A Cure for Numerical Instability of Discrete Adjoint Methods to Quasi-1D Flow Equations Near Boundaries

Algorithm Developments for Discrete Adjoint Methods

AIAA Journal ◽

10.2514/2.1961 ◽

2003 ◽

Vol 41 (2) ◽

pp. 198-205 ◽

Cited By ~ 187

Author(s):

Michael B. Giles ◽

Mihai C. Duta ◽

Jens-Dominik Muller ◽

Niles A. Pierce

Keyword(s):

Adjoint Methods ◽

Discrete Adjoint

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Fully Implicit Discrete Adjoint Methods

53rd AIAA Aerospace Sciences Meeting ◽

10.2514/6.2015-1491 ◽

2015 ◽

Author(s):

Massimo Biava ◽

Mark Woodgate ◽

George N. Barakos

Keyword(s):

Adjoint Methods ◽

Fully Implicit ◽

Discrete Adjoint

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Fully Implicit Discrete-Adjoint Methods for Rotorcraft Applications

AIAA Journal ◽

10.2514/1.j054006 ◽

2016 ◽

Vol 54 (2) ◽

pp. 735-749 ◽

Cited By ~ 11

Author(s):

Massimo Biava ◽

Mark Woodgate ◽

George N. Barakos

Keyword(s):

Adjoint Methods ◽

Fully Implicit ◽

Discrete Adjoint

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Discrete Adjoint Solution of Unsteady Turbulent Flow in Compressor

Volume 2C: Turbomachinery ◽

10.1115/gt2015-42948 ◽

2015 ◽

Cited By ~ 2

Author(s):

Can Ma ◽

Xinrong Su ◽

Xin Yuan

Keyword(s):

Unsteady Flow ◽

Stokes Equations ◽

Flow Simulation ◽

Adjoint Equations ◽

Navier Stokes ◽

Aerodynamic Optimization ◽

Flow Equations ◽

Discrete Adjoint ◽

Continuous Adjoint ◽

Unsteady Flow Simulation

Unsteady blade row interactions play an important role in the performance of the compressor stages. However, due to the large cost of the unsteady flow simulation, most aerodynamic optimizations of the compressor are based on the steady flow simulation. This paper adopts the time spectral method to reduce the cost of the unsteady flow simulation and a discrete adjoint solver based on the unsteady flow solver has been developed. The unsteady flow equations and the adjoint equations are solved using an in-house code. The in-house code is based on the finite volume method and solves the URANS (Unsteady Reynolds Averaged Navier-Stokes) equations on the multi-block structured mesh. For spatial discretization the 3rd order WENO (Weighted Essentially Nonoscillatory) upwind scheme is used for reconstruction and the convective flux is computed with Roe’s approximate Riemann solver. The widely used one-equation Spalart-Allmaras turbulence model is adopted for the flow simulation. For the adjoint solution, the constant-eddy viscosity assumption is adopted and only the main flow adjoint equations are solved. The adjoint equations are formed in a discrete manner, which leads to more accurate discrete objective function sensitivity than the continuous adjoint method. The present work serves as an essential part of the system for efficient unsteady aerodynamic optimization of turbomachinery.

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