极端条件下多介质流体力学计算的时空高精度紧致格式

The multi-physical problems in the fields of Weapon physics and inertial confinement fusion relating to national strategic security often involve fluid dynamics, radiation diffusion and neutron transport under the extreme conditions of high-temperature, high-pressure and high ratio of density,. In this project, we want to develop high order methods for numerical simulations of multi-materials flows in multi-physical coupling problems under these extreme conditions. We focus on the following issues:(1) Combine the advantages of high order space-time scheme ,based on flux splitting , and compact high order scheme to design a new, compact and high order space-time scheme which is simple and easy to implement.(2) Extend the new scheme to solve problems with general equations of state.(3)Apply the new scheme to solve the quasi-conservative Eulerian equations, one of typical models of multi-material flows.(4)Design the positivity-preserving limiter dealing with extreme conditions to ensure the positivity of density, temperature and fraction of materials. The capability of this new compact and high order space-time scheme for multi-material flows under extreme conditions is hopefully to provide an efficient technique for high order numerical simulations of practical applications.

武器物理、激光聚变研究关系国家战略安全，涉及高温、高压和高密度比等极端条件下的流体力学、辐射扩散和中子输运等多物理耦合问题。本项研究针对这类极端条件下多物理耦合问题中的多介质流体力学数值模拟发展高精度算法。重点开展如下工作: (1)结合基于通量分裂思想的时空高精度格式和高精度紧致格式的优点，设计简单、易实现的新型时空高精度紧致格式；(2)在此基础上进一步推广,使其适用于一般物质状态方程问题；(3)将上述格式应用于求解描述多介质流体力学问题的典型模型之一：拟守恒型可扩展欧拉方程组；(4)研究并设计适用于极端条件的保正限制器，确保密度、温度和物质组分非负，提高格式的健壮性。通过本项工作，获得能求解极端条件下多介质流体力学问题的时空高精度紧致格式，为实际应用问题的高精度数值模拟提供有效工具。

本项研究针对武器物理、激光聚变等实际应用问题中高温、高压和高密度比等极端条件下多物理耦合问题中的多介质流体力学问题，开展高精度算法研究。主要的进展包括: (1)结合基于通量分裂思想的时空高精度格式和高精度紧致格式的优点，设计简单、易实现的新型时空高精度紧致格式；(2)在此基础上进一步推广,使其适用于一般物质状态方程问题；(3)将上述格式应用于求解描述多介质流体力学问题的典型模型之一：拟守恒型可扩展欧拉方程组；(4)研究并设计适用于极端条件的保正限制器，确保密度、温度和物质组分非负，提高格式的健壮性。通过本项工作，获得能求解极端条件下多介质流体力学问题的时空高精度紧致格式。