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Paper detail

A Comprehensive Study of Adjoint-Based Optimization of Non-Linear Systems with Application to Burgers' Equation

In the context of adjoint-based optimization, nonlinear conservation laws pose significant problems regarding the existence and uniqueness of both direct and adjoint solutions, as well as the well-posedness of the problem for sensitivity analysis and gradient-based optimization algorithms. In this paper we will analyze the convergence of the adjoint equations to known exact solutions of the inviscid Burgers' equation for a variety of numerical schemes. The effect of the non-differentiability of the underlying approximate Riemann solver, complete vs. incomplete differentiation of the discrete schemes and inconsistencies in time advancement will be discussed.

preprint2022arXivOpen access
Alexandru FiklVincent Le ChenadecTaraneh SayadiPeter J. Schmid
physics.comp-ph
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Alexandru FiklVincent Le ChenadecTaraneh SayadiPeter J. Schmid

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