abstract 82

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

82

Kinetic undercooling regularization of the Hele-Shaw problem with obstacles

Sergei Rogosin

Preliminary results for an asymptotic analysis are provided for a new real-variable Hele-Shaw model with obstacles in the flow. The  corresponding free boundary value problem is formulated in terms of two unknowns, parametrization of the free boundary and Green's type (or the Robin-Neumann) function for the Laplace equation subject to a mixed boundary value problem. Mixed boundary conditions are the Neumann condition on the boundary of obstacles and the third type (or the Robin) condition on the free boundary. The obstacles are either fixed in the flow or can move. To avoid, at least partly, the possible instability we incorporate the kinetic undercooling condition into the model.

Keywords: Hele-Shaw flow; obstacles; Robin-Neumann function; kinetic undercooling condition.

Cite this paper:

Rogosin S. 

Kinetic undercooling regularization of the Hele-Shaw problem with obstacles.

Bull. Comput. Appl. Math. (Bull CompAMa)

Vol. 11, No.1 pp.251-263, 2023.