Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Maximum principle”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Restricted maximum principles for elastic bodies

A maximum principle for the equilibrium of an elastic material body which is free of body forces is described not all of the components of the displacement vector or of the principal stresses can simultaneously have a strict maximum or minimum at any point in the body which does not be either on the surface or on a material interface.

Rose, M. E.↗
NASA NTRS1989

Maximum principle solutions for time-optimal half-loop maneuvers of a high alpha fighter aircraft

An investigation was conducted of maximum principle solutions for an initial 0.6 Mach number and 15,000-ft altitude. The authors generate these solutions for a family of prescribed final times tf, starting with tf = 0.5 s. Using a nonlinear wind-tunnel model they construct maximum principle solutions. Above tf = 1.2 s some small nonlinear variations in the aerodynamic pitching moment coefficient presented difficulty with respect to numerical convergence. This was circumvented by fitting analytical models to the aerodynamic coefficients of the wind-tunnel model at Mach 0.4. Maximum principle solutions of the analytical model are shown to compare well with those obtained for tf of less than 1.2 s. Using the analytical model the authors extended the prescribed final time to a value of 13.65 s at which time the aircraft completes the half-loop maneuver. This is 0.53 s longer than that obtained using the singular perturbation feedback control law.

Stalford, Harold↗
NASA NTRS1965

A maximum principle re-entry study

Mathematical model of maximum principle of Pontryagin used to find point-to-point reentry trajectory of space vehicle

REENTRY TRAJECTORY↗
DOE OSTI2025

High-order limiting methods using maximum principle bounds derived from the Boltzmann equation I: Euler equations

The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution bounds and limiting for the Euler equations through the kinetic representation provided by the Boltzmann equation, which allows for extending limiters designed for linear advection directly to the Euler equations. Given an arbitrary set of solution values to compute bounds over (e.g., numerical stencil) and a desired linear advection limiter, the proposed approach yields an analytic expression for the admissible region of particle distribution function values, which may be numerically integrated to yield a set of bounds for the density, momentum, and total energy. Further, these solution bounds are shown to preserve positivity of density/pressure/internal energy and, when paired with a limiting technique, can robustly resolve strong discontinuities while recovering high-order accuracy in smooth regions without any ad hoc corrections (e.g., relaxing the bounds). This approach is demonstrated in the context of an explicit unstructured high-order discontinuous Galerkin/flux reconstruction scheme for a variety of difficult problems in gas dynamics, including cases with extreme shocks and shock-vortex interactions. Furthermore, this work presents a foundation for limiting techniques for more complex macroscopic governing equations that can be derived from an underlying kinetic representation for which admissible solution bounds are not well-understood.

42 ENGINEERING↗