The inverse design of a linear transport equation using the gradient-adjoint and MMOC schemes

The inverse design of transport equations can be approached using a gradient-adjoint methodology. In this methodology, the numerical schemes used for solving the adjoint problem determine the direction of descent in the iterative algorithm, which ultimately affects the CPU time consumed during the inverse design process. As the CPU time represents a significant bottleneck, it is essential to use efficient and accurate schemes for the adjoint problem. We proposed the use of the Modified Method of Characteristics (MMOC). Although the MMOC fails to preserve certain integral identities satisfied by the solution of the differential equations, it remains computationally competitive. In this work, we evaluated the computational performance of the MMOC in comparison with the Lax-Friedrichs and Lax-Wendroff schemes, in the context of the inverse design. By testing the Doswell frontogenesis equation, we observed that the MMOC can offer more efficient and accurate computations under more severe simulation configurations. 2020 MSC: 00-01, 99-00