Study of convection in a liquid with a free surface using exponential fitting discretization

The two-dimensional flow of viscous incompressible liquid in a square cavit y with a free boundary and differentially heated vertical sides is consider ed in the present work, The influence of gravitational and thermocapillary convection on temperature and velocity fields is studied in a large range o f dimensionless parameters and similarity criteria using method of exponent ial fitting discretization, Limiting cases of dimensionless parameters are analyzed numerically.