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Entropy and adjoint methods. (English) Zbl 1431.76082
Summary: Aerodynamic drag can be partially approximated by the entropy flux across fluid domain boundaries with a formula due to Oswatitsch. In this paper, we build the adjoint solution that corresponds to this representation of the drag and investigate its relation to the entropy variables, which are linked to the integrated residual of the entropy transport equation. For inviscid isentropic flows, the resulting adjoint variables are identical to the entropy variables, an observation originally due to [K. J. Fidkowski and P. L. Roe, SIAM J. Sci. Comput. 32, No. 3, 1261–1287 (2010; Zbl 1213.65142)], while for non-isentropic flows there is a significant difference that is explicitly demonstrated with analytic solutions in the shocked quasi-1D case. Both approaches are also investigated for viscous and inviscid flows in two and three dimensions, where the adjoint equations and boundary conditions are derived. The application of both approaches to mesh adaptation is investigated, with especial emphasis on inviscid flows with shocks.
76G25 General aerodynamics and subsonic flows
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics, general
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
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