The pEst version 2.1 user's manual

This report is a user's manual for version 2.1 of pEst, a FORTRAN 77 computer program for interactive parameter estimation in nonlinear dynamic systems. The pEst program allows the user complete generality in definig the nonlinear equations of motion used in the analysis. The equations of motion are specified by a set of FORTRAN subroutines; a set of routines for a general aircraft model is supplied with the program and is described in the report. The report also briefly discusses the scope of the parameter estimation problem the program addresses. The report gives detailed explanations of the purpose and usage of all available program commands and a description of the computational algorithms used in the program

Accuracy, Scalability, and Efficiency of Mixed-Element USM3D for Benchmark Three-Dimensional Flows

The unstructured, mixed-element, cell-centered, finite-volume flow solver USM3D is enhanced with new capabilities including parallelization, line generation for general unstructured grids, improved discretization scheme, and optimized iterative solver. The paper reports on the new developments to the flow solver and assesses the accuracy, scalability, and efficiency. The USM3D assessments are conducted using a baseline method and the recent hierarchical adaptive nonlinear iteration method framework. Two benchmark turbulent flows, namely, a subsonic separated flow around a three-dimensional hemisphere-cylinder configuration and a transonic flow around the ONERA M6 wing are considered

A Knowledge-Based Optimization Method for Aerodynamic Design

A new aerodynamic design method, CODISC, has been developed that combines a legacy knowledge-based design method, CDISC, with a simple optimization module known as SOUP. The primary goal of this new design system is to improve the performance gains obtained using CDISC without adding significant computational time. An additional objective of this approach is to reduce the need for a priori knowledge of good initial input variable values, as well as for subsequent manual revisions of those values as the design progresses. Several test cases illustrate the development of the process to date and some of the options available at transonic and supersonic speeds for turbulent flow designs. The test cases generally start from good baseline configurations and, in all cases, were able to improve the performance. Several new guidelines for good initial values for the design variables, as well as new design rules within CDISC itself, were developed from these cases

Optimistix: modular optimisation in JAX and Equinox

We introduce Optimistix: a nonlinear optimisation library built in JAX and Equinox. Optimistix introduces a novel, modular approach for its minimisers and least-squares solvers. This modularity relies on new practical abstractions for optimisation which we call search and descent, and which generalise classical notions of line search, trust-region, and learning-rate algorithms. It provides high-level APIs and solvers for minimisation, nonlinear least-squares, root-finding, and fixed-point iteration. Optimistix is available at https://github.com/patrick-kidger/optimistix.Comment: 8 pages, 4 figures, 2 table

Generalized Advanced Propeller Analysis System (GAPAS). Volume 2: Computer program user manual

The Generalized Advanced Propeller Analysis System (GAPAS) computer code is described. GAPAS was developed to analyze advanced technology multi-bladed propellers which operate on aircraft with speeds up to Mach 0.8 and altitudes up to 40,000 feet. GAPAS includes technology for analyzing aerodynamic, structural, and acoustic performance of propellers. The computer code was developed for the CDC 7600 computer and is currently available for industrial use on the NASA Langley computer. A description of all the analytical models incorporated in GAPAS is included. Sample calculations are also described as well as users requirements for modifying the analysis system. Computer system core requirements and running times are also discussed

Nonlinear calculation of arbitrarily shaped supercavitating hydrofoils near a free surface

A nonlinear exact solution to the problem of two-dimensional gravity-free incompressible potential flow around an arbitrarily shaped supercavitating hydrofoil near a free surface is obtained. A combination of Newton’s method with a functional iterative procedure is used to solve the nonlinear integral and algebraic equations of this problem. Fast and stable convergence results by starting the iteration with a readily chosen initial solution. Some representative numerical computations are made for practical hydrofoils having both generally shaped camber and leading-edge thickness distributions. The force coefficients, pressure distribution and free-streamline shapes of the cavity are calculated for each case with an execution time on an IBM 370-158 of 200-530s depending upon the initial trial solution

Multifidelity Analysis and Optimization for Supersonic Design

Supersonic aircraft design is a computationally expensive optimization problem and multifidelity approaches over a significant opportunity to reduce design time and computational cost. This report presents tools developed to improve supersonic aircraft design capabilities including: aerodynamic tools for supersonic aircraft configurations; a systematic way to manage model uncertainty; and multifidelity model management concepts that incorporate uncertainty. The aerodynamic analysis tools developed are appropriate for use in a multifidelity optimization framework, and include four analysis routines to estimate the lift and drag of a supersonic airfoil, a multifidelity supersonic drag code that estimates the drag of aircraft configurations with three different methods: an area rule method, a panel method, and an Euler solver. In addition, five multifidelity optimization methods are developed, which include local and global methods as well as gradient-based and gradient-free techniques

A problem-solving environment for the numerical solution of nonlinear algebraic equations

Nonlinear algebraic equations (NAEs) occur in many areas of science and engineering. The process of solving these NAEs is generally difficult, from finding a good initial guess that leads to a desired solution to deciding on convergence criteria for the approximate solution. In practice, Newton's method is the only robust general-purpose method for solving a system of NAEs. Many variants of Newton's method exist. However, it is generally impossible to know a priori which variant of Newton's method will be effective for a given problem.Many high-quality software libraries are available for the numerical solution of NAEs. However, the user usually has little control over many aspects of what the library does. For example, the user may not be able to easily switch between direct and indirect methods for the linear algebra. This thesis describes a problem-solving environment (PSE) called pythNon for studying the effects (e.g., performance) of different strategies for solving systems of NAEs. It provides the researcher, teacher, or student with a flexible environment for rapid prototyping and numerical experiments. In pythNon, users can directly influence the solution process on many levels, e.g., investigation of the effects of termination criteria and/or globalization strategies. In particular, to show the power, flexibility, and ease of use of the pythNon PSE, this thesis also describes the development of a novel forcing-term strategy for approximating the Newton direction efficiently in the pythNon PSE

An improved panel method for the solution of three-dimensional leading edge vortex flows Volume 2: User's guide and programmer's document

A computer program developed for solving the subsonic, three dimensional flow over wing-body configurations with leading edge vortex separation is presented. Instructions are given for the proper set up and input of a problem into the computer code. Program input formats and output are described, as well as the overlay structure of the program. The program is written in FORTRAN

Mathematical and computational studies of equilibrium capillary free surfaces

The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated