Adjoint‐based design of shock mitigation devices

Abstract

SUMMARYUnsteady Euler and adjoint Euler solvers have been combined in order to aid in the design of shock mitigation devices. The flowfield is integrated forward in time and stored. The adjoint is then integrated going backwards in time, restoring and interpolating the saved Euler solution to the current point in time. The gradient is obtained from a surface integral formulation during the adjoint run. Comparisons of adjoint-based and finite-differencing gradients for different verification cases show less than 10% deviation. The results obtained indicate that this is a very cost-effective way to obtain the gradients of an objective function with respect to surface design changes. Moreover, as the sensitivity information is determined over a complete surface, the procedure provides considerable insight, and can efficiently facilitate the design of shock mitigation devices such as architecturally appealing blast walls.

Recent advances in computational wind engineering and fluid–structure interaction

“…This begs the question whether the influence of the geometry could not be obtained via adjoints (Jameson, 1988;Reuther et al, 1999;Mohammadi and Pironneau, 2001;Soto et al, 2004;Stück et al, 2010). The cost or objective function is the load on the structure being analized.…”

Running large‐scale CFD applications on Intel‐KNL–based clusters

“…The code has had a long history of relevant applications involving compressible flow simulations in the areas of transonic flow, [21][22][23][24][25][26] store separation, [27][28][29][30][31] blast-structure interaction, [32][33][34][35][36][37][38][39][40][41] incompressible flows, 14,[42][43][44][45][46] free-surface hydrodynamics, [47][48][49] dispersion, 50-53 patient-based hemodynamics, 21,54-57 and aeroacoustics. 58…”

Partitioned solution of an unsteady adjoint for strongly coupled fluid-structure interactions and application to parameter identification of a one-dimensional problem

“…These methods can find the global optimum of non-differentiable functions but the number of cost function evaluations generally increases drastically as the number of parameters increases. As a result, the computational cost becomes prohibitive, especially when simulation of the forward problem is time-consuming [9].…”

“…Moreover, obtaining the gradient is in most cases not trivial. Because the number of parameters is high in the application of interest, gradient-based optimisation is applied in this work [9]. Both the gradient and the exact Hessian of the cost function are used by another class of optimisation algorithms, including Newton's method.…”

“…For example, an adjoint solver of the unsteady Euler equations has been used for the optimisation of blast mitigation devices [9]. Also adjoint solvers of the unsteady Navier-Stokes equations exist [35], even for moving and deforming grids [36].…”