Abstract
Impositions of proper continuity and discontinuity at interfaces between fluid and structures, and internal Dirichlet boundaries in a fluid domain are one of the major topics in development of high accuracy fluid computational method with non-boundary fitted meshes. This paper proposes an extended finite element method (X-FEM) with Lagrange-multiplier method as an advanced solution technique to the problem. The X-FEM with Lagrange-multiplier method, however, has two practical issues in completing the implementation thereof. The first is the domain integral of enriched fluid elements that reproduce the discontinuity. The second is construction of Lagrange-multiplier mesh for imposing the Dirichlet condition at the boundary. This paper examines high-order Gaussian quadrature of the enriched elements and the non-intersection point method for the Lagrange-multiplier. Detailed numerical tests in a fixed boundary problem provide computational guideline of the proposed method. Application to a moving boundary problem demonstrates that the proposed method has scalability to fluid-thin structure interfaces.
