基于多介质Riemann问题的流体-固体耦合数值方法及其在爆炸与冲击问题中的应用

为提高爆炸与冲击下多介质大变形问题的数值模拟精度，针对具有高度非线性特征、通用形式的Mie-Grüneisen状态方程和流体弹塑性本构方程的多种介质间相互作用问题，提出一种通用、健壮的多介质Riemann问题求解方法，以有效提高物质界面上各物理量的计算精度。结合Euler坐标系下具有锐利界面的守恒型多介质流动数值方法，建立一套能够模拟可压缩流体和弹塑性固体在极端物理条件下大变形动力学行为的数值计算体系。对流体-固体耦合、固体-固体耦合Riemann问题，地下强爆炸、空中强爆炸以及高速冲击等问题开展了数值模拟，计算结果和理论、实测数据符合较好，表明该数值方法能够对典型爆炸与冲击等多介质问题进行有效的模拟。

A Numerical Scheme for Fluid-solid Interactions Based on Multi-medium Riemann Problem and Its Application in Explosion and Impact Problems

In order to improve the accuracy of numerical simulation of multi-medium large deformation under explosive and impact loading, a general and robust multi-medium Riemann solver is proposed to solve the multi-medium interactions for the highly non-linear Mie-Grüneisen equation of state and hydro-elastoplastic constitutive equation. The solver can be used to improve the calculation accuracy of physical quantities at material interface. A numerical system is established to simulate the large deformation of compressible fluid and elastoplastic solid under extreme conditions by using the compressible multi-medium flow scheme. The fluid-solid Riemann problem, solid-solid Riemann problem, underground explosion problem, air blast problem and high-speed impact problem were simulated. The numerical results agree well with the analytical and experimental data, which reveals the capacity of the proposed algorithm in solving multi-medium flows, such as typical explosion and impact problems.