由于可压缩多介质流体问题在工程领域的应用价值和科学上的重要意义，近年来受到诸多学者越来越多的关注；围绕着物质界面的分析和数值模拟已成为科学计算领域的研究热点问题之一。 基于该领域典型问题的物理特征， 本项目拟研究该领域广义黎曼解法器以及相应的时空耦合的高阶有限体积方法。 内容包括: (1) 可压缩多介质流体模型数学分析; (2) 关于多个组份复杂状态方程的快速黎曼解法器；(3) 适用于任意拉格朗日－欧拉框架的时空耦合广义黎曼解法器; (4)基于广义黎曼解法器的任意高阶精度、真正多维有限体积方法。研究目标在于建立一套鲁棒、适用于ICF等工程应用的实用算法。

In recent years, the study of compressible multifluid problems receives much attention due to their engineering values and scientific significance. The analysis and numerical simulations of material interfaces have been one of research focuses in the field of scientific computations. This project aims to provide a set of reliable generalized Riemann problem (GRP) solvers for multifluid problems and corresponding high order finite volume schemes. The contents include: (1) the mathematical analysis of compressible multifluid models and their closure; (2) Fast Riemann solvers for multi-components with complex equations of states; (3) Spatial-temporal coupled GRP solvers adapted to the Arbitrary Lagrangian-Eulerian (ALE) framework; (4) arbitrarily high order GRP-based multi-dimensional finite volume methods. The final goal is to design a set of robust and practical algorithms for engineering problems such as Inertial Confinement Fusion (ICF).