Unstructured Adjoint Method for Navier-Stokes Equations

Numerical Methods in Fluids

2012

SUMMARYOver the last decade, the adjoint method has been consolidated as one of the most versatile and successful tools for aerodynamic design. It has become a research area on its own, spawning a large variety of applications and a prolific literature. Yet, some relevant aspects of the method remain relatively less explored in the literature. Such is the case with the adjoint boundary problem. In particular for Euler flows, both fluid dynamic and adjoint equations entail complementary Riemann problems, and these yield boundary conditions that are fully consistent with well‐posedness. In the literature, this approach has been pursued solely in terms of Riemann variables. This work formulates the adjoint boundary problem so as to correspond precisely to that imposed on the flow, as it is given in terms of primitive variables. Test results have shown to be in agreement with the traditional approach for external flow problems. Copyright © 2012 John Wiley & Sons, Ltd.

Section: Introductionmentioning

confidence: 99%

Characteristics‐based boundary conditions for the Euler adjoint problem

Hayashi

Ceze

Numerical Methods in Fluids

2012

“…those two terms drop from (21), and one imposes the continuity of the Lagrange multipliers through the shock wave. Then, on introducing the variations (16) into the above equation and collecting like terms, one has…”

Section: Statement Of the Problemmentioning

confidence: 99%

Boundary and internal conditions for adjoint fluid-flow problems

Santos

2008

J Eng Math

The ever-increasing robustness and reliability of flow-simulation methods have consolidated CFD as a major tool in virtually all branches of fluid mechanics. Traditionally, those methods have played a crucial role in the analysis of flow physics. In more recent years, though, the subject has broadened considerably, with the development of optimization and inverse design applications. Since then, the search for efficient ways to evaluate flow-sensitivity gradients has received the attention of numerous researchers. In this scenario, the adjoint method has emerged as, quite possibly, the most powerful tool for the job, which heightens the need for a clear understanding of its conceptual basis. Yet, some of its underlying aspects are still subject to debate in the literature, despite all the research that has been carried out on the method. Such is the case with the adjoint boundary and internal conditions, in particular. The present work aims to shed more light on that topic, with emphasis on the need for an internal shock condition. By following the path of previous authors, the quasi-1D Euler problem is used as a vehicle to explore those concepts. The results clearly indicate that the behavior of the adjoint solution through a shock wave ultimately depends upon the nature of the objective functional.

“…In aerodynamics, the developments of the adjoint method encompass design applications regarding internal and external flows [13,14,15,16], as well as unsteady flows [17,18,19,20]. The applications, however, also include error analysis [21,22] and grid adaptation [23,24,22,25].…”

Section: Introductionmentioning

confidence: 99%

An Extension of Adjoint Method Capabilities

Hayashi

46th AIAA Fluid Dynamics Conference

2016

This paper presents an alternative approach for the continuous formulation of the adjoint method applied to the Euler equations. On doing so, one could compute sensitivity gradients in a more general framework. The novel approach opens up the possibility of employing the adjoint method to assess the sensitivity of a given measure of merit with respect to changes in aerodynamic variables, in addition to the usual geometry design applications. One of the main goals of the research is to use the method as a reliable cost-effective tool to evaluate sensitivies of aerodynamic forces and moments of a given geometry with respect to control parameters at inflow boundaries from a steady flow solution.