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Keywords:

  • piecewise parabolic method;
  • adaptive mesh refinement;
  • shock–bubble interactions

SUMMARY

A high-resolution method is developed to capture the material interfaces of compressible two-fluid flows in multiple dimensions. A fluid mixture model system with single velocity and pressure is used, and viscous effect can also be taken into account. A consistent thermodynamic law based on the assumption of pressure equilibrium is employed to describe the thermodynamic behaviors of the pure fluids and mixture of two components. The splitting and unsplit Eulerian formulations of piecewise parabolic method are extended to numerically integrate the hyperbolic part of the model system, whereas the system of diffusion equations is solved using an explicit, central difference scheme. The block-structured adaptive mesh refinement (AMR) capability is built in the hydrodynamic code to locally improve grid resolution. The resulting method is verified to be at least second-order accurate in space. Numerical results show that the discontinuities, particularly contact discontinuities, can be resolved sharply. The use of AMR allows flow features at disparate scales to be resolved sufficiently. In addition, three-dimensional shock–bubble interactions are simulated to investigate effects of Mach number on bubble evolution. The flow structures including those peculiar to three-dimensional bubble are resolved correctly, and some physical phenomena with increasing Mach number are reported. Copyright © 2012 John Wiley & Sons, Ltd.