Computation of convective flows using the quasi-hydrodynamic equations (Q1291212)

This paper presents the results of numerical modeling of gravitational and thermocapillary convection in rectangular cavities at small Prandtl numbers. The results are obtained by using the quasi-hydrodynamic system of equations, which is dissipative and has a number of exact physically meaningful solutions. The authors employ the finite difference method to solve the governing equations. The practical necessity for such computations arises due to the fact that periodic oscillations of temperature in metallic melts (liquids at small Prandtl number) present a severe problem in growing semiconducting crystals. The authors show that their results are in agreement with the results obtained from the Navier-Stokes equations. However, unlike the classical system, the quasi-hydrodynamic equations allow to perform numerical computations by using simple explicit difference schemes on coarse grids in a wide range of parameters.