A variable time step Galerkin method for a one-dimensional Stefan problem

A variable time-step (VTS) method is presented for the solution of a one-dimensional Stefan problem describing the evaporation of droplets. The method uses a simple coordinate transformation and transforms the moving boundary problem into a problem on a fixed domain. The weak or Galerkin formulation of the resulting initial-boundary value problem is then used to derive a system of initial-value problems in ordinary differential equations. The solution is advanced in time by an implicit marching technique coupled with an iterative computation of the time-step for a given advancement of the moving boundary. An integral relationship is used to correct the time-step in each iteration. The numerical results obtained by the present method exhibit very good agreement with those obtained by previous methods.

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