The numerical solution of two-dimensional moving boundary problems using curvilinear co-ordinate transformations

Abstract

A numerical method is described for the solution of two-dimensional moving boundary problems by tansforming the curved, fixed and moving boundaries in the originalco-ordinate system (x,y) into an orthogonal or, in general, nonorthogonal curvilinear system (ξ,η) such that the curved boundaries become (ξ,η) co-ordinate lines. All computations are then carried out in the transformed region using a fixed, rectangular (ξ,η) mesh which corresponds to a moving, non-rectangular (x,y) mesh. A one-phase, two-dimensional problem is solved by using two different such transformations and the results are compared with those from finite-element, enthalpy and isotherm migration methods.