针对天体物理、生物学、武器物理和惯性约束聚变等应用领域中多群限流扩散方程，研究一般网格上保持重要物理特性的离散格式和迭代方法。与经典的热传导方程相比，限流热传导方程描述一类传播速度有限的热波，当梯度趋于无界时其通量趋于饱和，它是一类由于梯度趋于无界导致退化的非一致抛物的强非线性方程。理论研究目前局限于单介质、单温、各向同性限流等特殊情形，而数值求解基本上是采用不限流情形的均匀网格上的计算方法，未充分考虑限流的非线性退化特性。本项目将针对实际应用中的多介质、多温、多群限流扩散等情形，提出新的单元中心型有限体积格式和非线性迭代方法，在反映主要物理特征的典型模型上进行测试分析，使其适用于在一般网格上模拟这类传播速度有限的热波，实现对限流问题的高精度高效计算，并进行理论分析，确保能量的守恒性、正性(极值性)、以及传播速度准确，为武器物理和ICF等应用领域中能量方程的精密化数值模拟提供坚实基础。

Aiming at the multi-group flux-limited diffusion equations in the fields of astrophysics, biology, weapon physics and inertial confinement fusion (ICF), this project studies the discrete schemes and iterative methods on general grids which maintain the important physical features. Compared with the classical heat conduction equation, the flux-limited heat conduction equations describe a kind of heat wave with limited propagation speed. When the gradient tends to be unbounded, its flux tends to be saturated. Therefore, it is a kind of non-uniform parabolic and strongly nonlinear partial differential equation, which is degraded because the gradient tends to be unbounded. It is difficult to study theoretically. At present, it is mainly confined to the special cases of single medium, single temperature and isotropic flux-limiting, moreover, the existing numerical methods are basically based on the uniform grid, and adopt those of flux-unlimited case without taking into consideration nonlinear degeneration features. In this project, new finite volume schemes and non-linear iteration methods are proposed for solving multi-material, multi-temperature or multi-group flux-limited diffusion problems, and numerical tests will be performed to examine the numerical performance of these discrete schemes iteration methods on typical models reflecting the main physical characteristics in practical applications. Then it shows that these new methods are suitable for simulating such heat waves with limited propagation speed on general grids, so that high accurate and efficient calculations are realized for solving multi-group flux-limited diffusion equations. Moreover, a rigorous theoretical analysis is carried out to ensure energy conservation, positivity (extremum property), and accurate propagation speed, which can provide a solid foundation for precise numerical simulation of energy equation in weapon physics and ICF applications.