Scalable discrete adjoint for the transient Savage–Hutter equation on the primal consistent adaptive grid

Computing the adjoint for a transient non-linear hyperbolic PDE, like the Savage–Hutter equation for modeling dry granular mass flows, is a challenge with often unaffordable computing and memory costs. The challenges are further compounded for an adaptive mesh refinement (AMR) parallel code. For legacy codes, addressing these difficulties are constrained with the original design and data structures which refactoring those to be well-suited for the adjoint computation may end up to almost a new design of the code. In this paper, we develop a framework to compute the discrete adjoint for our parallel finite volume solver which supports AMR with a lower computational cost of the forward run. This is achieved using appropriate data structures and methods to reuse the computation of the forward AMR and repartitioning and eliminating any interpolation and prolongation errors in computing the adjoint. Furthermore, using analytical differentiation of the discrete forward solver, approximation error was avoided and the adjoint computed accurately. We illustrate our approach for the Savage–Hutter equation and use the adjoint for the gradient enhanced surrogate construction.