Local-in-time adjoint-based method for design optimization of unsteady flows

  • Authors:

  • Nail K. Yamaleev;Boris Diskin;Eric J. Nielsen

  • Affiliations:

  • Department of Mathematics, North Carolina A&T State University, Greensboro, NC 27411, USA;National Institute of Aerospace, Hampton, VA 23666, USA and Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904, USA;Computational AeroSciences Branch, NASA Langley Research Center, Hampton, VA 23681, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

We present a new local-in-time discrete adjoint-based methodology for solving design optimization problems arising in unsteady aerodynamic applications. The new methodology circumvents storage requirements associated with the straightforward implementation of a global adjoint-based optimization method that stores the entire flow solution history for all time levels. This storage cost may quickly become prohibitive for large-scale applications. The key idea of the local-in-time method is to divide the entire time interval into several subintervals and to approximate the solution of the unsteady adjoint equations and the sensitivity derivative as a combination of the corresponding local quantities computed on each time subinterval. Since each subinterval contains relatively few time levels, the storage cost of the local-in-time method is much lower than that of the global methods, thus making the time-dependent adjoint optimization feasible for practical applications. Another attractive feature of the new technique is that the converged solution obtained with the local-in-time method is a local extremum of the original optimization problem. The new method carries no computational overhead as compared with the global implementation of adjoint-based methods. The paper presents a detailed comparison of the global- and local-in-time adjoint-based methods for design optimization problems governed by the unsteady compressible 2-D Euler equations.