Abstract
This article presents a methodology whereby adjoint solutions for partitioned multiphysics problems can be computed efficiently, in a way that is completely independent of the underlying physical sub-problems, the associated numerical solution methods, and the number and type of couplings between them. By applying the reverse mode of algorithmic differentiation to each discipline, and by using a specialized recording strategy, diagonal and cross terms can be evaluated individually, thereby allowing different solution methods for the generic coupled problem (for example block-Jacobi or block-Gauss-Seidel). Based on an implementation in the open-source multiphysics simulation and design software SU2, we demonstrate how the same algorithm can be applied for shape sensitivity analysis on a heat exchanger (conjugate heat transfer), a deforming wing (fluid–structure interaction), and a cooled turbine blade where both effects are simultaneously taken into account.
Highlights
Especially those concerned with fluid flow problems, one finds important cases where multiphysics effects play a crucial role in the design of new parts
For optimization methods relying on discrete adjoint solutions, the couplings between the different physics models must be considered to obtain accurate sensitivities
This final test case highlights the modularity of the approach presented in this paper. As it allows for handling multiphysics setups where the number and type of physical domains is unknown, and for arbitrary interfaces between them. In this example a single zone acts as a heat conducting body with a conjugate heat transfer (CHT) interface to a surrounding fluid zone, simultaneously, the same physical interface receives solid displacements by being marked as an fluid–structure interaction (FSI) interface
Summary
Especially those concerned with fluid flow problems, one finds important cases where multiphysics effects play a crucial role in the design of new parts. The differentiation of multiphysics solvers for topology optimization is common (Dunning et al 2015; Lundgaard et al 2018; Picelli et al 2020) In such applications solvers tend to be of the monolithic type (for example so that locations of the domain can be either fluid or solid), or the discrete adjoint methodology is developed for the primal methods used. G(j) is regarded as a fixed-point iterator with respect to the solution variables ui(j) and all ui(k) with j ≠ k as solver parameters, this distinction will later be used to define adjoint cross terms This view naturally maps to the common block-Gauss-Seidel (BGS) solution approach, but in practice the solution method for the primal coupled problem is not restricted. Throughout this article, subscripts will indicate the zone number, whereas superscripts refer to the iteration count unless otherwise specified
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