Trent Lukaczyk

Stanford University Unstructured (SU 2 ): An open-source integrated computational environment for multi-physics simulation and design

This paper describes the history, objectives, structure, and current capabilities of the Stanford University Unstructured (SU 2 ) tool suite. This computational analysis and design software collection is being developed to solve complex, multi-physics analysis and optimization tasks using arbitrary unstructured meshes, and it has been designed so that it is easily extensible for the solution of Partial Differential Equation-based (PDE) problems not directly envisioned by the authors. At its core, SU 2 is an open-source collection of C++ software tools to discretize and solve problems described by PDEs and is able to solve PDE-constrained optimization problems, including optimal shape design. Although the toolset has been designed with Computational Fluid Dynamics (CFD) and aerodynamic shape optimization in mind, it has also been extended to treat other sets of governing equations including potential flow, electrodynamics, chemically reacting flows, and several others. In our experience, capabilities for computational analysis and optimization have improved considerably over the past two decades. However, the ability to integrate the resulting software packages into coupled multi-physics analysis and design optimization solvers has remained a challenge: the variety of approaches chosen for the independent components of the overall problem (flow solvers, adjoint solvers, optimizers, shape parameterization, shape deformation, mesh adaption, mesh deformation, etc) make it difficult to (a) expand the range of applicability to situations not originally envisioned, and (b) to reduce the overall burden of creating integrated applications. By leveraging well-established object-oriented software architectures (using C++) and by enabling a common interface for all the necessary components, SU 2 is able to remove these barriers for both the beginner and the seasoned analyst. In this paper we attempt to describe our efforts to develop SU 2 as an integrated platform. In some senses, the paper can also be used as a software reference manual for those who might be interested in modifying it to suit their own needs. We carefully describe the C++ framework and object hierarchy, the sets of equations that can be currently modeled by SU 2 , the available choices for numerical discretization, and conclude with a set of relevant validation and verification test cases that are included with the SU 2 distribution. We intend for SU 2 to remain open source and to serve as a starting point for new capabilities not included in SU 2 today, that will hopefully be contributed by users in both academic and industrial environments.

SU2: An Open-Source Suite for Multiphysics Simulation and Design

This paper presents the main objectives and a description of the SU2 suite, including the novel software architecture and open-source software engineering strategy. SU2 is a computational analysis and design package that has been developed to solve multiphysics analysis and optimization tasks using unstructured mesh topologies. Its unique architecture is well suited for extensibility to treat partial-differential-equation-based problems not initially envisioned. The common framework adopted enables the rapid implementation of new physics packages that can be tightly coupled to form a powerful ensemble of analysis tools to address complex problems facing many engineering communities. The framework is demonstrated on a number, solving both the flow and adjoint systems of equations to provide a high-fidelity predictive capability and sensitivity information that can be used for optimal shape design using a gradient-based framework, goal-oriented adaptive mesh refinement, or uncertainty quantification.

Active Subspaces for Shape Optimization

Aerodynamic shape optimization plays a fundamental role in aircraft design. However, useful parameterizations of shapes for engineering models often result in high-dimensional design spaces which can create challenges for both local and global optimizers. In this paper, we employ an active subspace method (ASM) to discover and exploit low-dimensional, monotonic trends in the quantity of interest as a function of the design variables. The trend enables us to eciently and eectively nd an optimal design in appropriate areas of the design space. We apply this approach to the ONERA-M6 transonic wing, parameterized with 50 Free-Form Deformation (FFD) design variables. Given an initial set of 300 designs, the ASM discovered a low-dimensional linear subspace of the input space that explained the majority of the variability in the drag and lift coecients. This revealed a global trend that we exploited to nd an optimal design with reduced computational cost.

