Parallel Implementation and Assessment of Adjoint-Based Data Assimilation with the Hybridizable DG algorithm

This work develops an adjoint-based data assimilation algorithm for flows governed by the incompressible Navier-Stokes (N-S) equations, aiming to minimize discrepancies between simulations and PTV or PIV experiments. The problem is formulated as minimizing the velocity differences between numerical and experimental data, with the N-S equations as equality constraints using Lagrange multipliers. The optimization parameters are the initial condition and time-varying Dirichlet boundary conditions for velocity. The forward and adjoint solutions for the N-S system are obtained using an arbitrarily high-order Hybridizable Discontinuous Galerkin (HDG) method. The optimization problem is solved by the quasi-Newton method.

Given the high computational costs for assimilating flows of a wide range of scales, a parallel implementation of the adjoint-based assimilation algorithm is completed. Key features of the assimilation solver involve a scalable iterative solution scheme to solve the HDG equations, a parallel quasi-Newton solver with the L-BFGS approximation to solve the nonlinear optimization, and memory-efficient I/O strategy for the forward and adjoint computation.

The parallel performance and scalability of the data assimilation solver will be discussed. Effects of data sample density and spatial order of the assimilation solver on assimilation accuracy will be examined. Assimilation results for canonical and realistic flow data will be presented.