We present a new local-in-time discrete adjoint-based methodology for solving design optimization problems arising in unsteady aerodynamic applications. The new methodology circumvents storage requirements associated with the straightforward implementation of a global adjoint-based optimization method that stores the entire flow solution history for all time levels. This storage cost may quickl...

We prove a result of uniqueness of the entropy weak solution to the Cauchy problem for a class of nonlinear hyperbolic systems of conservation laws, that includes in particular the p-system of isentropic gas dynamics. Our result concerns weak solutions satisfying the, as we call it, Wave Entropy Condition or WEC, for short, introduced in this paper. The main feature of this condition is that it...

Adjoint methods form a class of importance sampling methods that are used to accelerate Monte Carlo (MC) simulations of transport equations. Ideally, adjoint methods allow for zero-variance MC estimators provided that the solution to an adjoint transport equation is known. Hybrid methods aim at (i) approximately solving the adjoint transport equation with a deterministic method; and (ii) use th...

The objective of this note is to show how one can combine Polynomial Chaos Expansions (PCE) and adjoint theory to efficiently obtain sensitivities for robust optimal control. A non-intrusive PCE method is used to analyze the constraint equations for the state (which depends on uncertain inputs), namely the governing equations of the dynamical system. Adjoint solutions are constructed for each o...

| Lagrangian stochastic models and algorithms are constructed and justi ed for solving the footprint problem, namely, the problem of calculation of the mean concentration and the ux of particles at a xed point released from a source arbitrarily situated in the space. The direct and adjoint Monte Carlo algorithms are suggested, and rigorous justi cations are given. Two di erent backward trajecto...