Error Comparison in Tracked and Untracked 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. c © 2004 Elsevier Science Ltd. All rights reserved. This work has been supported by the following research grants. Dutta was supported by the U.S. Department of Energy under grant DE-FG02-90ER25084, the National Science Foundation Grant DMS-0102480, and by the Los Alamos National Laboratory under contract number 26730001014L. Glimm was supported by the Los Alamos National Laboratory under contract number 26730001014L. Grove and Sharp were supported by the U.S. Department of Energy. 0898-1221/04/$ see front matter c © 2004 Elsevier Science Ltd. All rights reserved. Typeset by AMS-TEX PII:00

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