A new approach to estimate discretization error for multidisciplinary and multidirectional mesh refinement

Discretization error estimation in the system output of multidisciplinary simulations, where each disciplinary simulation has multidirectional mesh refinement, is considered in this paper. In such systems, the governing equations for each discipline are numerically solved by a different computational code, and each discipline has different mesh size parameters. The general case of three-dimensional steady state problems is considered in the current paper. Two aspects of discretization error, that are of interest in multidisciplinary analysis, are considered: disciplinary mesh sizes, and the mismatch of disciplinary meshes at the interface at which boundary conditions are exchanged. Two alternate representations for discretization error for the above specified generic case are presented: (1) ignoring mesh mismatch at the interface, and (2) considering mesh mismatch at the interface. Polynomial, rational function, and Gaussian process error models are used to represent the discretization error. The proposed error models are illustrated using a three-dimensional fluid-structure interaction problem of an aircraft wing using ANSYS multifield module.