Research Papers: Fundamental Issues and Canonical Flows

A Hybrid Compressible–Incompressible Computational Fluid Dynamics Method for Richtmyer–Meshkov Mixing

[+] Author and Article Information
Tommaso Oggian

Cranfield University,
Cranfield MK43 0AL,

Dimitris Drikakis

Cranfield University,
Cranfield MK43 0AL,
e-mail: d.drikakis@cranfield.ac.uk

David L. Youngs, Robin J. R. Williams

Aldermaston RG7 4PR,

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 4, 2013; final manuscript received April 17, 2014; published online July 9, 2014. Assoc. Editor: Oleg Schilling.

J. Fluids Eng 136(9), 091210 (Jul 09, 2014) (7 pages) Paper No: FE-13-1218; doi: 10.1115/1.4027484 History: Received April 04, 2013; Revised April 17, 2014

This paper presents a hybrid compressible–incompressible approach for simulating the Richtmyer–Meshkov instability (RMI) and associated mixing. The proposed numerical approach aims to circumvent the numerical deficiencies of compressible methods at low Mach (LM) numbers, when the flow has become essentially incompressible. A compressible flow solver is used at the initial stage of the interaction of the shock wave with the fluids interface and the development of the RMI. When the flow becomes sufficiently incompressible, based on a Mach number prescribed threshold, the simulation is carried out using an incompressible flow solver. Both the compressible and incompressible solvers use Godunov-type methods and high-resolution numerical reconstruction schemes for computing the fluxes at the cell interfaces. The accuracy of the model is assessed by using results for a two-dimensional (2D) single-mode RMI.

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Grahic Jump Location
Fig. 1

Grid convergence for a single-mode instability (H)

Grahic Jump Location
Fig. 2

Absolute average value of velocity divergence at t > tNT≈0.052 s for C + LM and H solutions

Grahic Jump Location
Fig. 3

Divergence of velocity along the central line (y = π) for C + LM (solid lines) and H (dashed lines) simulations at different time instants t > tNT. The mushroomlike interface between the fluids at each instant is displayed in the background of the graphs.

Grahic Jump Location
Fig. 4

Predicted growth of the single-mode instability using the compressible (C), compressible with low-Mach correction (C + LM), and hybrid (H) methods

Grahic Jump Location
Fig. 5

Comparison of volume fractions at different time instants for the C, C + LM, and H methods on grid G2

Grahic Jump Location
Fig. 6

Comparison of volume fractions at different time instants for the C, C + LM, and H methods on grid G4



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