High-order Gaussian quadrature in X-FEM with the Lagrange-multiplier for fluid-structure coupling

This paper presents an alternative choice for the construction of integration cells and an additional Lagrange-multiplier mesh in computations using the eXtended finite element method (X-FEM) with the Lagrange-multiplier. The proposed computational target is flow simulations with the Dirichlet boundary conditions on a non-boundary-fitted mesh. The methods studied in this paper make use of a high-order Gaussian quadrature to relax the complexity in implementing the X-FEM with the Lagrange-multiplier. The first of these is the straightforward employment of the Gaussian quadrature as a numerical integration scheme for enriched fluid elements. The second makes use of free Lagrange-multipliers that are not placed at crossing points between fluid elements and the Dirichlet boundary. This method considers the scalability of fluid-structure and fluid-thin object interactions. A unique benchmark problem in which a computational fluid domain is partitioned into two physical domains with the Lagrange-multipliers is introduced to validate the proposed method. Numerical results show that this method is applicable in practice with acceptable numerical accuracy. Copyright (C) 2010 John Wiley & Sons, Ltd.