Exact and approximate solutions of Riemann problems in non-linear elasticity
Exact and approximate solutions of Riemann problems in non-linear elasticity
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DOI：
10.1016/j.jcp.2009.06.014
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发表时间：
2009-10-01
影响因子：
4.1
通讯作者：
Titarev, V. A.
中科院分区：
文献类型：
--
作者：
Barton, P. T.;Drikakis, D.;Titarev, V. A.
欧拉激波捕获方案在模拟涉及复杂非线性波结构和固体介质中大变形的问题时具有优势。目前存在求解双曲型守恒律的各种数值方法，但这些方法尚未应用于非线性弹性理论。本文研究了一类基于特征跟踪与高阶保持单调性加权本质非振荡（MPWENO）重构相结合的求解方法。在此基础上，提出了一种求非线性弹性力学中Riemann问题精确解的迭代方法。获得精确的解决方案可以评估数值技术的性能，重点关注七波结构的分辨率。控制模型代表了描述附加物理（如材料塑性）的更一般理论的特殊情况。因此，数值格式为模拟更复杂的物理现象提供了坚实的基础。对三维变形的一维初值问题的精确解和数值解进行了比较。(C) 2009爱思唯尔公司版权所有。
Eulerian shock-capturing schemes have advantages for modelling problems involving complex non-linear wave structures and large deformations in solid media. Various numerical methods now exist for solving hyperbolic conservation laws that have yet to be applied to non-linear elastic theory. In this paper one such class of solver is examined based upon characteristic tracing in conjunction with high-order monotonicity preserving weighted essentially non-oscillatory (MPWENO) reconstruction. Furthermore, a new iterative method for finding exact solutions of the Riemann problem in non-linear elasticity is presented. Access to exact solutions enables an assessment of the performance of the numerical techniques with focus on the resolution of the seven wave structure. The governing model represents a special case of a more general theory describing additional physics such as material plasticity. The numerical scheme therefore provides a firm basis for extension to simulate more complex physical phenomena. Comparison of exact and numerical solutions of one-dimensional initial values problems involving three-dimensional deformations is presented. (C) 2009 Elsevier Inc. All rights reserved.