二维拉氏辐射流体力学人为解构造方法

刘学哲; 林忠; 王瑞利; 余云龙

doi:10.11883/bzycj-2017-0199

二维拉氏辐射流体力学人为解构造方法

doi: 10.11883/bzycj-2017-0199

北京应用物理与计算数学研究所, 北京 100094

基金项目:

国家自然科学基金 11201035

国家自然科学基金 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

详细信息

作者简介:
刘学哲(1977-), 男, 博士, 副研究员

通讯作者:
王瑞利, wang_ruili@iapcm.ac.cn

中图分类号: O368;O241
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- 被引次数: 0
出版历程
- 收稿日期: 2017-06-10
- 修回日期: 2017-08-09
- 刊出日期: 2019-01-05

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

Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

摘要

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。
- 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
Abstract: 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 for 2D 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 the 2D Lagrangian radiation hydrodynamic codes. The numerical results show that the observed order of accuracy matches the formal order of accuracy.
- 2D Lagrangian radiation hydrodynamic equations /
- method of manufactured solutions (MMS) /
- Eulerian space /
- Lagrangian space /
- coordinate transformation /
- code verification

HTML全文

图 1 不同时刻流体运动网格

Figure 1. Fluid meshes at different times

下载: 全尺寸图片幻灯片

图 2 t=0.125时刻流体运动网格上密度、温度、x方向速度、y方向速度等值线(红：数值解绿：精确解)

Figure 2. Contours of density, temperature, x and y components of velocity(red: numerical solution; green: exact solution)

下载: 全尺寸图片幻灯片

图 3 不同时刻流体运动网格上温度等值线

(红：数值解绿：精确解)

Figure 3. Contours of temperature on fluid meshes at different time

(red: numerical solution; green: exact solution)

下载: 全尺寸图片幻灯片

表 1 温度收敛误差和收敛阶

Table 1. Convergence errors and orders for temperature

网格数	L2模误差	L2模误差收敛阶	最大模误差	最大模误差收敛阶
8×8	2.82×10^-2		1.04×10^-1
16×16	7.13×10^-3	1.98	3.06×10^-2	1.76
32×32	1.79×10^-3	1.99	7.97×10^-3	1.94
64×64	4.49×10^-4	2.00	2.01×10^-3	1.99
128×128	1.12×10^-4	2.00	5.03×10^-4	2.00

下载: 导出CSV

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