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Discrete direct and adjoint sensitivity analysis for arbitrary Mach number flows
Author(s) -
Balasubramanian R.,
Newman J. C.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1558
Subject(s) - sensitivity (control systems) , solver , linearization , inviscid flow , unstructured grid , mathematics , mach number , stencil , grid , flux limiter , laminar flow , computer science , discretization , mathematical optimization , computational science , mathematical analysis , geometry , physics , mechanics , nonlinear system , quantum mechanics , electronic engineering , engineering
Parallel discrete direct and adjoint sensitivity analysis capabilities are developed for arbitrary Mach flows on mixed‐element unstructured grids. The discrete direct and adjoint methods need a consistent and complete linearization of the flow‐solver to obtain accurate derivatives. The discontinuous nature of the commonly used unstructured flux‐limiters, like Barth–Jespersen and Venkatakrishnan, make them unsuitable for sensitivity analysis. A modification is proposed to make these limiters piecewise continuous and numerically differentiable , without compromising the monotonicity conditions. An improved version of Symmetric Gauss–Seidel that significantly reduces the computational cost is implemented. A distributed‐memory message passing model is employed for the parallelization of sensitivity analysis solver. These algorithms are implemented within a three‐dimensional unstructured grid framework and results are presented for inviscid, laminar and turbulent flows. Copyright © 2005 John Wiley & Sons, Ltd.