二维拉氏辐射流体力学人为解构造方法  

A constructed method of manufactured solutions and code verification for 2D Lagrangian radiation hydrodynamic equations

作　　者：刘学哲[1] 林忠[1] 王瑞利[1] 余云龙[1] LIU Xuezhe;LIN Zhong;WANG Ruili;YU Yunlong(Institute of Applied Physics and Computational Mathematics, Beijing 100094, China)

机构地区：[1]北京应用物理与计算数学研究所,北京100094

出　　处：《爆炸与冲击》2019年第1期89-97,共9页Explosion and Shock Waves

基　　金：国家自然科学基金(11201035;91630312);国防基础科研计划(C1520110002);中国工程物理研究院科学发展基金(2015B0202045);科学挑战专题(TZ2018001)

摘　　要：人为构造解方法是复杂多物理过程耦合程序正确性验证的重要方法之一,适用于二维拉氏大变形网格的流体、辐射耦合人为解模型较为少见。针对拉氏辐射流体力学程序正确性验证的需要,从二维拉氏辐射流体力学方程组出发,基于坐标变换技术,给出了拉氏空间到欧氏空间的物理变量导数关系式,开展了辐射流体耦合的人为解构造方法研究,构造了一类质量方程无源项的二维人为解模型,并应用于非结构拉氏程序LAD2D辐射流体力学计算的正确性考核,为流体运动网格上的辐射扩散计算提供了一种有效手段。数值结果显示观测到的数值模拟收敛阶与理论分析一致。The method of manufactured solutions(MMS)is a fundamental part of code verification for the coupling codes with complex multi-physics process,the MMS for multi-dimension Lagrangian radiation hydrodynamics with large deformation meshes is very sparse yet.In this paper,a new constructed method of manufactured solutions for2D Lagrangian radiation hydrodynamic equations was proposed based on the derivative relations of physical variables between the Lagrangian space and the Eulerian space.The manufactured solution models without additional source terms in the mass equation could be used to solve diffusion problems on fluid moving meshes and were applied to the verification of the2D Lagrangian radiation hydrodynamic codes.The numerical results show that the observed order of accuracy matches the formal order of accuracy.

关 键 词：二维拉氏辐射流体力学 人为解构造方法 欧氏空间 拉氏空间 坐标变换 程序验证 

分 类 号：O368[理学—流体力学] O241[理学—力学]