Adjoint computational methods for 2D inverse design of linear transport equations on unstructured grids

Abstract

We address the problem of inverse design of linear hyperbolic transport equations in 2D heterogeneous media. We develop numerical algorithms based on gradient-adjoint methodologies on unstructured grids. While the flow equation is compulsorily solved by means of a second order upwind scheme so to guarantee sufficient accuracy, the necessity of using the same order of approximation when solving the sensitivity or adjoint equation is examined. Two test cases, including Doswell frontogenesis, are analysed. We show the convenience of using a low order method for the adjoint resolution, both in terms of accuracy and efficiency. An analytical explanation for this fact is also provided in the sense that, when employing higher order schemes for the adjoint problem, spurious high frequency numerical components slow down the convergence process.