Discretization Error Estimation in Multidisciplinary Simulations

This paper proposes methods to estimate the discretization error in the system output of coupled multidisciplinary simulations. 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. A classic example of multidisciplinary analysis involves fluid-structure interaction, where the element sizes in fluid and structure meshes are typically different. The general case of three-dimensional steady-state problems is considered in the current paper, where mesh refinement is possible in all three spatial directions for each discipline. Two aspects of discretization error, which 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 the discretization error for the previously 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.