Tim A. Albring

Development of a Consistent Discrete Adjoint Solver in an Evolving Aerodynamic Design Framework

Typically the development of adjoint solvers for the use in aerodynamic design is challenging. In this paper we will give an update on the development of a discrete adjoint solver that enables the computation of consistent gradients within the open-source multi-physics framework SU2. Due to the use of advanced programming techniques like Expression Templates and the application of Algorithmic Differentiation we obtain an automatic adaption to modifications and extensions of the flow/state solver while maintaining robustness and efficiency.

A Discrete Adjoint Framework for Unsteady Aerodynamic and Aeroacoustic Optimization

In this paper, we present an unsteady aerodynamic and aeroacoustic optimization framework in which algorithmic differentiation (AD) is applied to the open-source multi-physics solver SU2 to obtain design sensitivities. An AD-based consistent discrete adjoint solver is developed which directly inherits the convergence properties of the primal flow solver due to the differentiation of the entire nonlinear fixed-point iterator. In addition, a coupled CFD-CAA far-field noise prediction framework using a permeable surface Ffowcs WilliamsHawkings approach is also developed. The resultant AD-based discrete adjoint solver is applied to both drag and noise minimization problems. The results suggest that the unsteady adjoint information provided by this AD-based discrete adjoint framework is accurate and robust, due to the algorithmic differentiation of the entire design chain including the dynamic mesh movement routine and various turbulence model, as well as the hybrid CFD-CAA model.

Adjoint Formulation Investigations of Benchmark Aerodynamic Design Cases in SU2

We investigate multiple adjoint formulations within the SU2 suite: a continuous adjoint in surface integral form, a continuous adjoint in field integral form, and a discrete adjoint leveraging algorithmic differentiation. The formulations are applied to the computation of drag sensitivities with respect to shape changes for four different external flow test cases, including the NACA 0012, RAE 2822, NACA 4412, and the Ahmed car body configuration. The main objective of this article is to draw meaningful conclusions about the performance of the available adjoint technologies for computing shape design gradients with a particular emphasis on accuracy. While all formulations provide gradients suitable for optimization purposes, we find that the inclusion of mesh effects in the field integral formulation of the continuous adjoint can provide improvements in sensitivity accuracy and robustness over the surface integral formulation.

Fully turbulent discrete adjoint solver for non-ideal compressible flow applications

Non-Ideal Compressible Fluid-Dynamics (NICFD) has recently been established as a sector of fluid mechanics dealing with the flows of dense vapors, supercritical fluids, and two-phase fluids, whose properties significantly depart from those of the ideal gas. The flow through an Organic Rankine Cycle (ORC) turbine is an exemplary application, as stators often operate in the supersonic and transonic regime, and are affected by NICFD effects. Other applications are turbomachinery using supercritical CO2 as working fluid or other fluids typical of the oil and gas industry, and components of air conditioning and refrigeration systems. Due to the comparably lower level of experience in the design of this fluid machinery, and the lack of experimental information on NICFD flows, the design of the main components of these processes (i.e., turbomachinery and nozzles) may benefit from adjoint-based automated fluid-dynamic shape optimization. Hence, this work is related to the development and testing of a fully-turbulent adjoint method capable of treating NICFD flows. The method was implemented within the SU2 open-source software infrastructure. The adjoint solver was obtained by linearizing the discretized flow equations and the fluid thermodynamic models by means of advanced Automatic Differentiation (AD) techniques. The new adjoint solver was tested on exemplary turbomachinery cases. Results demonstrate the method effectiveness in improving simulated fluid-dynamic performance, and underline the importance of accurately modeling non-ideal thermodynamic and viscous effects when optimizing internal flows influenced by NICFD phenomena.

A Consistent and Robust Discrete Adjoint Solver for the SU^2 Framework—Validation and Application

In this work we introduce a robust and consistent discrete adjoint solver that has been embedded into the open-source multiphysics framework SU\(^2\) by exploitation of the fixed-point structure of the flow solver. At inviscid and turbulent optimization test cases we demonstrate the capabilities of the implementation and compare it with the continuous adjoint method and the common frozen eddy viscosity assumption.

