ABSTRACT

The stationary problem on planar flow of viscous incompressible fluid with evaporating non-compact free boundary is considered. The solvability of this problem and smoothness of its solution are studied. The technique of artificial restriction of the domain is used for obtaining the approximate solution. It is shown that if the restricted domain is sufficiently wide, then the solution on it differs little from that on the original domain. A finite-element approximation of the problem on the restricted domain is constructed. For this the curvilinear C 1-elements are used along the free boundary to approximate velocity and temperature and C 0-elements – for pressure. Special algorithm for mesh refinement in the vicinity of the corner point of the boundary is presented to obtain optimal estimates of approximation. Also estimates for the rate of convergence of the finite-element solution to the exact one are given.

We consider the problem on viscous flow with free evaporating surface, which has numerous applications in coating and drying processes encountered during the production of paper and polymers. The surface of the fluid is non-compact, and the gravitational field and heat sources are taken into account as external factors.