Space-time Galerkin Finite Element Method Research Articles

A variational projection scheme for nonmatching surface-to-line coupling between 3D flexible multibody system and incompressible turbulent flow

This paper is concerned with the partitioned iterative formulation to simulate the fluid-structure interaction of a nonlinear multibody system in an incompressible turbulent flow. The proposed formulation relies on a three-dimensional (3D) incompressible turbulent flow solver, a nonlinear monolithic elastic structural solver for constrained flexible multibody system and the nonlinear iterative force correction scheme for coupling of the turbulent fluid-flexible multibody system with nonmatching interface meshes. While the fluid equations are discretized using a stabilized Petrov–Galerkin formulation in space and the generalized-α updates in time, the multibody system utilizes a discontinuous space-time Galerkin finite element method. We address two key challenges in the present formulation. Firstly, the coupling of the incompressible turbulent flow with a system of nonlinear elastic bodies described in a co-rotated frame. Secondly, the projection of the tractions and displacements across the nonmatching 3D fluid surface elements and the one-dimensional line elements for the flexible multibody system in a conservative manner. Through the nonlinear iterative correction and the conservative projection, the developed fluid-flexible multibody interaction solver is stable for problems involving strong inertial effects between the fluid-flexible multibody system and the coupled interactions among each multibody component. The accuracy of the proposed coupled finite element framework is validated against the available experimental data for a long flexible cylinder undergoing vortex-induced vibration in a uniform current flow condition. Finally, a practical application of the proposed framework is demonstrated by simulating the flow-induced vibration of a realistic offshore floating platform connected to a long riser and an elastic mooring system.

Space-time finite elements for the analysis of transient wave propagation in unbounded layered media

A new method is proposed for the analysis of transient wave propagation in a layered stratum. It makes use of the separation of variables technique and reduces the spatial dimension of analysis to one. The resulting system of hyperbolic partial differential equations is solved via element-by-element computations based on a space-time Galerkin finite element method. This method is shown to be more efficient than the methods based on convolution. Numerical examples are presented to illustrate the effectiveness of the method. Current limitations and possible extensions are also discussed.