Abstract: We introduce a high-order cell-centered Lagrangian scheme for one dimensional elastic-plastic problems. The problem with the hypo-elastic constitutive model and the von Mises yield criterion is a classical problem and there are many numerical methods for it, including staggered Lagrangian schemes, Eulerian Godunov schemes and cell-centered Lagrangian schemes. In these methods, however, the wave structure of the problem is not exploited in the construction of the methods. Because the hypo-elastic constitutive model is a non-conservative equation, it is difficult to build an approximate Riemann solver for the governing equations with the hypo-elastic constitutive model. In this paper, we analyze the wave structure of the Riemann problem for elastic-plastic materials and then develop a two-rarefaction-wave Riemann solver with elastic waves (TRRSE). During building TRRSE, we use numerical quadrature to approximate the integral terms of Riemann invariants with high-order accuracy. Based on the developed TRRSE, we propose a second-order cell-centered Lagrangian scheme for one-dimensional elastic-plastic solid problems. Moreover, we use a second-order scheme to discretize the constitutive equation based on geometry conservation law in order to keep high accuracy. A number of numerical experiments are carried out, and the numerical results are compared with the \exact" solution and the results obtained by other authors. The comparison shows that the current scheme is convergent, stable and essentially non-oscillatory. For shock waves the current scheme is almost as good as Maire et al.'s scheme in accuracy and resolution, while for rarefaction waves the current scheme performs better.

  

报告人简介: 程军波, 北京应用物理与计算数学所研究员, 研究方向为计算流体力学, 在国内外刊物上发表十几篇文章。程军波早期从事界面不稳定性研究, 后来研究大变形弹塑性流体力学的ALE格式。现在主要研究弹塑性流体的精确或近似Rieman解、可压缩流体和弹塑性流体的高精度格式、爆轰流体的高精度计算等。

 

Date&Time: January 19, 2015 (Monday), 16:00 - 17:00
Location: 606 Conference Room