理想弹塑性固体Riemann问题的解结构与初值条件

针对理想弹塑性固体材料的一维Riemann问题，在不考虑真空的情况下，讨论其所有可能存在的解结构，给出每一种解结构下对应的初值条件且证明该系列初值条件的完备性，即任意给定的物理量初值均有且只有一种解结构与之对应.基于该理论，在设计精确或近似理想弹塑性Riemann问题求解器时，可以依据初值条件对任意物理量初值直接判断其对应的解结构，从而提高求解器的精度和效率.数值试验验证了该系列初值条件的正确性和有效性.

Initial Value Conditions of Solutions of Riemann Problem for Elastic Perfectly Plastic Solid

For a given solution of Riemann problem for elastic perfectly plastic solid Euler equations ignoring vacuum, we give condition that the initial physical quantity should be satisfied and prove completeness of the initial condition corresponding to a particular solution. That is, for any given initial physical quantity, it corresponds to only one solution of Riemann problem. Therefore, the solution of Riemann problem can be judged directly and accurately according to the initial condition in the design of exact or approximate Riemann solvers.