辐射输运问题的新型模型约简和高效数值方法研究

Fusion energy is a very important one in the future energy resources. Inertial Confined Fusion (ICF) is one of the most possible ways to achieve controllable fusion energy. A lot of research has been done on it. Radiative transport is an important process in ICF. The accuracy and computing efficiency of the numerical simulation of radiative transport affect the reliability and the computing efficiency of the ICF simulation. Our proposal will do research on model reduction and numerical algorithm of the radiative transport process in the complex multimedia in high-energy-density physics, and integrate the new model and algorithm on the ICF simulation platform. We will conduct our research in:. (1)Integrating the model and numerical algorithm of the radiative transport on the ICF simulation platform, and validating the effectiveness and efficiency of the model and numerical algorithm.. (2)Developing the model reduction and numerical algorithm of the radiative transport further to construct numerical regularized moment model which can describe the effect very far from equilibrium and is globally stable and effectively convergent. . (3)Developing the approximation-preserving discretize method and the rotation-preserving discrete ordinates method of the radiative transport equation to get over the ray-effect problem of the discrete ordinates method and the positive-preserving problem of the spherical harmonics method.

聚变能源是国际上新能源发展的重要方向，惯性约束聚变（ICF）作为聚变能源最重要、最有可能的实现途径之一而被广泛研究。辐射输运是ICF的重要物理过程之一，其数值模拟置信度和计算效率直接影响了ICF全过程数值模拟的可信度和模拟时间。本项目以ICF研究为牵引，针对高能量密度物理中复杂介质背景下辐射输运的数值计算难点，开展模型约化、算法研究，以及新模型和算法在ICF中的集成应用工作。内容如下：（1）将已有的和新发展的约化模型和算法集成到ICF数值模拟平台上，验证模型和算法的有效性和高效性。（2）进一步改进并发展辐射输运约化模型，建立实用的能够刻画强非平衡态效应的全局稳定、具有高效数值收敛性的数值正则化矩模型。（3）研究辐射输运方程的渐近保持离散方法和保旋转不变性的离散纵标方法，解决离散纵标方法所固有的射线效应和球谐函数方法的出负等问题。

项目以激光惯性约束聚变（ICF）数值模拟需求为牵引,针对高能量密度物理中复杂介质背景下辐射输运的数值计算难点，针对辐射输运方程，发展了任意阶保旋转不变的近似矩模型，验证了模型的双曲性与旋转不变性，构建相应数值格式，并通过数值模拟结果验证模型效果；针对辐射输运方程时间步长问题，构建了隐式渐近保持统一分子动力学格式以及辐射输运隐式蒙特卡罗计算功能；针对相对论磁流体力学提出了约化的矩模型以及零扩散极限下辐射流体力学方程组的二阶精确直接欧拉型广义Riemann问题（GRP）格式；通过辐射输运基准模型验证新模型和新算法在抑制射线效应和计算效率方面的有效性，并应用于ICF内爆典型模型的数值模拟。部分研究成果已应用于惯性约束聚变物理问题，有力地支持了我国的国防科研事业。