在非线性弹性动力学中用保守有限体积方案捕捉非经典冲击波
Capturing nonclassical shocks in nonlinear elastodynamic with a conservative finite volume scheme
AI总结：
本文提出一种能捕捉非经典冲击波的保守有限体积方案，该方案在初始数据为孤立非经典冲击波时精确，且不引入扩散，正确近似非经典解。
摘要：
对于非线性弹性动力学模型，我们构造了一种有限体积方案，能够捕捉非经典冲击波（也称为亚压缩性冲击波）。这些冲击波满足熵不等式但不符合Liu意义下的可接受性。它们满足一种描述跃迁的动能关系，并保持了消失的色散与消失的扩散之间的平衡。本文提出的方案在初始数据为孤立非经典冲击波时是精确的。一般情况下，它在冲击波附近不引入任何扩散，因此非经典解被正确近似。该方法完全守恒，不使用任何冲击追踪网格。此方法在多个测试案例中进行了测试和验证。特别是，由于非经典冲击波不被扩散，因此可以得到长时间渐进行为。
英文摘要：
For a model of nonlinear elastodynamics, we construct a finite volume scheme which is able to capture nonclassical shocks (also called undercompressive shocks). Those shocks verify an entropy inequality but are not admissible in the sense of Liu. They verify a kinetic relation which describes the jump, and keeps an information on the equilibrium between a vanishing dispersion and a vanishing diffusion. The scheme pre-sented here is by construction exact when the initial data is an isolated nonclassical shock. In general, it does not introduce any diffusion near shocks, and hence nonclas-sical solutions are correctly approximated. The method is fully conservative and does not use any shock-tracking mesh. This approach is tested and validated on several test cases. In particular, as the nonclassical shocks are not diffused at all, it is possible to obtain large time asymptotics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
