多介质五方程简化模型及界面捕捉的人工压缩算法

doi:10.19596/j.cnki.1001-246x.8248

摘要/Abstract

摘要：

根据两介质五方程简化模型的基本假设，发展了适用于任意多种介质的体积分数方程。为了捕捉多介质界面，将HLLC-HLLCM混合型数值通量的计算格式推广应用于二维平面和柱几何的多介质复杂流动问题，在高阶精度的数据重构过程中采用斜率修正型人工压缩方法ACM。通过一维、二维多介质黎曼问题算例测试，结果表明：发展的计算格式能够较好地分辨接触间断和激波，间断附近物理量无振荡；对于添加了初始扰动的激波问题，能够有效抑制激波数值不稳定性；使用二维柱球SOD问题和接触间断型黎曼问题检验计算格式对多介质复杂流动问题的适应性。

关键词: 多介质五方程模型, 人工压缩方法, HLLC-HLLCM混合通量, 激波数值不稳定性

Abstract:

The volume fraction equations of five-equation-reduced model were studied and numerical scheme was developed in two-dimensional Eulerian frame in planar and cylindrical geometry. To capture material interfaces, Yang's slope modification of artificial compression method was adopted in MUSCL, PPM and WENO type data reconstruction processes. HLLC-HLLCM hybrid flux was applied in Godunov type scheme to avoid numerical shock instability. For multi-material Riemann problems, numerical results show that the scheme captures shock and contact discontinuities with non-oscillatory character. No numerical shock instabilities growing shows as small perturbations was adding on initial physical variables. SOD problems in cylindrical and spherical geometries and contact-type two-dimensional Riemann problem were studied.

Key words: multi-material five-equation model, artificial compression method, HLLC-HLLCM hybrid flux, numerical shock instability

中图分类号:

薛创, 李馨东, 孙文俊, 叶文华, 彭先觉. 多介质五方程简化模型及界面捕捉的人工压缩算法[J]. 计算物理, 2021, 38(3): 257-268.

Chuang XUE, Xingdong LI, Wenjun SUN, Wenhua YE, Xianjue PENG. A Multi-material Five-equation-reduced Model and Artificial Compression Method for Interface Capture[J]. Chinese Journal of Computational Physics, 2021, 38(3): 257-268.

图/表 8

图1 HLLC和HLLCM通量采用的间断状态和激波结构(a) HLLC间断状态; (b) HLLCM间断状态

Fig.1 Discontinuity states and wave structures of HLLC and HLLCM flux (a) discontinuity states for HLLC; (b) discontinuity states for HLLCM

图2 判断混合通量时网格界面与6个相邻网格的位置关系

Fig.2 Mesh interface and six neighbor-meshes for adjusting hybrid flux

图3 网格和计算方法对接触间断计算的影响(a) 两介质静态接触间断(MUSCL); (b) 两介质运动接触间断(MUSCL); (c) 两介质运动接触间断(PPM); (d) 两介质运动接触间断(WENO)

Fig.3 Influence of mesh number and numerical method on contact discontinuity calculation (a) static contact discontinuity calculated by MUSCL; (b) moving contact discontinuity calculated by MUSCL; (c) moving contact discontinuity calculated by PPM; (d) moving contact discontinuity calculated by WENO

图4 两个爆炸波相互作用后的密度和体积分数分布(a) 不同计算方法的结果; (b) 不同物理模型的结果

Fig.4 Profiles of density and volume fractions after two blast waves interaction (a) results of different schemes; (b) results of different models

图5 采用两种数值通量计算的密度分布(a) 采用HLLC-HLLCM通量的密度等值线; (b) 采用HLLC通量的密度等值线；(c) 采用HLLC-HLLCM通量的X方向密度分布; (d) 采用HLLC通量的X方向密度分布

Fig.5 Profile of density calculated by different numerical flux (a) density isolines calculated by HLLC-HLLCM flux; (b) density isolines calculated by HLLC flux; (c) profiles of density calculated by HLLC-HLLCM flux; (d) profiles of density calculated by HLLC flux

图6 采用MUSCL+ACM+Hybrid算法的柱球SOD问题的密度分布(a) 柱SOD问题的二维密度分布; (b) 球SOD问题的二维密度分布; (c) 柱SOD问题的一维密度分布; (d) 球SOD问题的一维密度分布

Fig.6 Profiles of density for cylindrical and spherical SOD problems with MUSCL+ACM+Hybrid scheme (a) 2D density contours for cylindrical SOD problem; (b) 2D density contours for spherical SOD problem; (c) 1D density profile for cylindrical SOD problem; (d) 1D density profile for spherical SOD problem

图7 采用MUSCL+HLL格式计算柱球SOD问题的密度分布(a) 柱SOD问题的二维密度分布; (b) 球SOD问题的二维密度分布; (c) 柱SOD问题的一维密度分布; (d) 球SOD问题的一维密度分布

Fig.7 Profiles of density for cylindrical and spherical SOD problems with MUSCL+HLL scheme (a) 2D density contours for cylindrical SOD problem; (b) 2D density contours for spherical SOD problem; (c) 1D density profile for cylindrical SOD problem; (d) 1D density profile for spherical SOD problem

图8 二维黎曼问题的密度分布和物质界面(a) 未采用ACM的密度等值线; (b) 采用ACM的密度等值线; (c) 未采用ACM的物质界面; (d) 采用ACM的物质界面

Fig.8 Density profile and material interfaces of 2D Riemann problems (a) density isolines without ACM; (b) density isolines with ACM; (c) four material interfaces without ACM; (d) four material interfaces with ACM

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