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Inflation of a Balloon
A balloon, initially spherical, is inflated by pumping an airlike fluid through a circular hole as shown in Fig. 1. The inflow is pulsating in the form of a Cosine wave with period 2 s. The minimum and maximum values of the magnitude of the inflow velocity are 0.0 m/s and 2.0 m/s. Initially, the diameter of the balloon is 2 m and the diameter of the circular hole is 0.63 m. The thickness, density and stiffness of the balloon are 2.0 mm, 100 kg/m3 and 1000 N/m2, respectively. The density and viscosity of the fluid are 1.0 kg/m3 and 0.000015 m2/s.
The numerical methods used in this computation were introduced and implemented on parallel computing platforms by the T*AFSM. The set of numerical methods introduced by the T*AFSM over the years and used in this computation includes the DSD/SST formulation [14], the quasidirect FSI method [5, 6], the stabilized spacetime FSI (SSTFSI) technique [7], and a number of special FSI techniques [7]. The main purpose of this test problem is to show that direct and quasidirect coupling techniques have no difficulty with handling the class of problems where there is no outflow boundary. The computation was carried out on the ADA system at Rice University. For more details on this computation, see [7].

Fig. 1. Problem geometry. For details, see [7]. 

Fig. 2. Volumetric flow rate for the inflow and the rate of change for the balloon volume. This shows that our computational technique yields a very good mass balance. For details, see [7]. 

















Fig. 3. Velocity vectors colored by air pressure, from 0 to 4 s. For details, see [7]. 
References
1. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28 (1992) 144.
2. T.E. Tezduyar, M. Behr and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces  The DeformingSpatialDomain/SpaceTime Procedure: I. The Concept and the Preliminary Numerical Tests", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 339351.
3. T.E. Tezduyar, M. Behr, S. Mittal and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces  The DeformingSpatialDomain/SpaceTime Procedure: II. Computation of Freesurface Flows, Twoliquid Flows, and Flows with Drifting Cylinders", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 353371.
4. T.E. Tezduyar, "Computation of Moving Boundaries and Interfaces and Stabilization Parameters", International Journal for Numerical Methods in Fluids, 43 (2003) 555575.
5. T.E. Tezduyar, S. Sathe, R. Keedy and K. Stein, "SpaceTime Techniques for Finite Element Computation of Flows with Moving Boundaries and Interfaces", Proceedings of the III International Congress on Numerical Methods in Engineering and Applied Sciences, Monterrey, Mexico, CDROM (2004).
6. T.E. Tezduyar, S. Sathe, R. Keedy and K. Stein, "SpaceTime Finite Element Techniques for Computation of FluidStructure Interactions", Computer Methods in Applied Mechanics and Engineering, 195 (2006) 20022027.
7. T.E. Tezduyar and S. Sathe, "Modeling of FluidStructure Interactions with the SpaceTime Finite Elements: Solution Techniques", International Journal for Numerical Methods in Fluids, 54 (2007) 855900.
