with time-dependent diffusivity

In this paper, we deal with an asymmetric case of the non-homogeneous backward parabolic problem associated with time-dependent diffusivity in polar coordinates which arises in describing the heat transfer in cylinder. In general, this problem is severely ill-posed by the Hadamard instability. To subdue the instability of this problem, we apply the modified quasi-boundary value method. According to some a priori assumptions on the exact solution, we get an explicit error estimate of Hölder type for all t∈(0,T]. In addition, a numerical experiment is given to illustrate the efficiency and flexibility of our method.

42 ENGINEERING↗
NASA NTRS1981

Elasto visco-plastic flow with special attention to boundary conditions

A simple but nontrivial steady-state creeping elasto visco-plastic (Maxwell fluid) radial flow problem is analyzed, with special attention given to the effects of the boundary conditions. Solutions are obtained through integration of a governing equation on stress using the Runge-Kutta method for initial value problems and finite differences for boundary value problems. A more general approach through the finite element method, an approach that solves for the velocity field rather than the stress field and that is applicable to a wide range of problems, is presented and tested using the radial flow example. It is found that steady-state flows of elasto visco-plastic materials are strongly influenced by the state of stress of material as it enters the region of interest. The importance of this boundary or initial condition in analyses involving materials coming into control volumes from unusual stress environments is emphasized.

Shimazaki, Y.↗
NASA NTRS1989

Guidance analysis of the aeroglide plane change maneuver as a turning point problem

The development of guidance approximations for the atmospheric (aeroglide) portion of the minimum fuel, orbital plane change, trajectory optimization problem is described. Asymptotic methods are used to reduce the two point, boundary value, optimization problem to a turning point problem from the bank angle control. The turning point problem solution, which yields an approximate optimal control policy, is given in terms of parabolic cylinder functions, which are tabulated, and integral expressions, which must be numerically computed. Comparisons of the former, over their region of validity, with optimal control solutions show good qualitative agreement. Additional work and analysis is needed to compute the guidance approximation work.

Gracey, Christopher↗
DOE OSTI2024

Analysis of Control Behavior in Eco-Driving Speed Optimization Using Pontryagin’s Minimum Principle

The energy efficiency of autonomous vehicles can be improved by selecting an optimized speed profile. Energy savings can be maximized by performing control optimization with knowledge of the powertrain characteristics and future driving conditions. Previous studies have shown that Pontryagin’s minimum principle (PMP) performs well in vehicle speed optimization problems. Building on the methods proposed in previous studies, the contribution of this study is to derive meaningful observations from the concepts and results of PMP to enhance the understanding of the control problem. In particular, the switching behavior of the control mode is analyzed with supportive variables, such as ξ and mv, which dictates the changes in the control modes. Additionally, the existence of the singular control is analyzed, which helps in understanding the cruise driving in the control problem. Finally, we obtain several solutions that satisfy various boundary conditions along with a map of the reachable states, and discuss the impact of cruise driving. This is helpful for designing practical control concepts for real-world applications based on this map. Previous studies have contributed significantly to this control problem; however, this study provides a better understanding of the issue and offers guidance and inspiration for future real-world applications based on these meaningful observations.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1975

Solution of an optimal control lifting body entry problem by an improved method of perturbation functions

This paper presents a solution to a complex lifting reentry three-degree-of-freedom problem by using the calculus of variations to minimize the integral of the sum of the aerodynamics loads and heat rate input to the vehicle. The entry problem considered does not have state and/or control constraints along the trajectory. The calculus of variations method applied to this problem gives rise to a set of necessary conditions which are used to formulate a two point boundary value (TPBV) problem. This TPBV problem is then numerically solved by an improved method of perturbation functions (IMPF) using several starting co-state vectors. These vectors were chosen so that each one had a larger norm with respect to show how the envelope of convergence is significantly increased using this method and cases are presented to point this out.

Garcia, F., Jr.↗
DOE OSTI2016

Estimates of the eigenvalues of operator arising in swelling pressure model

Swelling pressures from materials confined by structures can cause structural deformations and instability. Due to the complexity of interactions between expansive solid and solid-liquid equilibrium, the forces exerting on retaining structures from swelling are highly nonlinear. This work is our initial attempt to study a simplistic spectral problem based on the Euler-elastic beam theory and some simplistic swelling pressure model. In this work estimates of the eigenvalues of some initial/boundary value problem for nonlinear Euler-elastic beam equation are obtained.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Classical Solvability of the Radial Viscous Fingering Problem in a Hele–Shaw Cell with Surface Tension

We consider the one-phase problem on radial viscous fingering structures in a Hele–Shaw cell with surface tension. This problem is a nonlinear free-boundary problem for elliptic equations. Unlike the Stefan problem for the heat equation, we deal with a problem of hydrodynamic type. We establish the classical solvability of the one-phase Hele–Shaw problem with radial geometry by using the same method as that used for the Stefan problem and justifying the vanishing coefficient of the time-derivative in the parabolic equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Analytical Solution for Three-Dimensional, Unsteady Heat Conduction in a Multilayer Sphere

An analytical solution has been obtained for the transient problem of three-dimensional multilayer heat conduction in a sphere with layers in the radial direction. The solution procedure can be applied to a hollow sphere or a solid sphere composed of several layers of various materials. In general, the separation of variables applied to 3D spherical coordinates has unique characteristics due to the presence of associated Legendre functions as the eigenfunctions. Moreover, an eigenvalue problem in the azimuthal direction also requires solution; again, its properties are unique owing to periodicity in the azimuthal direction. Therefore, extending existing solutions in 2D spherical coordinates to 3D spherical coordinates is not straightforward. In a spherical coordinate system, one can solve a 3D transient multilayer heat conduction problem without the presence of imaginary eigenvalues. A 2D cylindrical polar coordinate system is the only other case in which such multidimensional problems can be solved without the use of imaginary eigenvalues. The absence of imaginary eigenvalues renders the solution methodology significantly more useful for practical applications. The methodology described can be used for all three types of boundary conditions in the outer and inner surface of the sphere. Lastly, the solution procedure is demonstrated on an illustrative problem for which results are obtained.

36 MATERIALS SCIENCE↗