Modeling Transport Processes in Nonlinear Systems: The Example of Solidification and Convection

Abstract

Although convection is commonly associated with phase change in the earth, numerical modeling of phase change and convection has not received as much attention as the modeling of either process alone. Recently formulated continuum models of phase change and convection are readily amenable to numerical solution. In the continuum models, one set of equations is used over the entire solution domain. Iteration within each time step accommodates the nonlinearity and strong coupling of the transport equations and the supplementary equations which relate enthalpy to temperature, fraction solid, and composition under the assumption of local thermodynamic equilibrium. We present a comparison of a set of laboratory experiments of the solidification and convection of aqueous ammonium chloride solution with two-dimensional numerical experiments using the continuum model. The numerical experiments reproduce the behavior observed in the laboratory experiments and show the profound effects of solidification on convective systems.