带复杂本构弹塑性流体高精度保物理特性中心型拉格朗日方法研究

The deformation problems of compressible axisymmetrical elastic-plastic flows have important application background in the Implosion Dynamics of weapon and Inertial Confine Fusion (ICF). In these problems, materials are always under strong dynamics loading, such as explosive, high-speed impact, the constitutive models of these materials are relatively complex. In order to simulate efficiently these problems with high-order accuracy, it is necessary to build efficient, high-order import-physical-property-preserving cell-centered Lagrangian schemes in two-dimensional cylindrical coordinates for axisymmetrical elastic-plastic flows with complex constitutive models under strong dynamics loading..For this purpose, we will do the following researches: ①build efficient adaptive approximate Riemann solvers for one-dimensional and two-dimensional split elastic-plastic equations with complex constitutive models (hypo-elastic constitutive model with strain hardening and Steinberg - Guinan model which is temperature, pressure and strain rate dependent); ②For elastic-plastic flows, build self-similar, consistent with the conservative system and satisfying the yielding condition two-dimensional approximate Riemann solvers (MuSciE and 2D HLLCE) with elastic waves for evaluating velocity of nodes; ③Build high-order cell-centered Lagrangian schemes for elastic-plastic flows in two-dimensional cylindrical coordinates and the schemes are demanded to be conservative, satisfy entropy condition and have the positivity-preserving and symmetry-preserving characters; ④ Develop the high-order schemes for the hypo-elastic constitutive equations in two-dimensional cylindrical coordinates. We demand the schemes have symmetry-preserving character and satisfy the quality of rigid body rotation invariance. At last these studies will give supports for the researches of Implosion Dynamics of weapon and other areas.

可压缩轴对称弹塑性流体的变形问题在武器内爆和惯性约束聚变等领域有重要的应用背景。这类问题的材料经常受爆炸、高速冲击等强动载荷作用，本构模型较为复杂。为高精度且高效地模拟这类问题，有必要针对强动载荷作用下带复杂本构的轴对称弹塑性流体，建立高精度且保重要物理特性的柱坐标弹塑性中心型拉格朗日格式。.为此，本文将开展如下研究：①建立带复杂本构（带应变硬化效应的次弹-塑性本构和考虑温度、压力和应变率影响的SG本构）的一维和二维分裂弹塑性流体方程组的高效自适应近似黎曼解；②针对弹塑性流体，构造带弹性波、自相似、与守恒方程组相容，且满足屈服条件的二维近似黎曼解（MuSciE和2D HLLCE）来计算节点速度；③构造弹塑性流体二维柱坐标高精度中心型拉格朗日格式，要求守恒、满足熵条件、保正保对称；④发展柱坐标亚弹性本构方程的高精度离散格式，要求保对称保刚体旋转不变性。最终将为武器内爆等领域的研究提供支撑。

可压缩轴对称弹塑性流体的变形问题在武器内爆和惯性约束聚变等领域有重要的应用背景。这类问题的材料经常受爆炸、高速冲击等强动载荷作用，本构模型较为复杂。为高精度且高效地模拟这类问题，有必要针对强动载荷作用下带复杂本构的轴对称弹塑性流体，建立高精度且保重要物理特性的柱坐标弹塑性中心型拉格朗日格式。.为此，本文开展了如下研究：.(1) 针对带完全弹性和理想塑性的本构模型以及复杂状态方程的二维弹塑性流体力学问题，发展了两个近似黎曼解，包括基于稀疏波假设的四稀疏波近似解Riemann解(FRRSE)以及基于HLLC和自相似假设的HLLCEP近似Riemann解，并以此发展了二阶精度守恒的二维弹塑性中心型拉格朗日格式。数值实验显示，新格式达到了设计精度，具有较好的对称性、基本不振荡，且FRRSE对稀疏波比节点解法器有更高的分辨率，而HLLCEP具有简单快速且分辨率高等特点。.(2) 针对考虑温度、压力和应变率影响的SG本构的一维和二维分裂弹塑性流体方程组，基于HLLC思想发展了HLLCEP-SG近似黎曼解，并以此建立了带SG本构的二阶精度守恒的二维弹塑性中心型拉格朗日格式。与交错型拉氏格式结果的比较证明了SG本构离散以及HLLCEP-SG近似黎曼解的正确性。.(3) 针对带亚弹性本构、von Mises屈服条件和复杂状态方程的二维柱对称弹塑性流体力学问题，在HLLCEP的基础上发展了保对称的中心型拉格朗日格式。数值实验结果证明了格式的性质。.(4) 将上述近似黎曼解推广到多介质问题，从而发展了多介质黎曼解；将上述弹塑性流体力学方程组离散方法与自适应移动网格方法MMPDE耦合，发展了弹塑性流体自适应网格移动算法.本课题对带多种本构的弹塑性流体黎曼问题和高精度中心型拉氏格式的研究对解决武器物理中内爆动力学多介质弹塑性流体相互作用问题，具有重要的理论价值和现实意义。