Numerical investigation of Richtmyer-Meshkov instability driven by cylindrical shocks

• Published in: Acta mechanica Sinica Vol. 22; no. 1; pp. 9 - 16
• Main Authors: Tian, Baolin, Fu, Dexun, Ma, Yanwen
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.02.2006
• Edition: English ed.
• Subjects: Adaptive control; Compressibility; Cylindrical coordinates; Cylindrical waves; Euler-Lagrange equation; Evolution; Numerical analysis; Numerical methods; Perturbation; Richtmeyer-Meshkov instability; Richtmyer-Meshkov不稳定性; Shock waves; 准确性; 分辨率; 圆柱振动; 数字调查; 欧拉方程
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-005-0083-1

In this paper, a numerical method with high order accuracy and high resolution was developed to simulate the Richtmyer-Meshkov（RM） instability driven by cylindrical shock waves. Compressible Euler equations in cylindrical coordinate were adopted for the cylindrical geometry and a third order accurate group control scheme was adopted to discretize the equations. Moreover, an adaptive grid technique was developed to refine the grid near the moving interface to improve the resolution of numerical solutions. The results of simulation exhibited the evolution process of RM instability, and the effect of Atwood number was studied. The larger the absolute value of Atwood number, the larger the perturbation amplitude. The nonlinear effect manifests more evidently in cylindrical geometry. The shock reflected from the pole center accelerates the interface for the second time, considerably complicating the interface evolution process, and such phenomena of reshock and secondary shock were studied.