Tritschler, V.K., Hu, X.Y., Hickel, S., Adams, N.A. (2013)
Physica Scripta 2013: 014016. doi: 10.1088/0031-8949/2013/T155/014016

Two-dimensional simulations of the single-mode Richtmyer–Meshkov instability (RMI) are conducted and compared to experimental results of Jacobs and Krivets (2005).

The employed adaptive central-upwind sixth-order weighted essentially non-oscillatory (WENO) scheme introduces only very small numerical dissipation while preserving the good shock-capturing properties of other standard WENO schemes. Hence, it is well suited for simulations with both small-scale features and strong gradients. A generalized Roe average is proposed to make the multicomponent model of Shyue (1998) suitable for high-order accurate reconstruction schemes. A first sequence of single-fluid simulations is conducted and compared to the experiment. We find that the WENO-CU6 method better resolves small-scale structures, leading to earlier symmetry breaking and increased mixing. The first simulation, however, fails to correctly predict the global characteristic structures of the RMI. This is due to a mismatch of the post-shock parameters in single-fluid simulations when the pre-shock states are matched with the experiment. When the post-shock parameters are matched, much better agreement with the experimental data is achieved. In a sequence of multifluid simulations, the uncertainty in the density gradient associated with transition between the fluids is assessed. Thereby the multifluid simulations show a considerable improvement over the single-fluid simulations.


Effect of the diffusion layer thickness on the late-time Richtmyer–Meshkov development (a) experiments of Jacobs and Krivets (2005), simulation with (b) D = 4 to (c) D = 8 to (d) D = 16 at times t = 4.16 ms and t = 6.06 ms.