Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Improved bicharacteristic schemes for two-dimensional elastodynamic equations

Authors: X. Lin and J. Ballmann
Journal: Quart. Appl. Math. 53 (1995), 383-398
MSC: Primary 73V15; Secondary 73D99, 73M25
DOI: https://doi.org/10.1090/qam/1330658
MathSciNet review: MR1330658
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Abstract: Several authors have used explicit numerical schemes of bicharacteristics to solve the system of hyperbolic partial differential equations describing the two-dimensional propagation of stress waves in elastic solids. However, their numerical approaches differ slightly, which results in different limits of the CFL number for stable solutions and in different defects of numerical accuracy near singular points like, e.g., a numerically caused cutting trace emanating from a crack tip. After reviewing the different approaches, some techniques are presented to set up stable explicit schemes with CFL number up to the limiting values 1 for the fastest mode. Finally, the schemes are applied to the crack problem of a shock loaded body, where the main reasons for the appearance of a cutting trace become apparent.

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DOI: https://doi.org/10.1090/qam/1330658
Article copyright: © Copyright 1995 American Mathematical Society

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