An exponentially fitted enthalpy control volume algorithm for coupled fluid flow and heat transfer

Abstract

This paper develops an efficient numerical method for solving the coupled fluid flow and heat transfer with solidification problem. The governing equations are the continuity equation, the Navier-Stokes equations and the convection-diffusion equation with a source term due to phase change. Fluid flow in the mushy region is modeled on the basis of Darcy's law for porous media and the solidification process is simulated using a single domain approach via the use of an enthalpy scheme for the convection-diffusion equation. The formulation of the numerical method is cast into the framework of the Petrov-Galerkin finite element method with a step test function across the control volume and locally constant approximation to the fluxes of heat and fluid. The formulation leads to the derivation of exponential interpolating functions for the control volume. The use of the exponentially fitted control volume improves the accuracy of results especially for problems with sharp interior or boundary layers such as the solution around the solidification front. The method is then illustrated through a numerical example.