Extended Space-time Finite Elements for Two-fluid Flows in Fluid-structure Interaction

摘要

To investigate interaction phenomena of elastic bodies and free surface flow a numerical model is introduced. While the incompressible Navier-Stokes equations are used to model two-fluid flow in an Eulerian view, the linear elastic solid is described by nonlinear kinematics in a total Lagrangian manner. A discretization method based on stabilized space-time finite elements is applied for a monolithic analysis of immiscible two-fluid flow around lightweight elastic structures. The use of the level set method provides an implicitly given description of the moving fluid domains and information on geometrical properties of the topological changing fluid-fluid interface. The choice of a proper enriched basis within the partition of unity concept enables the method to capture strong and weak discontinuous solutions in the flow introduced by interfacial jump conditions and different material properties of the two fluids. Conservative coupling of fluid and solid is ensured by Lagrangian multipliers. The uniform approach in space and time allows a continuous matching of the fluid domain to the structural motion. Numerical examples demonstrate the preservation of convergence properties even in the existence of solutions containing jumps and discontinuous gradients. Further examples emphasize the ability of the method to handle complex free surface flow situations and their interplay with elastic bodies.