Continuous and discrete adjoints to the Euler equations for fluids

SUMMARY Adjoints are used in optimization to speed‐up computations, simplify optimality conditions or compute sensitivities. Because time is reversed in adjoint equations with first‐order time derivatives, boundary conditions, and transmission conditions through shocks can be difficult to understand. In this article, we analyze the adjoint equations that arise in the context of compressible flows governed by the Euler equations of fluid dynamics. We show that the continuous and discrete adjoints computed by automatic differentiation agree numerically; in particular, the adjoint is found to be continuous at the shocks and usually discontinuous at contact discontinuities by both.Copyright © 2011 John Wiley & Sons, Ltd.