一维理想弹塑性体的SPH-HLLC耦合算法  

SPH-HLLC coupled method for one-dimentional elastic-perfectly plastic model

作　　者：王展铭 陈龙奎 黄生洪[1] WANG Zhanming;CHEN Longkui;HUANG Shenghong(Key Laboratory of Mechanical Behavior and Design of Materials,School of Engineering Science,University of Science and Technology of China,Hefei 230026,Anhui,China)

机构地区：[1]中国科学技术大学工程科学学院材料力学行为与设计重点实验室,安徽合肥230026

出　　处：《爆炸与冲击》2024年第8期72-81,共10页Explosion and Shock Waves

摘　　要：通过弹塑性波分析求得HLLC(Harten-Lax-van Leer-contact)近似黎曼解,提出了SPH(smoothed particle hydrodynamics)与一维理想弹塑性体模型下近似的HLLC黎曼求解器耦合的一种构造简单的算法。在SPH计算中,支持域内每个粒子对都存在一个黎曼间断问题,它的黎曼解被代入控制方程中计算。其中一维理想弹塑性体的HLLC近似黎曼解的思想是:先假设整体处于弹性状态计算黎曼解,然后对计算结果进行塑性条件修正,最后用修正后的物理变量计算HLLC近似黎曼解。将提出的SPH-HLLC耦合算法与传统SPH算法在一维算例下的计算结果进行对比,结果表明,该算法能有效模拟一维理想弹塑性体材料的碰撞,并能有效抑制在不同材料之间的压强和偏应力震荡,这是传统SPH方法很难做到的。A 1D SPH(smoothed particle hydrodynamics)and approximate HLLC(Harten-Lax-van Leer-contact)Riemann solver coupled method for elastic-perfectly plastic model is proposed through elastic and plastic wave analysis.In SPH simulations,each particle pair in the supporting domain generates a Riemann problem,whose solutions are substituted into governing equations.The philosophy of HLLC approximate Riemann solver is to divide the procedure into three steps:assume the whole state in elastic deformation and compute Riemann problem,and then reconstruct flux under von Mises yielding conditions and compute the final HLLC Riemann solution with reconstructed fluxes.We compare the new SPH-HLLC method with the traditional SPH method in several numerical tests,which show that this method can effectively simulate collision and reflected rarefaction waves between the materials,and it can profoundly suppress oscillations of pressure and deviatoric stress at contact interface between different materials,which the traditional SPH method finds difficult to realize.Moreover,the new SPH-HLLC scheme shows better energy performance than the traditional SPH method in 2D test case where initial kinetic energy is successfully transformed into internal energy with new SPH-HLLC scheme while total energy significantly decreases with time using the traditional SPH method.

关 键 词：弹塑性数值模拟 固体碰撞 SPH黎曼耦合算法 

分 类 号：O389[理学—流体力学]