Stanford University Unstructured (SU2): Analysis and Design Technology for Turbulent Flows

This paper presents a comprehensive set of test cases for the verification and validation (V & V) of the Stanford University Unstructured (SU) software suite within the context of compressible, turbulent flows described by the Reynolds-averaged Navier-Stokes (RANS) equations. SU is an open-source (Lesser General Public License, version 2.1), integrated analysis and design tool for solving multi-disciplinary problems governed by partial differential equations (PDEs) on general, unstructured meshes. As such, SU is able to handle arbitrarily complex geometries, mesh adaptation, and a variety of physical problems. At its core, the software suite is a collection of C++ modules embedded within a Python framework that are built specifically for both PDE analysis and PDE-constrained optimization, including surface gradient computations using the continuous adjoint technique. V & V studies of twoand three-dimensional problems are presented for turbulent flows across a wide range of Mach numbers (from subsonic flat plate studies to a complex, transonic aircraft configuration). The presentation of this comprehensive V & V of SU is intended to be the main contribution of this paper: the results generated with SU in a variety of standard test cases compare well with experimental data and established flow solvers that have undergone similar V & V efforts. For completeness, the adjoint-based shape design capability within SU is also illustrated.

Adjoint-based method for supersonic aircraft design using equivalent area distribution

This paper describes the e orts in the development of new adjoint-based techniques for the design of supersonic aircraft that must match a target equivalent area distribution at constant lift coe cients. This speci c approach is meant to be part of a larger e ort to create multidisciplinary analysis and optimization capabilities that can be used to design low-boom supersonic aircraft with adequate aerodynamic and structural performance. The paper focuses on the description of an inverse equivalent area distribution capability that includes the ow analysis, the formulation and implementation of an adjoint solver for the equivalent area distribution, and the shape design process of a trijet supersonic aircraft. This shape design e ort is challenging due to three factors: the complexity of the geometric details involved that require a full unstructured ow and adjoint solver methodology, the apriori grid adaptation process needed for capturing the shock and expansion waves in the neareld (without the need for additional mesh adaptation), and the selected objective function for the calculation of sensitivities and the ultimate application in aircraft design. The viability of our approach is demonstrated with some preliminary examples. Ongoing work is targeting actual con gurations that can result in an actual low-boom aircraft.

SUAVE: An Open-Source Environment for Multi-Fidelity Conceptual Vehicle Design

SUAVE, a conceptual level aircraft design environment, incorporates multiple information sources to analyze unconventional configurations. Developing the capability of producing credible conceptual level design conclusions for futuristic aircraft with advanced technologies is a primary directive. Many software tools for aircraft conceptual design rely upon empirical correlations and other handbook approximations. SUAVE proposes a way to design aircraft featuring advanced technologies by augmenting relevant correlations with physics-based methods. SUAVE is constructed as a modular set of analysis tools written compactly and evaluated with minimal programming effort. Additional capabilities can be incorporated using extensible interfaces and prototyped with a top-level script. The flexibility of the environment allows the creation of arbitrary mission profiles, unconventional propulsion networks, and right-fidelity at right-time discipline analyses. This article will first explain how SUAVE’s analysis capabilities are organized to enable flexibility. Then, it will summarize the analysis strategies for the various disciplines required to evaluate a mission. Of particular interest will be the construction of unconventional energy networks necessary to evaluate configurations such as hybrid-electric commercial transports and solar-electric unmanned aerial vehicles (UAVs). Finally, verification and validation studies will be presented to demonstrate the capabilities of SUAVE, including cases for conventional and unconventional vehicles. While some of these cases will be optimized results, discussion of SUAVE’s interface with optimization will be reserved for a future publication.