A Mixed Approach to Adjoint Computation with Algorithmic Differentiation

Various algorithmic differentiation tools have been developed and applied to large-scale simulation software for physical phenomena. Until now, two strictly disconnected approaches have been used to implement algorithmic differentiation (AD), namely, source transformation and operator overloading. This separation was motivated by different features of the programming languages such as Fortran and C++. In this work we have for the first time combined the two approaches to implement AD for C++ codes. Source transformation is used for core routines that are repetitive, where the transformed source can be optimized much better by modern compilers, and operator overloading is used to interconnect at the upper level, where source transformation is not possible because of complex language constructs of C++. We have also devised a method to apply the mixed approach in the same application semi-automatically. We demonstrate the benefit of this approach using some real-world applications.

A one-shot optimization framework with additional equality constraints applied to multi-objective aerodynamic shape optimization

This paper concerns the implementation and application of the extended one-shot approach including additional equality constraints to achieve a direct transition from simulation to optimization. The approach can be applied for different areas of scientific computing where partial differential equations are treated by using a fixed-point solver. The solver is extended in a semi-automated fashion. In a first step it is augmented with a consistent adjoint solver using algorithmic differentiation. Then the obtained reduced derivative information is directly employed to simultaneously achieve optimality and primal as well as adjoint feasibility. The methodology is implemented in the multi-physics package SU2 and applied for multi-objective aerodynamic shape optimization.

Expression templates for primal value taping in the reverse mode of algorithmic differentiation

ABSTRACT The reverse mode of Algorithmic Differentiation (AD) can be implemented in several ways. The major choices are primal value taping vs. Jacobian taping, managed indices vs. unmanaged indices and operator level taping vs. statement level taping. Most of the current AD tools have implemented only one of the eight possible choices, and the data management of the implementation adds another complexity hierarchy. The focus in this paper is the implementation of primal value taping on a statement level. Statement level taping removes the need to create intermediate values on the AD tape which results in reduced memory compared to operator level taping. The implementation will be done for managed and unmanaged indices in the AD tool CoDiPack. Primal value taping with statement level taping has not yet been implemented in any other AD tool, thus we will analyse the properties of the taping approaches and highlight the important details for an efficient implementation. Furthermore, all existing taping approaches in CoDiPack will be compared with the new primal value taping approach. The comparison have been conducted on a simple toy problem and a fully featured computational fluid dynamics solver in the multi-physics suite SU2.

Adjoint-based fluid dynamic design optimization in quasi-periodic unsteady flow problems using a harmonic balance method

Abstract Shape optimization in unsteady flow problems enables the consideration of dynamic effects on design. The ability to treat unsteady effects is attractive, as it can provide performance gains when compared to steady-state design methods for a variety of applications in which time-varying flows are of paramount importance. This is the case, for example, in turbomachinery or rotorcraft design. Given the high computational cost involved in time-accurate design problems, adjoint-based shape optimization is a promising option. However, efficient sensitivity analysis should also be accompanied by a significant decrease in computational cost for the primal flow solution, as well. Reduced-order models, like those based on the harmonic balance concept, in combination with the calculation of gradients via adjoint methods, are proposed for the efficient solution of a certain class of aerodynamics optimization problems. The harmonic balance method is applicable if the flow is characterized by discrete finite dominant flow frequencies that do not need to be integer multiples of a fundamental harmonic. A fully-turbulent harmonic balance discrete adjoint formulation based on a duality-preserving approach is proposed. The method is implemented by leveraging algorithmic differentiation and is applied to two test cases: the constrained shape optimization of both a pitching airfoil and a turbine cascade. A key advantage of the current approach is the accurate computation of gradients as compared to second order finite differences without any approximation in the linearization of the turbulent viscosity. The shape optimization results show significant improvements for the selected time-dependent objective functions, demonstrating that design problems involving almost-periodic unsteady flows can be tackled with manageable computational effort.