Stabilized and Coupled Meshfree/Meshbased Method for Fluid-Structure Interaction ProblemsA

Abstract

A method is presented which combines features of meshfree and meshbased methods in order to enable the simulation of complex flow problems involving large deformations of the domain or moving and rotating objects. Conventional meshbased methods like the finite element method have matured as standard tools for the simulation of fluid and structure problems. They offer efficient and reliable approximations, provided that a conforming mesh with sufficient quality can be maintained throughout the simulation. This, however, may not be guaranteed for complex fluid and fluid-structure interaction problems. Meshfree methods on the other hand approximate partial differential equations based on a set of nodes without the need for an additional mesh. Therefore, these methods are frequently used for problems where suitable meshes are prohibitively expensive to construct and maintain. This advantage of meshfree methods comes at the price of being considerably more time-consuming than their meshbased counterparts. A coupled meshfree/meshbased fluid solver is developed which combines the advantages of both methodologies. A meshfree method, closely related to the element-free Galerkin method, is used in small parts of the domain where a mesh is difficult to maintain, whereas the efficient meshbased finite element method is employed in the rest of the domain. Major steps in the development of the coupled flow solver are the extension of standard stabilization methods to meshfree approximations, and the realization of the coupling on the level of the shape functions, which are involved in the approximation of the governing equations. Concerning the stabilization, it is found that the same structure of the standard stabilization schemes may be used for meshfree approximations, however, the aspect of the stabilization parameter, weighing the stabilization terms, requires special care. For the coupling, these requirements for a reliable stabilization lead to modifications of the existing coupling approaches. The stabilized and coupled flow solver is verified and used for the simulation of geometrically complex fluid-structure interaction problems. Conventional meshbased methods are not suitable for the approximation of these test cases due to the prohibitively large deformations of the geometry.