SUAVE: An Open-Source Environment for Conceptual Vehicle Design and Optimization

SUAVE, a conceptual level aircraft design environment, incorporates multiple information sources to analyze unconventional configurations. Developing the capability to produce credible conceptual level design conclusions for futuristic aircraft with advanced technologies is a primary directive. This work builds upon previous work where SUAVE analyzed aircraft to show how SUAVE may be integrated into external packages to optimize aerospace vehicles. In the context of optimization, SUAVE operates as a “black-box” function with multiple inputs and multiple outputs. Several convenient functions are provided to enable connecting the optimization packages to SUAVE more easily. Assuming an optimization algorithm is minimizing an objective subject to constraints by iteratively modifying input variables, SUAVE’s code structure is general enough to be driven from a variety of optimization packages. To this point, connections to PyOpt and SciPy have been integrated into SUAVE. We present results for a multi-mission regional aircraft, a family of UAVs and a tradeoff between noise and fuel burn on a large single-aisle aircraft. These designs show the immense amount of flexibility and diversity that SUAVE can handle. This includes various levels of fidelity. While SUAVE is setup from the beginning to handle multi-fidelity analysis, further study is necessary to integrate multiple fidelity levels into a single vehicle optimization.

On Active Subspaces in Car Aerodynamics

The Active Subspace Method (ASM) is an emerging set of tools for dimensionality reduction in complex physical systems. It allows to discover low-dimensional trends in the quantity of interest by exploiting redundancies in the input variables and combining them linearly into so-called active variables. The purpose of this study is to assess the applicability and the benefit of the ASM in car aerodynamics. To that end, we apply the ASM to drag and lift computations of three different parameterized vehicle geometries of increasing complexity. We thereby assess the impact of adjoint-based gradient inaccuracies on the results of the ASM, devise and validate a methodology to apply the ASM in the absence of adjoint-based gradients, and exemplify the practical use of this methodology in car aerodynamics. For all investigated cases, the ASM reveals that a large portion of the overall variability of drag or lift is captured already by an active subspace of dimension one, thus providing physical insight into the main shape parameter dependencies. By projection into an active subspace of a suitably chosen dimension larger than one, it is demonstrated that the predictive accuracy of surrogate models for drag and lift can consistently be improved.

Response Surface Methodologies for Low-Boom Supersonic Aircraft Design using Equivalent Area Distributions

The use of response surface models (also known as surrogate models) to describe the performance of aerospace systems within a given design space is by now fairly well established in the MDO community. Despite such widespread use, surrogate-based optimization techniques can incur signicant computational expense when high-dimensional spaces must be modeled. In this paper we describe an adaptive, constrained optimization methodology that is based on (a) Gaussian Process Regression (GPR), (b) the use of gradient information, inexpensively obtained via adjoint methods throughout the design space, (c) an adaptive sampling technique based on the notion of expected improvement, and (d) the treatment of nonlinear constraints (within the adaptive sampling loop) so that the number of unnecessary infeasible samples is signicantly reduced. The methodology is demonstrated using a number of analytic examples as well as with CFD-based low-boom airfoil and aircraft design problems using constraints based on target equivalent area distributions. This work is part of a larger eort (jointly with Lockheed Martin) to develop a multidisciplinary analysis and optimization framework for the high-delity design of lowboom supersonic aircraft within the NASA N+2 Supersonics eort.

Managing Gradient Inaccuracies while Enhancing Optimal Shape Design Methods

gradient calculations from adjoint formulations. The key goal of these enhancements is to increase the accuracy of the solution while reducing the computational wall-time. This study is specically interested in quantifying the impact of mesh adaptation and approximate gradients from continuous adjoint methodologies while performing Gradient Based Optimization (GBO) or Surrogate Based Optimization (SBO). In the course of this work we have discovered conditions in which these various gradient methods can actually degrade the performance of the optimizer. For example, we have observed that bias errors from continuous adjoint gradients, which are traditionally acceptable for GBO methods, are not acceptable for basic SBO methods, which make a stronger assumption of objective-gradient correlation. We have also observed that applying mesh adaptation to continuous adjoint solutions can exacerbate this error enough to eect GBO convergence rates. In attempting to improve the convergence of the optimizers, we have built several approaches to better condition gradient accuracies. In one approach we lter the surface sensitivities before projecting them into a parameterized design space. In another approach, we build surrogate models capable of learning the noise of the system. This paper will present the work completed towards developing these methods, and will provide examples in the form of analytical test cases and demonstrative aerodynamic problems.