Note: Different Date and Location
Lozinski021105 Abstract:
We present an approach to the simulation of incompressible viscous flow past moving, possibly deformable bodies of negligible mass whose position and shape are described by a small number of parameters. The motion of the bodies results from the hydrodynamic forces exerted by the surrounding fluid and from the external forces such as gravitation. We believe that this technique is well suited for the numerical simulation of the motion of gas bubbles, which arises, for example, in the modeling of aluminum production cells. For each bubble the force balance equations are obtained by equating to zero the work of the forces applied on the bubble surface (hydrodynamic forces, pressure inside the bubble and the surface tension) for the displacements compatible with the constraints imposed on the shape of the bubbles. We illustrate this approach by two examples of bubble form families in 2D: rigid ellipses and deformable ellipses with constant area. Some results in 3D will also be presented.
The numerical treatment of the governing equations is based on a variant of the fictitious domain technique [R. Glowinski et al, J. Comp. Phys. 169, 363-426 (2001)] and the Gauge method [W. E and J.-G. Liu, Comm. Math. Sci 1, 317-323 (2003)]. The coalescence of bubbles is taken into account by assuming that the coalescence process starts when two bubbles are sufficiently close and the small bubble is then swallowed up by the large one in a small number of time steps.
Future talks in Scientific Computing Seminar
Feb. 17: Hans-Joachim Bungartz, IPVS, Universitaet Stuttgart, Germany.
Mar. 3: Bernd Simeon, Center of Mathematics, Munich University of Technology, Germany.
Apr. 28: Gene H Golub, Department of Computer Science, Stanford University.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.