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Vietnam Journal of Mathematics 38:3 (2010) 323-339  

Numerical Simulation of a Single-Mode Richtmyer-Meshkov

Instability Using Conservative Front Tracking Method

M.A. Ullah, Gao Wenbin and Mao De-kang

 

Abstract. The conservative front-tracking method developed in [15, 16], with the 5th-order WENO scheme developed in [11] as the underlying scheme, uses 1D hyperbolic onservation laws to describe the motion of the interface and discretizes them by the Lax-Wendroff (LxW) scheme in some way. In this paper, we use this method to simulate a single-mode Richtmyer-Meshkov instability (RMI). The purpose is to test the ability of this front-tracking method to simulate the RMI, especially its advantages over capturing schemes. On a coarse grid the simulation gives a much better result than the capturing simulation. The interface with roll-ups is well resolved, the discontinuity in density is sharply represented without width, and the smooth solution on the two sides of the interface is well computed. This is because the method includes no numerical dissipation across the tracked interface, and the numerical dispersion of the LxW scheme for tracking the interface serves as a numerical surface tension, which regularizes the interface in the simulation. However, in the simulation on a finer grid, though the main structure of the interface is well resolved, the discontinuity in density is sharply represented and the smooth solution on the two sides of the interface is well computed, the roll-ups of the interface develop complex, maybe incorrect, structures, which finally terminates the simulation at an intermediate time. The reason is that the LxW scheme for tracking the interface is not yet good enough for regularizing the interface. In our future development of the method the LxW scheme will be replaced with better schemes, such as the TVD schemes that include numerical dissipation.

 

2000 Mathematics Subject Classification: 65M06, 35Q53.

Keywords: Richtmyer-Meshkov instability, conservative front-tracking, Lax-Wendroff scheme, numerial surface tension.

 

 

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