The adjoint characteristics boundary conditions for the treatment of multi-block grid interface

Adjoint equations have been used for some time in optimal control theory. The adjoint method has played a prominent role in aerodynamic design due to the flexibility it offers in terms of choosing the flow physics model and cost functions. However, most of the applications in the literature are limited to simple geometries. This paper presents a methodology to deal with complex geometries when using adjoint based optimization technique. Complex geometries are meshed in a fashion such that the whole domain has been divided in multiple simple blocks so that each block is considered independently. The issue arises when the communication of the information at the interfaces of these blocks is considered. A method has been provided to ensure correct communication based on the direction of the propagation of information. The direction of propagation of information and the correction is determined based on the characteristics of the flow field.