## Team for Advanced Flow Simulation and Modeling |

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## Multiscale Space-Time TechniqueThe Enhanced-Discretization Space-Time Technique (EDSTT) provides a multiscale space-time framework where fluid-structure interaction (FSI) computations can be carried efficiently and accurately even when the structural dynamics part requires a much smaller time-step size. Only the time-step size for one or a few layers of fluid mechanics elements needs to match the structural dynamics time-step size, and for the rest of the fluid mechanics elements the time-step size is determined based on the requirements of the fluid dynamics part. The EDSTT was introduced in [1-2], and the test computations were reported in [3]. The EDSTT is based on using, in the context of the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation [4-7], multiscale function spaces associated with multiple space-time finite element meshes. For the fluid mechanics part, the second space-time mesh, which has the smaller time-step size, is built on top of the first one, adjacent to the structure and covering only one or a few layers of the first mesh. The efficiency of the EDSTT becomes even more dramatic when the structural dynamics part has a lower dimension than the fluid dynamics part. In the EDSTT, the two different time-step sizes are used in the fluid dynamics part in an implicit fashion, and therefore the technique possesses the desirable features of the implicit methods. In the 2D FSI test problem reported in [3], flow past a thin, flexible beam is computed with a structural dynamics time-step size that has to be 20 times smaller than the fluid dynamics time-step size.
## References1. T. Tezduyar, "Finite Element Interface-Tracking and Interface-Capturing Techniques for Flows with Moving Boundaries and Interfaces", ASME Paper IMECE2001/HTD-24206, 2. T.E. Tezduyar, "Finite Element Methods for Fluid Dynamics with Moving Boundaries and Interfaces", Chapter 17 in 3. T.E. Tezduyar and S. Sathe, "Enhanced-Discretization Space-Time Technique (EDSTT)", 4. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", 5. T.E. Tezduyar, M. Behr and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces -- The Deforming-Spatial-Domain/Space-Time Procedure: I. The Concept and the Preliminary Numerical Tests", 6. T.E. Tezduyar, M. Behr, S. Mittal and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces -- The Deforming-Spatial-Domain/Space-Time Procedure: II. Computation of Free-surface Flows, Two-liquid Flows, and Flows with Drifting Cylinders", 7. T.E. Tezduyar, "Computation of Moving Boundaries and Interfaces and Stabilization Parameters", |