Publikacje

Abstract:

This paper presents an extended finite element method applied to solve phasechange problems taking into account natural convection in the liquid phase. It is as-sumed that the transition from one state to another, e.g., during the solidification ofpure metals, is discontinuous and that the physical properties of the phases vary acrossthe interface. According to the classical Stefan condition, the location, topology andrate of the interface changes are determined by the jump in the heat flux. The incom-pressible Navier–Stokes equations with the Boussinesq approximation of the naturalconvection flow are solved for the liquid phase. The no-slip condition for velocityand the melting/freezing condition for temperature are imposed on the interface usingpenalty method. The fractional four-step method is employed for analysing conjugateheat transfer and unsteady viscous flow. The phase interface is tracked by the levelset method defined on the same finite element mesh. A new combination of extendedbasis functions is proposed to approximate the discontinuity in the derivative of thetemperature, velocity and the pressure fields. The single-mesh approach is demon-strated using three two-dimensional benchmark problems. The results are comparedwith the numerical and experimental data obtained by other authors.

POWRÓT

Strona główna > Publikacje

The modified XFEM for solving problems of a phase change with natural convection