Error comparison in tracked anduntracked spherical simulations

This paper follows our earlier work on axisymmetric flows [1-4] where algorithms, theories, experiments, simulations, applications, and validations were presented. Here we study the effectiveness and efficiency of explicit front tracking by comparing the L₁-error for spherical shock refraction simulations with and without tracking. We find that front tracking reduces the level of mesh refinement needed to achieve a specified error tolerance by a significant factor compared to corresponding methods without tracking, thus substantially reducing the computational time as well as memory usage for simulations with contacts or material interfaces.