Numerical aberrations in a Stefan problem from detonation theory

Abstract

The velocity of the moving boundary in a Stefan problem from detonation theory is examined analytically. Motivation comes from computations in which the velocity profile exhibited cusps and terminations (i.e. inability of the computer to find a velocity). Here we show that a solution exists with continuous velocity and acceleration at all times but that, under certain circumstances, another (singular) solution may bifurcate off. If a similar phenomenon occurs in the finite-difference schemes used, the analysis suggests that the aberrations (cusps and terminations) are due to numerical inaccuracies. The next step, apparently a difficult one, is to modify the schemes so as to follow the non-singular solution.

Supported by the U.S. Army Research Office