Application of Lagrange multipliers for coupled problems in fluid and structural interactions

One challenging aspect of the computation of multidisciplinary phenomenas is the accurate prediction of physical effects in space and time domain. The present paper focuses on the data transmission over non-matching grids. To fulfil energy conservation, a weak formulation of the continuity conditions on the common interface is used by introducing Lagrange multipliers. The coupling approach of the full system utilizes Hamilton’s principle. Several transfer schemes based on Galerkin’s method, dual-Lagrange multipliers, or the Sobolev-norm are presented. Two strategies to improve the accuracy of the transmission method are shown; namely use of merged mesh and quadtree-based h-refinement of the integration mesh. Simulations of an oscillating three-dimensional wing structure are presented to show the applicability and performance of the concepts. Further, computations of thin-walled structures with nonlinear behavior in transonic fluid flows are given. The impact of the presented transfer methods on the accuracy of the results are discussed.