EXPLICIT VARIABLE TIME-STEP METHOD FOR IMPLICIT MOVING BOUNDARY-PROBLEMS

The diffusion of oxygen into an absorbing medium as an example of an implicit moving boundary problem has been dealt with by a number of authors using various numerical techniques, and, where appropriate, approximate analytical expressions. To evaluate the time for complete absorption, extrapolation is usually employed. An unconditionally stable explicit numerical scheme that avoids the limitations of such methods is presented and tested herein. Unlike existing schemes this method is fully numerical; it avoids the large array size, generally required for existing methods, by using a variable-length time step. The time for complete absorption emerges from the final step in the normal computing procedure with no recourse to extrapolation. Furthermore, owing to the implicit condition prevailing at the moving boundary, no iterations are needed to evaluate the time step required for the moving boundary to move a single space increment. The numerical results obtained compare very favourably with those due to earlier authors.