Modelling high-velocity impact phenomena using unstructured dynamically-adaptive Eulerian meshes

摘要

Presented herein is an adaptive-mesh computational method for the efficient solution of the continuum equations of compressible flow for high-velocity impact dynamics. The integral forms of the governing equations are used to derive a stable form of energy equation, using internal rather than total energy, after which the corresponding differential forms are solved approximately in two dimensions via a three-stage--pressure, stress and addiction--finite-difference scheme. The finite-difference equations are applied on a fully-unstructured adaptive mesh which, as time proceeds, both coarsens or refines locally and automatically in response to a prescribed adaptation criterion. The truncation errors of the scheme are studied, and the scheme is first verified on a test problem of a collapsing hollow spherical shell, for which an analytical solution is known, before being applied to more general configurations motivated by the study of penetration mechanics. Results indicate that, for both CPU and memory requirements, the adaptive scheme is considerably cheaper than the corresponding comparable-resolution regular-mesh scheme, both schemes calculating results to a similar degree of accuracy.