武器物理和惯性约束聚变(ICF)领域中的流体力学数值方法仍然存在诸多困难和挑战，如置信度低，有时难以准确反映实际物理系统的真实状态；目前该领域中湍流混合阶段的研究几乎是空白，首先因为湍流问题高度复杂，其次几乎所有的数值模拟都是基于欧拉方法发展的，而该领域中主要以拉格朗日和ALE(任意拉格朗日和欧拉)方法为主。本项目拟针对上述问题，研究基于物理考量的、保证定量熵增的、满足熵条件且尽可能低耗散的相容中心型拉格朗日方法，主要包括格式离散框架设计、引入弱化的熵条件概念及具有上述性质的近似Riemann解法器，以提高方法对流场模拟的置信度，并推广到ALE框架；在上述基础上引入不同湍流模型，探索研究新相容中心型ALE方法框架下的雷诺平均（RANS）方法，并探索研究方法对湍流混合问题的模拟能力。为武器物理和ICF领域中的内爆压缩问题、尤其是后期湍流混合问题的物理分析和机理研究提供方法和程序支撑。

The numerical methods for the hydrodynamics nowadays are facing difficulties and challenges, especially in the regions of weapon physics and inertial confinement fusion (ICF), in which high density and pressure ratios are often involved. The problem is that numerical results are often with low quality and validity, which can not well explore the real physics of the problems. Moreover, the numerical investigation of the turbulence mixing in these regions is still quite open with few research results in numerical simulation. The reasons are as follows: 1) The problem itself is highly difficult. 2) Almost all the numerical methods for the turbulence mixing are developed in the Eulerian framework; however, the Lagrangian and Arbitrary Lagrangian and Eulerian (ALE) methods are still the principal numerical methods used in the regions of weapon physics and ICF. This project aims to develop compatible cell-centered Lagrangian and ALE methods, which will satisfy the entropy condition, however with numerically low dissipation, and then applies them in the numerical study of the turbulence mixing problems to develop new Reynolds Average Navier-Stokes (RANS) methods. The research will provide supports of numerical methods for the investigation of the turbulence mixing in the weapon physics and ICF.