DSD/SST Formulation
The Deforming-Spatial-Domain/Stabilized-Space-Time (DSD/SST) finite element formulation has been introduced in two articles:
- 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 tests, Computer Methods in Applied Mechanics and Engineering, 94 (1992) 339–351.
[Preprint PDF (680K)] [Elsevier PDF (998K)] - 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. Computer Methods in Applied Mechanics and Engineering, 94 (1992) 353–371.
[Preprint PDF (4054K)] [Elsevier PDF (1405K)]
Additional examples and details can be found in the theses:
- M. Behr, Stabilized Finite Element Methods for Incompressible Flows with Emphasis on Moving Boundaries and Interfaces, Ph.D. thesis, Department of Aerospace Engineering and Mechanics, University of Minnesota, (1992).
[Abstract and Chapter Links] - S. Mittal, Stabilized Space-Time Finite Element Formulations for Unsteady Incompressible Flows Involving Fluid-Body Interactions, Ph.D. thesis, Department of Aerospace Engineering and Mechanics, University of Minnesota, (1992).
The formulation uses the concept of space-time discretization (simultaneous discretization in space and time via finite elements) together with least-squares-type stabilization to solve problems governed by the Navier-Stokes equations in deforming domains. The first paper (submitted in 1990, appeared in 1992) has been cited over 280 times according to ISI.
The DSD/SST is used at CATS today to solve a variety of fluid flow problems that involve moving boundaries and interfaces, from free-surface flows in spillways and channels, to blood flows in centrifugal and axial rotary ventricular assist devices, flows involving colloidal aggregates, as well as flows around fully-appended helicopters and submarines.
