High‐order gaussian quadrature in X‐FEM with the lagrange‐multiplier for fluid–structure coupling

Abstract

Abstract 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 © 2010 John Wiley & Sons, Ltd.