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arXiv · 2209.03270

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

Alexandru Fikl·Vincent Le Chenadec·Taraneh Sayadi·Peter J. Schmid
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Abstract

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.

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Alexandru Fikl, Vincent Le Chenadec, Taraneh Sayadi, Peter J. Schmid. 2022-09-07. A Comprehensive Study of Adjoint-Based Optimization of Non-Linear Systems with Application to Burgers' Equation. https://doi.org/10.2514/6.2016-3805

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