多介质大变形流体时空一致高阶动理学方法研究

本项目致力于研究多介质大变形流体的高精度数值方法，研制相关程序，为惯性约束聚变(ICF)内爆等问题的数值模拟服务。本项目研究的时空一致高阶模板紧致动理学格式是高精度动理学格式及CPR格式在求解多介质问题上的首次应用：首先基于气体动理学方法的思想，研究可避免物质界面处非物理振荡的高精度粒子速度分布函数；然后研究CPR方法中通量函数多项式近似及矫正算子的计算策略，结合状态量的连续性根据粒子速度分布函数得到时空一致高阶模板紧致动理学格式；最后借鉴拟守恒方法思想，根据粒子速度分布函数得到组分方程的离散。该方法结合了CPR方法与动理学方法的优点，时空可以达到一致高阶，且模板紧致，简便易行，有望成为求解多介质大变形流体的有效工具。

This project is devoted to the study of the high order numerical schemes for multi-component large distortion flow simulation and developing the corresponding programs for the simulation of ICF implosion process. We are among the first to apply the high order kinetic scheme and CPR scheme to the multi-component problems and finally can get a stencil compact and spatial and temporal consistent high-order kinetic scheme. First, according to the kinetic method, the velocity distribution function in high order accuracy and causing non-oscillation on material interface is evolved. Second, we study the strategy of how the correction operator and the flux vector polynomial approximation, and combine with the velocity distribution function of different status to get the spatial and temporal consistent and stencil compact high-order kinetic scheme. Finally, borrowed the idea of quasi-conservation scheme, we get the discretization scheme of component function by using the velocity distribution function. The scheme combines the advantage of the CPR method and the kinetic scheme, e.g. spatial and temporal consistent high order, stencil compact, easy to implement and efficient. And it is expected to be an effective tool for solving multi-component large distortion flows.