Browse > Article
http://dx.doi.org/10.6112/kscfe.2015.20.3.27

DEVELOPMENT OF A PRECONDITIONED ADJOINT METHOD FOR ALL-SPEED FLOW ANALYSES OF QUASI ONE-DIMENSIONAL EULER EQUATIONS  

Lee, H.R. (Dept. of Aerospace Engineering, Inha Univ.)
Lee, S. (Dept. of Aerospace Engineering, Inha Univ.)
Publication Information
Journal of computational fluids engineering / v.20, no.3, 2015 , pp. 27-34 More about this Journal
Abstract
In this study, preconditioned adjoint equations for the quasi one-dimensional Euler equations are developed, and their computational benefit at all speed is assessed numerically. The preconditioned adjoint equations are derived without any assumptions on the preconditioning matrix. The dissipation for Roe type numerical flux is also suggested to scale the dissipation term properly at low Mach numbers as well as at high Mach numbers. The new preconditioned method is validated against analytical solutions. The convergence characteristics over wide range of Mach numbers is evaluated. Finally, several inverse designs for the nozzle are conducted and the applicability of the method is demonstrated.
Keywords
CFD; Adjoint method; Precondition; All-speed Range; Quasi 1-D Nozzle;
Citations & Related Records
연도 인용수 순위
  • Reference
1 1988, Jameson, A., "Aerodynamic Design via Control Theory," Journal of Scientific Computing, Vol.3, No.3, pp.233-260.   DOI
2 1999, Anderson, W.K. and Venkatakrishnan, V., "Aerodynamic Design Optimization on Unstructured Grids with a Continuous Adjoint Formulation," Computers & Fluids, Vol.28, No.4, pp.443-480.   DOI
3 2006, Lee, S.W. and Kwon, O.J., "Aerodynamic Shape Optimization of Hovering Rotor Blades in Transonic Flow Using Unstructured Meshes," AIAA Journal, Vol.44, No.8, pp.1816-1825.   DOI
4 2012, Mader, C.A. and Martins, J., "Optimal Flying Wings: A Numerical Optimization Study," 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.
5 1987, Turkel, E., "Preconditioned Methods for Solving the Incompressible and Low Speed Compressible Equations," Journal of computational physics, Vol.72 No.2, pp.277-298.   DOI
6 1993, Choi, Y.H. and Merkle, C.A., "The Application of Preconditioning in Viscous Flows," Journal of Computational Physics, Vol.105, No.2, pp.207-223.   DOI
7 1996, Eriksson, L.E., "A Preconditioned Navier-Stokes Solver for Low Mach Number Flows," ECCOMAS computational fluid dynamics conference.
8 1995, Weiss, J.M. and Smith, W.A., "Preconditioning Applied to Variable and Constant Density Flows," AIAA Journal, Vol.33, No.11, pp.2050-2057.   DOI
9 2007, Asouti, V.G., Zymaris, A.S., Papadimitriou, D.I. and Giannakoglou, K.C., "Continuous and Discrete Adjoint Approaches for Aerodynamic Shape Optimization with Low Mach Number Preconditioning," International journal for Numerical Methods in Fluids, Vol.57, No.10, pp.1485-1504.   DOI
10 2014, Boger, D.A. and Paterson, E.G., "A Continuous Adjoint Approach to Design Optimization in Cavitating Flow using a Barotropic Model," Computer & Fluids, Vol.101, pp.155-169.   DOI
11 2001, Giles, M.B. and Pierce, N.A., "Analytic Adjoint Solutions for the Quasi-one-dimensional Euler Equations," Journal of Fluid Mechanics, Vol.426, pp.327-345.   DOI
12 2009, Volpe, E.V. and de Castro Santos L.C., "Boundary and Internal Conditions for Adjoint Fluid-flow Problems," Journal of Engineering Mathematics, Vol.65, No.1, pp.1-24.   DOI
13 2013, Thang, N., "Design Optimization of Quasi-One Dimensional Nozzle Using Adjoint Method," Master Thesis, Ulsan University Korea.
14 2002, Xie, L., "Gradient-Based Optimum Aerodynamic Design Using Adjoint Methods," Ph. D. Thesis, Virginia Polytechnic Institute and State University, USA.
15 2013, lozanorc, "Remarks on The Numerical Solution of the Adjoint Quasi-one-dimensional Euler Equations," International Journal for Numerical Methods in Fluids, Vol.69, No.5, pp.1-23.
16 1981, Roe, R.L., "Approximate Riemann Solvers, Parameter Vector and Difference Scheme," Journal of Computational Physics, Vol.43, No.2, pp.357-372.   DOI   ScienceOn
17 1982, Beam, R.M. and Warming, R.F., "Implicit Numerical Methods for the Compressible Navier Stokes and Euler Equations," von Karman Institute for Fluid Dynamics Lecture Series.